Help for package manymome

Title:

Mediation, Moderation and Moderated-Mediation After Model Fitting

Version:

0.2.9

Description:

Computes indirect effects, conditional effects, and conditional indirect effects in a structural equation model or path model after model fitting, with no need to define any user parameters or label any paths in the model syntax, using the approach presented in Cheung and Cheung (2024) <doi:10.3758/s13428-023-02224-z>. Can also form bootstrap confidence intervals by doing bootstrapping only once and reusing the bootstrap estimates in all subsequent computations. Supports bootstrap confidence intervals for standardized (partially or completely) indirect effects, conditional effects, and conditional indirect effects as described in Cheung (2009) <doi:10.3758/BRM.41.2.425> and Cheung, Cheung, Lau, Hui, and Vong (2022) <doi:10.1037/hea0001188>. Model fitting can be done by structural equation modeling using lavaan() or regression using lm().

URL:

https://sfcheung.github.io/manymome/

BugReports:

https://github.com/sfcheung/manymome/issues

License:

GPL (≥ 3)

Encoding:

UTF-8

RoxygenNote:

7.3.2

Suggests:

knitr, rmarkdown, lavaan.mi, Amelia, mice, testthat (≥ 3.0.0)

Config/testthat/edition:

Config/testthat/parallel:

true

Config/testthat/start-first:

cond_indirect_*

Imports:

lavaan, boot, parallel, pbapply, stats, ggplot2, igraph, MASS, methods

Depends:

R (≥ 3.5.0)

LazyData:

true

VignetteBuilder:

knitr

NeedsCompilation:

Packaged:

2025-06-21 07:13:46 UTC; shufa

Author:

Shu Fai Cheung

[aut, cre], Sing-Hang Cheung

[aut]

Maintainer:

Shu Fai Cheung <shufai.cheung@gmail.com>

Repository:

CRAN

Date/Publication:

2025-06-21 08:00:02 UTC

manymome: Mediation, Moderation and Moderated-Mediation After Model Fitting

Description

Computes indirect effects, conditional effects, and conditional indirect effects in a structural equation model or path model after model fitting, with no need to define any user parameters or label any paths in the model syntax, using the approach presented in Cheung and Cheung (2024) doi:10.3758/s13428-023-02224-z. Can also form bootstrap confidence intervals by doing bootstrapping only once and reusing the bootstrap estimates in all subsequent computations. Supports bootstrap confidence intervals for standardized (partially or completely) indirect effects, conditional effects, and conditional indirect effects as described in Cheung (2009) doi:10.3758/BRM.41.2.425 and Cheung, Cheung, Lau, Hui, and Vong (2022) doi:10.1037/hea0001188. Model fitting can be done by structural equation modeling using lavaan() or regression using lm().

Author(s)

Maintainer: Shu Fai Cheung shufai.cheung@gmail.com (ORCID)

Authors:

Sing-Hang Cheung (ORCID)

Enumerate All Indirect Effects in a Model

Description

Check all indirect paths in a model and return them as a list of arguments of x, y, and m, to be used by indirect_effect().

Usage

all_indirect_paths(
  fit = NULL,
  exclude = NULL,
  x = NULL,
  y = NULL,
  group = NULL
)

all_paths_to_df(all_paths)

Arguments

fit

A fit object. It can be the output of lavaan::lavaan() or its wrapper such as lavaan::sem(), or a list of the output of lm() or the output of lm2list(). If it is a single model fitted by lm(), it will be automatically converted to a list by lm2list().

exclude

A character vector of variables to be excluded in the search, such as control variables.

x

A character vector of variables that will be included as the x variables. If supplied, only paths that start from these variables will be included in the search. If NULL, the default, then all variables that are one of the predictors in at least one regression equation will be included in the search.

y

A character vector of variables that will be included as the y variables. If supplied, only paths that start from these variables will be included in the search. If NULL, the default, then all variables that are the outcome variables in at least one regression equation will be included in the search.

group

Either the group number as appeared in the summary() or lavaan::parameterEstimates() output of a lavaan::lavaan object, or the group label as used in the lavaan::lavaan object. Used only when the number of groups is greater than one. Default is NULL. If not specified by the model has more than one group, than paths that appears in at least one group will be included in the output.

all_paths

An all_paths-class object. For example, the output of all_indirect_paths().

Details

It makes use of igraph::all_simple_paths() to identify paths in a model.

Multigroup Models

Since Version 0.1.14.2, support for multigroup models has been added for models fitted by lavaan. If a model has more than one group and group is not specified, than paths in all groups will be returned. If group is specified, than only paths in the selected group will be returned.

Value

all_indirect_paths() returns a list of the class all_paths. Each argument is a list of three character vectors, x, the name of the predictor that starts a path, y, the name of the outcome that ends a path, and m, a character vector of one or more names of the mediators, from x to y. This class has a print method.

all_paths_to_df() returns a data frame with three columns, x, y, and m, which can be used by functions such as indirect_effect().

Functions

all_indirect_paths(): Enumerate all indirect paths.
all_paths_to_df(): Convert the output of all_indirect_paths() to a data frame with three columns: x, y, and m.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
           fixed.x = FALSE)
# All indirect paths
out1 <- all_indirect_paths(fit)
out1
names(out1)

# Exclude c1 and c2 in the search
out2 <- all_indirect_paths(fit, exclude = c("c1", "c2"))
out2
names(out2)

# Exclude c1 and c2, and only consider paths start
# from x and end at y
out3 <- all_indirect_paths(fit, exclude = c("c1", "c2"),
                           x = "x",
                           y = "y")
out3
names(out3)

# Multigroup models

data(data_med_complicated_mg)
mod <-
"
m11 ~ x1 + x2 + c1 + c2
m12 ~ m11 + c1 + c2
m2 ~ x1 + x2 + c1 + c2
y1 ~ m11 + m12 + x1 + x2 + c1 + c2
y2 ~ m2 + x1 + x2 + c1 + c2
"
fit <- sem(mod, data_med_complicated_mg, group = "group")
summary(fit)

all_indirect_paths(fit,
                   x = "x1",
                   y = "y1")
all_indirect_paths(fit,
                   x = "x1",
                   y = "y1",
                   group = 1)
all_indirect_paths(fit,
                   x = "x1",
                   y = "y1",
                   group = "Group B")

Check a Path Exists in a Model

Description

It checks whether a path, usually an indirect path, exists in a model.

Usage

check_path(x, y, m = NULL, fit = NULL, est = NULL)

Arguments

x

Character. The name of predictor at the start of the path.

y

Character. The name of the outcome variable at the end of the path.

m

A vector of the variable names of the mediators. The path goes from the first mediator successively to the last mediator. If NULL, the default, the path goes from x to y.

fit

The fit object. Currently only supports a lavaan::lavaan-class object or a list of outputs of lm(). It can also be a lavaan.mi object returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi(). If it is a single model fitted by lm(), it will be automatically converted to a list by lm2list().

est

The output of lavaan::parameterEstimates(). If NULL, the default, it will be generated from fit. If supplied, fit will ge ignored.

Details

It checks whether the path defined by a predictor (x), an outcome (y), and optionally a sequence of mediators (m), exists in a model. It can check models in a lavaan::lavaan-class object or a list of outputs of lm(). It also support lavaan.mi objects returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi().

For example, in the following model in lavaan syntax

m1 ~ x
m2 ~ m1
m3 ~ x
y ~ m2 + m3

This path is valid: ⁠x = "x", y = "y", m = c("m1", "m2")⁠

This path is invalid: ⁠x = "x", y = "y", m = c("m2")⁠

This path is also invalid: ⁠x = "x", y = "y", m = c("m1", "m2")⁠

Value

A logical vector of length one. TRUE if the path is valid, FALSE if the path is invalid.

Examples


library(lavaan)
data(data_serial_parallel)
dat <- data_serial_parallel
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE)

# The following paths are valid
check_path(x = "x", y = "y", m = c("m11", "m12"), fit = fit)
check_path(x = "x", y = "y", m = "m2", fit = fit)
# The following paths are invalid
check_path(x = "x", y = "y", m = c("m11", "m2"), fit = fit)
check_path(x = "x", y = "y", m = c("m12", "m11"), fit = fit)

Print the Output of 'cond_indirect_diff()'

Description

Extract the change in conditional indirect effect.

Usage

## S3 method for class 'cond_indirect_diff'
coef(object, ...)

Arguments

object

The output of cond_indirect_diff().

...

Optional arguments. Ignored.

Details

The coef method of the cond_indirect_diff-class object.

Value

Scalar: The change of conditional indirect effect in object.

Estimates of Conditional Indirect Effects or Conditional Effects

Description

Return the estimates of the conditional indirect effects or conditional effects for all levels in the output of cond_indirect_effects().

Usage

## S3 method for class 'cond_indirect_effects'
coef(object, ...)

Arguments

object

The output of cond_indirect_effects().

...

Optional arguments. Ignored by the function.

Details

It extracts and returns the column ind or std in the output of cond_indirect_effects().

Value

A numeric vector: The estimates of the conditional effects or conditional indirect effects.

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x  + w1 + x:w1
m2 ~ m1
y  ~ m2 + x + w4 + m2:w4
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Conditional effects from x to m1 when w1 is equal to each of the levels
out1 <- cond_indirect_effects(x = "x", y = "m1",
                      wlevels = c("w1"), fit = fit)
out1
coef(out1)

# Conditional indirect effects from x1 through m1 and m2 to y,
out2 <- cond_indirect_effects(x = "x", y = "y", m = c("m1", "m2"),
                      wlevels = c("w1", "w4"), fit = fit)
out2
coef(out2)

# Standardized conditional indirect effects from x1 through m1 and m2 to y,
out2std <- cond_indirect_effects(x = "x", y = "y", m = c("m1", "m2"),
                      wlevels = c("w1", "w4"), fit = fit,
                      standardized_x = TRUE, standardized_y = TRUE)
out2std
coef(out2std)

Delta_Med in a 'delta_med'-Class Object

Description

Return the estimate of Delta_Med in a 'delta_med'-class object.

Usage

## S3 method for class 'delta_med'
coef(object, ...)

Arguments

object

The output of delta_med().

...

Optional arguments. Ignored.

Details

It just extracts and returns the element delta_med in the output of delta_med(), the estimate of the Delta_Med proposed by Liu, Yuan, and Li (2023), an R^2-like measure of indirect effect.

Value

A scalar: The estimate of Delta_Med.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

References

Liu, H., Yuan, K.-H., & Li, H. (2023). A systematic framework for defining R-squared measures in mediation analysis. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000571

Examples


library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)
dm <- delta_med(x = "x",
                y = "y",
                m = "m",
                fit = fit)
dm
print(dm, full = TRUE)
coef(dm)

Extract the Indirect Effect or Conditional Indirect Effect

Description

Return the estimate of the indirect effect in the output of indirect_effect() or or the conditional indirect in the output of cond_indirect().

Usage

## S3 method for class 'indirect'
coef(object, ...)

Arguments

object

The output of indirect_effect() or cond_indirect().

...

Optional arguments. Ignored by the function.

Details

It extracts and returns the element indirect. in an object.

If standardized effect is requested when calling indirect_effect() or cond_indirect(), the effect returned is also standardized.

Value

A scalar: The estimate of the indirect effect or conditional indirect effect.

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x + w1 + x:w1
m2 ~ x
y  ~ m1 + m2 + x
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Examples for indirect_effect():

# Inidrect effect from x through m2 to y
out1 <- indirect_effect(x = "x", y = "y", m = "m2", fit = fit)
out1
coef(out1)

# Conditional Indirect effect from x1 through m1 to y,
# when w1 is 1 SD above mean
hi_w1 <- mean(dat$w1) + sd(dat$w1)
out2 <- cond_indirect(x = "x", y = "y", m = "m1",
                      wvalues = c(w1 = hi_w1), fit = fit)
out2
coef(out2)

Extract the Indirect Effects from a 'indirect_list' Object

Description

Return the estimates of the indirect effects in the output of many_indirect_effects().

Usage

## S3 method for class 'indirect_list'
coef(object, ...)

Arguments

object

The output of many_indirect_effects().

...

Optional arguments. Ignored by the function.

Details

It extracts the estimates in each 'indirect'-class object in the list.

If standardized effect is requested when calling many_indirect_effects(), the effects returned are also standardized.

Value

A numeric vector of the indirect effects.

Examples


library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
           fixed.x = FALSE)
# All indirect paths from x to y
paths <- all_indirect_paths(fit,
                           x = "x",
                           y = "y")
paths
# Indirect effect estimates
out <- many_indirect_effects(paths,
                             fit = fit)
out
coef(out)

Extract the Proportion of Effect Mediated

Description

Return the proportion of effect mediated in the output of indirect_proportion().

Usage

## S3 method for class 'indirect_proportion'
coef(object, ...)

Arguments

object

The output of indirect_proportion()

...

Not used.

Details

It extracts and returns the element proportion in the input object.

Value

A scalar: The proportion of effect mediated.

Examples


library(lavaan)
dat <- data_med
head(dat)
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, fixed.x = FALSE)
out <- indirect_proportion(x = "x",
                           y = "y",
                           m = "m",
                           fit = fit)
out
coef(out)

Coefficients of an 'lm_from_lavaan'-Class Object

Description

Returns the path coefficients of the terms in an lm_from_lavaan-class object.

Usage

## S3 method for class 'lm_from_lavaan'
coef(object, ...)

Arguments

object

A 'lm_from_lavaan'-class object.

...

Additional arguments. Ignored.

Details

An lm_from_lavaan-class object converts a regression model for a variable in a lavaan-class object to a formula-class object. This function simply extracts the path coefficients estimates. Intercept is always included, and set to zero if mean structure is not in the source lavaan-class object.

This is an advanced helper used by plot.cond_indirect_effects(). Exported for advanced users and developers.

Value

A numeric vector of the path coefficients.

Examples

library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
coef(fit_list$m)
coef(fit_list$y)

Conditional, Indirect, and Conditional Indirect Effects

Description

Compute the conditional effects, indirect effects, or conditional indirect effects in a structural model fitted by lm(), lavaan::sem(), or lavaan.mi::sem.mi().

Usage

cond_indirect(
  x,
  y,
  m = NULL,
  fit = NULL,
  est = NULL,
  implied_stats = NULL,
  wvalues = NULL,
  standardized_x = FALSE,
  standardized_y = FALSE,
  boot_ci = FALSE,
  level = 0.95,
  boot_out = NULL,
  R = 100,
  seed = NULL,
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  make_cluster_args = list(),
  progress = TRUE,
  save_boot_full = FALSE,
  prods = NULL,
  get_prods_only = FALSE,
  save_boot_out = TRUE,
  mc_ci = FALSE,
  mc_out = NULL,
  save_mc_full = FALSE,
  save_mc_out = TRUE,
  ci_out = NULL,
  save_ci_full = FALSE,
  save_ci_out = TRUE,
  ci_type = NULL,
  group = NULL,
  boot_type = c("perc", "bc")
)

cond_indirect_effects(
  wlevels,
  x,
  y,
  m = NULL,
  fit = NULL,
  w_type = "auto",
  w_method = "sd",
  sd_from_mean = NULL,
  percentiles = NULL,
  est = NULL,
  implied_stats = NULL,
  boot_ci = FALSE,
  R = 100,
  seed = NULL,
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  make_cluster_args = list(),
  progress = TRUE,
  boot_out = NULL,
  output_type = "data.frame",
  mod_levels_list_args = list(),
  mc_ci = FALSE,
  mc_out = NULL,
  ci_out = NULL,
  ci_type = NULL,
  boot_type = c("perc", "bc"),
  groups = NULL,
  ...
)

indirect_effect(
  x,
  y,
  m = NULL,
  fit = NULL,
  est = NULL,
  implied_stats = NULL,
  standardized_x = FALSE,
  standardized_y = FALSE,
  boot_ci = FALSE,
  level = 0.95,
  boot_out = NULL,
  R = 100,
  seed = NULL,
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  make_cluster_args = list(),
  progress = TRUE,
  save_boot_full = FALSE,
  save_boot_out = TRUE,
  mc_ci = FALSE,
  mc_out = NULL,
  save_mc_full = FALSE,
  save_mc_out = TRUE,
  ci_out = NULL,
  save_ci_full = FALSE,
  save_ci_out = TRUE,
  ci_type = NULL,
  boot_type = c("perc", "bc"),
  group = NULL
)

cond_effects(
  wlevels,
  x,
  y,
  m = NULL,
  fit = NULL,
  w_type = "auto",
  w_method = "sd",
  sd_from_mean = NULL,
  percentiles = NULL,
  est = NULL,
  implied_stats = NULL,
  boot_ci = FALSE,
  R = 100,
  seed = NULL,
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  make_cluster_args = list(),
  progress = TRUE,
  boot_out = NULL,
  output_type = "data.frame",
  mod_levels_list_args = list(),
  mc_ci = FALSE,
  mc_out = NULL,
  ci_out = NULL,
  ci_type = NULL,
  boot_type = c("perc", "bc"),
  groups = NULL,
  ...
)

many_indirect_effects(paths, ...)

Arguments

x

Character. The name of the predictor at the start of the path.

y

Character. The name of the outcome variable at the end of the path. If the model has only one outcome variable (e.g., moderation only and no mediator), then this argument can be omitted.

m

A vector of the variable names of the mediator(s). The path goes from the first mediator successively to the last mediator. If NULL, the default, the path goes from x to y.

fit

The fit object. Can be a lavaan::lavaan object or a list of lm() outputs. It can also be a lavaan.mi object returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi(). If it is a single model fitted by lm(), it will be automatically converted to a list by lm2list().

est

The output of lavaan::parameterEstimates(). If NULL, the default, it will be generated from fit. If supplied, fit will be ignored.

implied_stats

Implied means, variances, and covariances of observed variables, of the form of the output of lavaan::lavInspect() with what set to "implied". The standard deviations are extracted from this object for standardization. Default is NULL, and implied statistics will be computed from fit if required.

wvalues

A numeric vector of named elements. The names are the variable names of the moderators, and the values are the values to which the moderators will be set to. Default is NULL.

standardized_x

Logical. Whether x will be standardized. Default is FALSE. For multigroup models, model implied standard deviation for the selected group will be used.

standardized_y

Logical. Whether y will be standardized. Default is FALSE. For multigroup models, model implied standard deviation for the selected group will be used.

boot_ci

Logical. Whether bootstrap confidence interval will be formed. Default is FALSE.

level

The level of confidence for the bootstrap confidence interval. Default is .95.

boot_out

If boot_ci is TRUE, users can supply pregenerated bootstrap estimates. This can be the output of do_boot(). For indirect_effect() and cond_indirect_effects(), this can be the output of a previous call to cond_indirect_effects(), indirect_effect(), or cond_indirect() with bootstrap confidence intervals requested. These stored estimates will be reused such that there is no need to do bootstrapping again. If not supplied, the function will try to generate them from fit.

R

Integer. If boot_ci is TRUE, boot_out is NULL, and bootstrap standard errors not requested if fit is a lavaan::lavaan object, this function will do bootstrapping on fit. R is the number of bootstrap samples. Default is 100. For Monte Carlo simulation, this is the number of replications.

seed

If bootstrapping or Monte Carlo simulation is conducted, this is the seed for the bootstrapping or simulation. Default is NULL and seed is not set.

parallel

Logical. If bootstrapping is conducted, whether parallel processing will be used. Default is TRUE. If fit is a list of lm() outputs, parallel processing will not be used.

ncores

Integer. The number of CPU cores to use when parallel is TRUE. Default is the number of non-logical cores minus one (one minimum). Will raise an error if greater than the number of cores detected by parallel::detectCores(). If ncores is set, it will override make_cluster_args in do_boot().

make_cluster_args

A named list of additional arguments to be passed to parallel::makeCluster(). For advanced users. See parallel::makeCluster() for details. Default is list().

progress

Logical. Display bootstrapping progress or not. Default is TRUE.

save_boot_full

If TRUE, full bootstrapping results will be stored. Default is FALSE.

prods

The product terms found. For internal use.

get_prods_only

IF TRUE, will quit early and return the product terms found. The results can be passed to the prod argument when calling this function. Default is FALSE. This function is for internal use.

save_boot_out

If boot_out is supplied, whether it will be saved in the output. Default is TRUE.

mc_ci

Logical. Whether Monte Carlo confidence interval will be formed. Default is FALSE.

mc_out

If mc_ci is TRUE, users can supply pregenerated Monte Carlo estimates. This can be the output of do_mc(). For indirect_effect() and cond_indirect_effects(), this can be the output of a previous call to cond_indirect_effects(), indirect_effect(), or cond_indirect() with Monte Carlo confidence intervals requested. These stored estimates will be reused such that there is no need to do Monte Carlo simulation again. If not supplied, the function will try to generate them from fit.

save_mc_full

If TRUE, full Monte Carlo results will be stored. Default is FALSE.

save_mc_out

If mc_out is supplied, whether it will be saved in the output. Default is TRUE.

ci_out

If ci_type is supplied, this is the corresponding argument. If ci_type is "boot", this argument will be used as boot_out. If ci_type is "mc", this argument will be used as mc_out.

save_ci_full

If TRUE, full bootstrapping or Monte Carlo results will be stored. Default is FALSE.

save_ci_out

If either mc_out or boot_out is supplied, whether it will be saved in the output. Default is TRUE.

ci_type

The type of confidence intervals to be formed. Can be either "boot" (bootstrapping) or "mc" (Monte Carlo). If not supplied or is NULL, will check other arguments (e.g, boot_ci and mc_ci). If supplied, will override boot_ci and mc_ci.

group

boot_type

If bootstrap confidence interval is to be formed, the type of bootstrap confidence interval. The supported types are "perc" (percentile bootstrap confidence interval, the default and recommended type) and "bc" (bias-corrected, or BC, bootstrap confidence interval).

wlevels

The output of merge_mod_levels(), or the moderator(s) to be passed to mod_levels_list(). If all the moderators can be represented by one variable, that is, each moderator is (a) a numeric variable, (b) a dichotomous categorical variable, or (c) a factor or string variable used in lm() in fit, then it is a vector of the names of the moderators as appeared in the data frame. If at least one of the moderators is a categorical variable represented by more than one variable, such as user-created dummy variables used in lavaan::sem(), then it must be a list of the names of the moderators, with such moderators represented by a vector of names. For example: ⁠list("w1", c("gpgp2", "gpgp3")⁠, the first moderator w1 and the second moderator a three-categorical variable represented by gpgp2 and gpgp3.

w_type

Character. Whether the moderator is a "numeric" variable or a "categorical" variable. If "auto", the function will try to determine the type automatically. See mod_levels_list() for further information.

w_method

Character, either "sd" or "percentile". If "sd", the levels are defined by the distance from the mean in terms of standard deviation. if "percentile", the levels are defined in percentiles. See mod_levels_list() for further information.

sd_from_mean

A numeric vector. Specify the distance in standard deviation from the mean for each level. Default is c(-1, 0, 1) when there is only one moderator, and c(-1, 1) when there are more than one moderator. Ignored if w_method is not equal to "sd". See mod_levels_list() for further information.

percentiles

A numeric vector. Specify the percentile (in proportion) for each level. Default is c(.16, .50, .84) if there is one moderator, and c(.16, .84) when there are more than one moderator. Ignored if w_method is not equal to "percentile". See mod_levels_list() for further information.

output_type

The type of output of cond_indirect_effects(). If "data.frame", the default, the output will be converted to a data frame. If any other values, the output is a list of the outputs from cond_indirect().

mod_levels_list_args

Additional arguments to be passed to mod_levels_list() if it is called for creating the levels of moderators. Default is list().

groups

Either a vector of group numbers as appeared in the summary() or lavaan::parameterEstimates() output of a lavaan::lavaan object, or a vector of group labels as used in the lavaan::lavaan object. Used only when the number of groups is greater than one. Default is NULL.

...

For many_indirect_effects(), these are arguments to be passed to indirect_effect().

paths

The output of all_indirect_paths()

Details

For a model with a mediation path moderated by one or more moderators, cond_indirect_effects() can be used to compute the conditional indirect effect from one variable to another variable, at one or more set of selected value(s) of the moderator(s).

If only the effect for one set of value(s) of the moderator(s) is needed, cond_indirect() can be used.

If only the mediator(s) is/are specified (m) and no values of moderator(s) are specified, then the indirect effect from one variable (x) to another variable (y) is computed. A convenient wrapper indirect_effect() can be used to compute the indirect effect.

If only the value(s) of moderator(s) is/are specified (wvalues or wlevels) and no mediators (m) are specified when calling cond_indirect_effects() or cond_indirect(), then the conditional direct effects from one variable to another are computed.

All three functions support using nonparametric bootstrapping (for lavaan or lm outputs) or Monte Carlo simulation (for lavaan outputs only) to form confidence intervals. Bootstrapping or Monte Carlo simulation only needs to be done once. These are the possible ways to form bootstrapping:

Do bootstrapping or Monte Carlo simulation in the first call to one of these functions, by setting boot_ci or mc_ci to TRUE and R to the number of bootstrap samples or replications, level to the level of confidence (default .95 or 95%), and seed to reproduce the results (parallel and ncores are optional for bootstrapping). This will take some time to run for bootstrapping. The output will have all bootstrap or Monte Carlo estimates stored. This output, whether it is from indirect_effect(), cond_indirect_effects(), or cond_indirect(), can be reused by any of these three functions by setting boot_out (for bootstrapping) or mc_out (for Monte Carlo simulation) to this output. They will form the confidence intervals using the stored bootstrap or Monte Carlo estimates.
Do bootstrapping using do_boot() or Monte Carlo simulation us8ing do_mc(). The output can be used in the boot_out (for bootstrapping) or mc_out (for Monte Carlo simulation) argument of indirect_effect(), cond_indirect_effects() and cond_indirect().
For bootstrapping, if lavaan::sem() is used to fit a model and se = "boot" is used, do_boot() can extract them to generate a boot_out-class object that again can be used in the boot_out argument.

If boot_out or mc_out is set, arguments such as R, seed, and parallel will be ignored.

Multigroup Models

Since Version 0.1.14.2, support for multigroup models has been added for models fitted by lavaan. Both bootstrapping and Monte Carlo confidence intervals are supported. When used on a multigroup model:

For cond_indirect() and indirect_effect(), users need to specify the group argument (by number or label). When using cond_indirect_effects(), if group is not set, all groups wil be used and the indirect effect in each group will be computed, kind of treating group as a moderator.
For many_indirect_effects(), the paths can be generated from a multigroup models.
Currently, cond_indirect_effects() does not support a multigroup model with moderators on the path selected. The function cond_indirect() does not have this limitation but users need to manually specify the desired value of the moderator(s).

`many_indirect_effects()`

If bootstrapping or Monte Carlo confidence intervals are requested, it is advised to use do_boot() first to simulate the estimates. Nevertheless, In Version 0.1.14.9 and later versions, if boot_ci or mc_ci is TRUE when calling many_indirect_effects() but boot_out or mc_out is not set, bootstrapping or simulation will be done only once, and then the bootstrapping or simulated estimates will be used for all paths. This prevents accidentally repeating the process once for each direct path.

Value

indirect_effect() and cond_indirect() return an indirect-class object.

cond_indirect_effects() returns a cond_indirect_effects-class object.

These two classes of objects have their own print methods for printing the results (see print.indirect() and print.cond_indirect_effects()). They also have a coef method for extracting the estimates (coef.indirect() and coef.cond_indirect_effects()) and a confint method for extracting the confidence intervals (confint.indirect() and confint.cond_indirect_effects()). Addition and subtraction can also be conducted on indirect-class object to estimate and test a function of effects (see math_indirect)

Functions

cond_indirect(): Compute conditional, indirect, or conditional indirect effects for one set of levels.
cond_indirect_effects(): Compute the conditional effects or conditional indirect effects for several sets of levels of the moderator(s).
indirect_effect(): Compute the indirect effect. A wrapper of cond_indirect(). Can be used when there is no moderator.
cond_effects(): Just an alias to cond_indirect_effects(), a better name when a path has no moderator.
many_indirect_effects(): Compute the indirect effects along more than one paths. It call indirect_effect() once for each of the path.

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x  + d1 * w1 + e1 * x:w1
m2 ~ a2 * x
y  ~ b1 * m1 + b2 * m2 + cp * x
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE)
est <- parameterEstimates(fit)
hi_w1 <- mean(dat$w1) + sd(dat$w1)

# Examples for cond_indirect():

# Conditional effect from x to m1 when w1 is 1 SD above mean
cond_indirect(x = "x", y = "m1",
              wvalues = c(w1 = hi_w1), fit = fit)

# Direct effect from x to y (direct because no 'm' variables)
indirect_effect(x = "x", y = "y", fit = fit)

# Conditional Indirect effect from x1 through m1 to y, when w1 is 1 SD above mean
cond_indirect(x = "x", y = "y", m = "m1",
              wvalues = c(w1 = hi_w1), fit = fit)



# Examples for cond_indirect_effects():

# Create levels of w1, the moderators
w1levels <- mod_levels("w1", fit = fit)
w1levels

# Conditional effects from x to m1 when w1 is equal to each of the levels
cond_indirect_effects(x = "x", y = "m1",
                      wlevels = w1levels, fit = fit)

# Conditional Indirect effect from x1 through m1 to y,
# when w1 is equal to each of the levels
cond_indirect_effects(x = "x", y = "y", m = "m1",
                      wlevels = w1levels, fit = fit)

# Multigroup models for cond_indirect_effects()

dat <- data_med_mg
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE,
           group = "group")

# If a model has more than one group,
# it will be used as a 'moderator'.
cond_indirect_effects(x = "x", y = "y", m = "m",
                      fit = fit)


# Multigroup model for indirect_effect()

dat <- data_med_mg
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE,
           group = "group")

# If a model has more than one group,
# the argument 'group' must be set.
ind1 <- indirect_effect(x = "x",
                        y = "y",
                        m = "m",
                        fit = fit,
                        group = "Group A")
ind1
ind2 <- indirect_effect(x = "x",
                        y = "y",
                        m = "m",
                        fit = fit,
                        group = 2)
ind2


# Examples for many_indirect_effects():

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
           fixed.x = FALSE)
# All indirect paths from x to y
paths <- all_indirect_paths(fit,
                           x = "x",
                           y = "y")
paths
# Indirect effect estimates
out <- many_indirect_effects(paths,
                             fit = fit)
out

# Multigroup models for many_indirect_effects()

data(data_med_complicated_mg)
mod <-
"
m11 ~ x1 + x2 + c1 + c2
m12 ~ m11 + c1 + c2
m2 ~ x1 + x2 + c1 + c2
y1 ~ m11 + m12 + x1 + x2 + c1 + c2
y2 ~ m2 + x1 + x2 + c1 + c2
"
fit <- sem(mod, data_med_complicated_mg, group = "group")
summary(fit)

paths <- all_indirect_paths(fit,
                            x = "x1",
                            y = "y1")
paths
# Indirect effect estimates for all paths in all groups
out <- many_indirect_effects(paths,
                             fit = fit)
out

Differences In Conditional Indirect Effects

Description

Compute the difference in conditional indirect effects between two sets of levels of the moderators.

Usage

cond_indirect_diff(output, from = NULL, to = NULL, level = 0.95)

Arguments

output

A cond_indirect_effects-class object: The output of cond_indirect_effects().

from

A row number of output.

to

A row number of output. The change in indirect effects is computed by the change in the level(s) of the moderator(s) from Row from to Row to.

level

The level of confidence for the confidence interval. Default is .95.

Details

Ths function takes the output of cond_indirect_effects() and computes the difference in conditional indirect effects between any two rows, that is, between levels of the moderator, or two sets of levels of the moderators when the path has more than one moderator.

The difference is meaningful when the difference between the two levels or sets of levels are meaningful. For example, if the two levels are the mean of the moderator and one standard deviation above mean of the moderator, then this difference is the change in indirect effect when the moderator increases by one standard deviation.

If the two levels are 0 and 1, then this difference is the index of moderated mediation as proposed by Hayes (2015). (This index can also be computed directly by index_of_mome(), designed specifically for this purpose.)

The function can also compute the change in the standardized indirect effect between two levels of a moderator or two sets of levels of the moderators.

This function is intended to be a general purpose function that allows users to compute the difference between any two levels or sets of levels that are meaningful in a context.

This function itself does not set the levels of comparison. The levels to be compared need to be set when calling cond_indirect_effects(). This function extracts required information from the output of cond_indirect_effects().

If bootstrap or Monte Carlo estimates are available in the input or bootstrap or Monte Carlo confidence intervals are requested in calling cond_indirect_effects(), cond_indirect_diff() will also form the bootstrap confidence interval for the difference in conditional indirect effects using the stored estimates.

If bootstrap confidence interval is to be formed and both effects used the same type of interval, then that type will be used. Otherwise, percentile confidence interval will be formed.

Value

A cond_indirect_diff-class object. This class has a print method (print.cond_indirect_diff()), a coef method (coef.cond_indirect_diff()), and a confint method (confint.cond_indirect_diff()).

Functions

cond_indirect_diff(): Compute the difference in in conditional indirect effect between two rows in the output of cond_indirect_effects().

References

Hayes, A. F. (2015). An index and test of linear moderated mediation. Multivariate Behavioral Research, 50(1), 1-22. doi:10.1080/00273171.2014.962683

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
dat$xw1 <- dat$x * dat$w1
mod <-
"
m1 ~ a * x  + f * w1 + d * xw1
y  ~ b * m1 + cp * x
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Create levels of w1, the moderators
w1levels <- mod_levels("w1", fit = fit)
w1levels

# Conditional effects from x to y when w1 is equal to each of the levels
boot_out <- fit2boot_out_do_boot(fit, R = 40, seed = 4314, progress = FALSE)
out <- cond_indirect_effects(x = "x", y = "y", m = "m1",
                             wlevels = w1levels, fit = fit,
                             boot_ci = TRUE, boot_out = boot_out)
out
out_ind <- cond_indirect_diff(out, from = 2, to = 1)
out_ind
coef(out_ind)
confint(out_ind)

Confidence Interval of the Output of 'cond_indirect_diff()'

Description

Extract the confidence interval the output of cond_indirect_diff().

Usage

## S3 method for class 'cond_indirect_diff'
confint(object, parm, level = 0.95, ...)

Arguments

object

The output of cond_indirect_diff().

parm

Ignored.

level

The level of confidence for the confidence interval. Default is .95. Must match the level of the stored confidence interval.

...

Optional arguments. Ignored.

Details

The confint method of the cond_indirect_diff-class object.

The type of confidence intervals depends on the call used to create the object. This function merely extracts the stored confidence intervals.

Value

A one-row-two-column data frame of the confidence limits. If confidence interval is not available, the limits are NAs.

Confidence Intervals of Indirect Effects or Conditional Indirect Effects

Description

Return the confidence intervals of the conditional indirect effects or conditional effects in the output of cond_indirect_effects().

Usage

## S3 method for class 'cond_indirect_effects'
confint(object, parm, level = 0.95, ...)

Arguments

object

The output of cond_indirect_effects().

parm

Ignored. Always returns the confidence intervals of the effects for all levels stored.

level

The level of confidence, default is .95, returning the 95% confidence interval. Ignored for now and will use the level of the stored intervals.

...

Additional arguments. Ignored by the function.

Details

It extracts and returns the columns for confidence intervals, if available.

The type of confidence intervals depends on the call used to compute the effects. If confidence intervals have already been formed (e.g., by bootstrapping or Monte Carlo), then this function merely retrieves the confidence intervals stored.

If the following conditions are met, the stored standard errors, if available, will be used test an effect and form it confidence interval:

Confidence intervals have not been formed (e.g., by bootstrapping or Monte Carlo).
The path has no mediators.
The model has only one group.
The path is moderated by one or more moderator.
Both the x-variable and the y-variable are not standardized.

If the model is fitted by OLS regression (e.g., using stats::lm()), then the variance-covariance matrix of the coefficient estimates will be used, and confidence intervals are computed from the t statistic.

If the model is fitted by structural equation modeling using lavaan, then the variance-covariance computed by lavaan will be used, and confidence intervals are computed from the z statistic.

Caution

If the model is fitted by structural equation modeling and has moderators, the standard errors, p-values, and confidence interval computed from the variance-covariance matrices for conditional effects can only be trusted if all covariances involving the product terms are free. If any of them are fixed, for example, fixed to zero, it is possible that the model is not invariant to linear transformation of the variables.

Value

A data frame with two columns, one for each confidence limit of the confidence intervals. The number of rows is equal to the number of rows of object.

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x  + w1 + x:w1
m2 ~ m1
y  ~ m2 + x + w4 + m2:w4
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Examples for cond_indirect():

# Create levels of w1 and w4
w1levels <- mod_levels("w1", fit = fit)
w1levels
w4levels <- mod_levels("w4", fit = fit)
w4levels
w1w4levels <- merge_mod_levels(w1levels, w4levels)

# Conditional effects from x to m1 when w1 is equal to each of the levels
# R should be at least 2000 or 5000 in real research.
out1 <- suppressWarnings(cond_indirect_effects(x = "x", y = "m1",
                      wlevels = w1levels, fit = fit,
                      boot_ci = TRUE, R = 20, seed = 54151,
                      parallel = FALSE,
                      progress = FALSE))
confint(out1)

Confidence Interval for Delta_Med in a 'delta_med'-Class Object

Description

Return the confidence interval of the Delta_Med in the output of delta_med().

Usage

## S3 method for class 'delta_med'
confint(object, parm, level = NULL, boot_type, ...)

Arguments

object

The output of delta_med().

parm

Not used because only one parameter, the Delta_Med, is allowed.

level

The level of confidence, default is NULL and the level used when the object was created will be used.

boot_type

If bootstrap confidence interval is to be formed, the type of bootstrap confidence interval. The supported types are "perc" (percentile bootstrap confidence interval, the recommended method) and "bc" (bias-corrected, or BC, bootstrap confidence interval). If not supplied, the stored boot_type will be used.

...

Optional arguments. Ignored.

Details

It returns the nonparametric bootstrap percentile confidence interval of Delta_Med, proposed byLiu, Yuan, and Li (2023). The object must be the output of delta_med(), with bootstrap confidence interval requested when calling delta_med(). However, the level of confidence can be different from that used when call delta_med().

Value

A one-row matrix of the confidence interval. All values are NA if bootstrap confidence interval was not requested when calling delta_med().

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

Examples


library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)

# Call do_boot() to generate
# bootstrap estimates
# Use 2000 or even 5000 for R in real studies
# Set parallel to TRUE in real studies for faster bootstrapping
boot_out <- do_boot(fit,
                    R = 45,
                    seed = 879,
                    parallel = FALSE,
                    progress = FALSE)
# Remove 'progress = FALSE' in practice
dm_boot <- delta_med(x = "x",
                     y = "y",
                     m = "m",
                     fit = fit,
                     boot_out = boot_out,
                     progress = FALSE)
dm_boot
confint(dm_boot)

Confidence Interval of Indirect Effect or Conditional Indirect Effect

Description

Return the confidence interval of the indirect effect or conditional indirect effect stored in the output of indirect_effect() or cond_indirect().

Usage

## S3 method for class 'indirect'
confint(object, parm, level = 0.95, boot_type, ...)

Arguments

object

The output of indirect_effect() or cond_indirect().

parm

Ignored because the stored object always has only one parameter.

level

The level of confidence, default is .95, returning the 95% confidence interval.

boot_type

...

Additional arguments. Ignored by the function.

Details

It extracts and returns the stored confidence interval if available.

The type of confidence interval depends on the call used to compute the effect. This function merely retrieves the stored estimates, which could be generated by nonparametric bootstrapping, Monte Carlo simulation, or other methods to be supported in the future, and uses them to form the percentile confidence interval.

If the following conditions are met, the stored standard errors, if available, will be used test an effect and form it confidence interval:

Confidence intervals have not been formed (e.g., by bootstrapping or Monte Carlo).
The path has no mediators.
The model has only one group.
The path is moderated by one or more moderator.
Both the x-variable and the y-variable are not standardized.

If the model is fitted by structural equation modeling using lavaan, then the variance-covariance computed by lavaan will be used, and confidence intervals are computed from the z statistic.

Caution

Value

A numeric vector of two elements, the limits of the confidence interval.

Examples


dat <- modmed_x1m3w4y1

# Indirect Effect

library(lavaan)
mod1 <-
"
m1 ~ x
m2 ~ m1
y  ~ m2 + x
"
fit <- sem(mod1, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
# R should be at least 2000 or 5000 in real research.
out1 <- indirect_effect(x = "x", y = "y",
                        m = c("m1", "m2"),
                        fit = fit,
                        boot_ci = TRUE, R = 45, seed = 54151,
                        parallel = FALSE,
                        progress = FALSE)
out1
confint(out1)

Confidence Intervals of Indirect Effects in an 'indirect_list' Object

Description

Return the confidence intervals of the indirect effects stored in the output of many_indirect_effects().

Usage

## S3 method for class 'indirect_list'
confint(object, parm = NULL, level = 0.95, ...)

Arguments

object

The output of many_indirect_effects().

parm

Ignored for now.

level

The level of confidence, default is .95, returning the 95% confidence interval.

...

Additional arguments. Ignored by the function.

Details

It extracts and returns the stored confidence interval if available.

The type of confidence intervals depends on the call used to compute the effects. This function merely retrieves the stored estimates, which could be generated by nonparametric bootstrapping, Monte Carlo simulation, or other methods to be supported in the future, and uses them to form the percentile confidence interval.

Value

A two-column data frame. The columns are the limits of the confidence intervals.

Examples


library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
           fixed.x = FALSE)
# All indirect paths from x to y
paths <- all_indirect_paths(fit,
                           x = "x",
                           y = "y")
paths
# Indirect effect estimates
# R should be 2000 or even 5000 in real research
# parallel should be used in real research.
fit_boot <- do_boot(fit, R = 45, seed = 8974,
                    parallel = FALSE,
                    progress = FALSE)
out <- many_indirect_effects(paths,
                             fit = fit,
                             boot_ci = TRUE,
                             boot_out = fit_boot)
out
confint(out)

Sample Dataset: Simple Mediation

Description

A simple mediation model.

Usage

data_med

Format

A data frame with 100 rows and 5 variables:

x: Predictor. Numeric.
m: Mediator. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
ab := a * b
"
fit <- sem(mod, data_med, fixed.x = FALSE)
parameterEstimates(fit)

Sample Dataset: A Complicated Mediation Model

Description

A mediation model with two predictors, two pathways,

Usage

data_med_complicated

Format

A data frame with 300 rows and 5 variables:

x1: Predictor 1. Numeric.
x2: Predictor 2. Numeric.
m11: Mediator 1 in Path 1. Numeric.
m12: Mediator 2 in Path 1. Numeric.
m2: Mediator in Path 2. Numeric.
y1: Outcome variable 1. Numeric.
y2: Outcome variable 2. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

data(data_med_complicated)
dat <- data_med_complicated
summary(lm_m11 <- lm(m11 ~ x1 + x1 + x2 + c1 + c2, dat))
summary(lm_m12 <- lm(m12 ~ m11 + x1 + x2 + c1 + c2, dat))
summary(lm_m2 <- lm(m2 ~ x1 + x2 + c1 + c2, dat))
summary(lm_y1 <- lm(y1 ~ m11 + m12 + m2 + x1 + x2 + c1 + c2, dat))
summary(lm_y2 <- lm(y2 ~ m11 + m12 + m2 + x1 + x2 + c1 + c2, dat))

Sample Dataset: A Complicated Mediation Model With Two Groups

Description

A mediation model with two predictors, two pathways, and two groups.

Usage

data_med_complicated_mg

Format

A data frame with 300 rows and 5 variables:

x1: Predictor 1. Numeric.
x2: Predictor 2. Numeric.
m11: Mediator 1 in Path 1. Numeric.
m12: Mediator 2 in Path 1. Numeric.
m2: Mediator in Path 2. Numeric.
y1: Outcome variable 1. Numeric.
y2: Outcome variable 2. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.
group: Group variable. Character. 'Group A' or 'Group B'

Examples

library(lavaan)
data(data_med_complicated_mg)
dat <- data_med_complicated_mg
mod <-
"
m11 ~ x1 + x2 + c1 + c2
m12 ~ m11 + c1 + c2
m2 ~ x1 + x2 + c1 + c2
y1 ~ m11 + m12 + x1 + x2 + c1 + c2
y2 ~ m2 + x1 + x2 + c1 + c2
"
fit <- sem(mod, dat, group = "group")
summary(fit)

Sample Dataset: Simple Mediation With Two Groups

Description

A simple mediation model with two groups.

Usage

data_med_mg

Format

A data frame with 100 rows and 5 variables:

x: Predictor. Numeric.
m: Mediator. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.
group: Group variable. Character. "Group A" or "Group B"

Examples

library(lavaan)
data(data_med_mg)
mod <-
"
m ~ c(a1, a2) * x + c1 + c2
y ~ c(b1, b2) * m + x + c1 + c2
a1b1 := a1 * b1
a2b2 := a2 * b2
abdiff := a2b2 - a1b1
"
fit <- sem(mod, data_med_mg, fixed.x = FALSE,
           group = "group")
parameterEstimates(fit)

Sample Dataset: Simple Mediation with a-Path Moderated

Description

A simple mediation model with a-path moderated.

Usage

data_med_mod_a

Format

A data frame with 100 rows and 6 variables:

x: Predictor. Numeric.
w: Moderator. Numeric.
m: Mediator. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_med_mod_a)
data_med_mod_a$xw <-
 data_med_mod_a$x *
 data_med_mod_a$w
mod <-
"
m ~ a * x + w + d * xw + c1 + c2
y ~ b * m + x + w + c1 + c2
w ~~ v_w * w
w ~ m_w * 1
ab := a * b
ab_lo := (a + d * (m_w - sqrt(v_w))) * b
ab_hi := (a + d * (m_w + sqrt(v_w))) * b
"
fit <- sem(mod, data_med_mod_a,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 11, 12, 31:33), ]

Sample Dataset: Simple Mediation with Both Paths Moderated (Two Moderators)

Description

A simple mediation model with a-path and b-path each moderated by a moderator.

Usage

data_med_mod_ab

Format

A data frame with 100 rows and 7 variables:

x: Predictor. Numeric.
w1: Moderator 1. Numeric.
w2: Moderator 2. Numeric.
m: Mediator. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_med_mod_ab)
data_med_mod_ab$xw1 <-
 data_med_mod_ab$x *
 data_med_mod_ab$w1
data_med_mod_ab$mw2 <-
 data_med_mod_ab$m *
 data_med_mod_ab$w2
mod <-
"
m ~ a * x + w1 + d1 * xw1 + c1 + c2
y ~ b * m + x + w1 + w2 + d2 * mw2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
ab := a * b
ab_lolo := (a + d1 * (m_w1 - sqrt(v_w1))) * (b + d2 * (m_w2 - sqrt(v_w2)))
ab_lohi := (a + d1 * (m_w1 - sqrt(v_w1))) * (b + d2 * (m_w2 + sqrt(v_w2)))
ab_hilo := (a + d1 * (m_w1 + sqrt(v_w1))) * (b + d2 * (m_w2 - sqrt(v_w2)))
ab_hihi := (a + d1 * (m_w1 + sqrt(v_w1))) * (b + d2 * (m_w2 + sqrt(v_w2)))
"
fit <- sem(mod, data_med_mod_ab,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 10, 41:45), ]

Sample Dataset: Simple Mediation with Both Paths Moderated By a Moderator

Description

A simple mediation model with a-path and b-path moderated by one moderator.

Usage

data_med_mod_ab1

Format

A data frame with 100 rows and 6 variables:

x: Predictor. Numeric.
w: Moderator. Numeric.
m: Mediator. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_med_mod_ab1)
data_med_mod_ab1$xw <-
 data_med_mod_ab1$x *
 data_med_mod_ab1$w
data_med_mod_ab1$mw <-
 data_med_mod_ab1$m *
 data_med_mod_ab1$w
mod <-
"
m ~ a * x + w + da * xw + c1 + c2
y ~ b * m + x + w + db * mw + c1 + c2
w ~~ v_w * w
w ~ m_w * 1
ab := a * b
ab_lo := (a + da * (m_w - sqrt(v_w))) * (b + db * (m_w - sqrt(v_w)))
ab_hi := (a + da * (m_w + sqrt(v_w))) * (b + db * (m_w + sqrt(v_w)))
"
fit <- sem(mod, data_med_mod_ab1,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 9, 38:40), ]

Sample Dataset: Simple Mediation with b-Path Moderated

Description

A simple mediation model with b-path moderated.

Usage

data_med_mod_b

Format

A data frame with 100 rows and 6 variables:

x: Predictor. Numeric.
w: Moderator. Numeric.
m: Mediator. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_med_mod_b)
data_med_mod_b$mw <-
 data_med_mod_b$m *
 data_med_mod_b$w
mod <-
"
m ~ a * x + w + c1 + c2
y ~ b * m + x + d * mw + c1 + c2
w ~~ v_w * w
w ~ m_w * 1
ab := a * b
ab_lo := a * (b + d * (m_w - sqrt(v_w)))
ab_hi := a * (b + d * (m_w + sqrt(v_w)))
"
fit <- sem(mod, data_med_mod_b,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 5, 7, 10, 11, 30:32), ]

Sample Dataset: A Simple Mediation Model with b-Path Moderated-Moderation

Description

A simple mediation model with moderated-mediation on the b-path.

Usage

data_med_mod_b_mod

Format

A data frame with 100 rows and 5 variables:

x: Predictor. Numeric.
w1: Moderator on b-path. Numeric.
w2: Moderator on the moderating effect of w1. Numeric.
m: Mediator. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

data(data_med_mod_b_mod)
dat <- data_med_mod_b_mod
summary(lm_m <- lm(m ~ x + c1 + c2, dat))
summary(lm_y <- lm(y ~ m*w1*w2 + x + c1 + c2, dat))

Sample Dataset: Parallel Mediation with Two Moderators

Description

A parallel mediation model with a1-path and b2-path moderated.

Usage

data_med_mod_parallel

Format

A data frame with 100 rows and 8 variables:

x: Predictor. Numeric.
w1: Moderator 1. Numeric.
w2: Moderator 2. Numeric.
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_med_mod_parallel)
data_med_mod_parallel$xw1 <-
 data_med_mod_parallel$x *
 data_med_mod_parallel$w1
data_med_mod_parallel$m2w2 <-
 data_med_mod_parallel$m2 *
 data_med_mod_parallel$w2
mod <-
"
m1 ~ a1 * x + w1 + da1 * xw1 + c1 + c2
m2 ~ a2 * x + w1 + c1 + c2
y ~ b1 * m1 + b2 * m2 + x + w1 + w2 + db2 * m2w2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
a1b1 := a1 * b1
a2b2 := a2 * b2
a1b1_w1lo := (a1 + da1 * (m_w1 - sqrt(v_w1))) * b1
a1b1_w1hi := (a1 + da1 * (m_w1 + sqrt(v_w1))) * b2
a2b2_w2lo := a2 * (b2 + db2 * (m_w2 - sqrt(v_w2)))
a2b2_w2hi := a2 * (b2 + db2 * (m_w2 + sqrt(v_w2)))
"
fit <- sem(mod, data_med_mod_parallel,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 10, 11, 15, 48:53), ]

Sample Dataset: Parallel Moderated Mediation with Two Categorical Moderators

Description

A parallel mediation model with two categorical moderators.

Usage

data_med_mod_parallel_cat

Format

A data frame with 300 rows and 8 variables:

x: Predictor. Numeric.
w1: Moderator. String. Values: "group1", "group2", "group3"
w2: Moderator. String. Values: "team1", "team2"
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

data(data_med_mod_parallel_cat)
dat <- data_med_mod_parallel_cat
summary(lm_m1 <- lm(m1 ~ x*w1 + c1 + c2, dat))
summary(lm_m2 <- lm(m2 ~ x*w1 + c1 + c2, dat))
summary(lm_y <- lm(y ~ m1*w2 + m2*w2 + m1 + x + w1 + c1 + c2, dat))

Sample Dataset: Serial Mediation with Two Moderators

Description

A simple mediation model with a-path and b2-path moderated.

Usage

data_med_mod_serial

Format

A data frame with 100 rows and 8 variables:

x: Predictor. Numeric.
w1: Moderator 1. Numeric.
w2: Moderator 2. Numeric.
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_med_mod_serial)
data_med_mod_serial$xw1 <-
 data_med_mod_serial$x *
 data_med_mod_serial$w1
data_med_mod_serial$m2w2 <-
 data_med_mod_serial$m2 *
 data_med_mod_serial$w2
mod <-
"
m1 ~ a * x + w1 + da1 * xw1 + c1 + c2
m2 ~ b1 * m1 + x + w1 + c1 + c2
y ~ b2 * m2 + m1 + x + w1 + w2 + db2 * m2w2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
ab1b2 := a * b1 * b2
ab1b2_lolo := (a + da1 * (m_w1 - sqrt(v_w1))) * b1 * (b2 + db2 * (m_w2 - sqrt(v_w2)))
ab1b2_lohi := (a + da1 * (m_w1 - sqrt(v_w1))) * b1 * (b2 + db2 * (m_w2 + sqrt(v_w2)))
ab1b2_hilo := (a + da1 * (m_w1 + sqrt(v_w1))) * b1 * (b2 + db2 * (m_w2 - sqrt(v_w2)))
ab1b2_hihi := (a + da1 * (m_w1 + sqrt(v_w1))) * b1 * (b2 + db2 * (m_w2 + sqrt(v_w2)))
"
fit <- sem(mod, data_med_mod_serial,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 11, 16, 49:53), ]

Sample Dataset: Serial Moderated Mediation with Two Categorical Moderators

Description

A serial mediation model with two categorical moderators.

Usage

data_med_mod_serial_cat

Format

A data frame with 300 rows and 8 variables:

x: Predictor. Numeric.
w1: Moderator. String. Values: "group1", "group2", "group3"
w2: Moderator. String. Values: "team1", "team2"
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

data(data_med_mod_serial_cat)
dat <- data_med_mod_serial_cat
summary(lm_m1 <- lm(m1 ~ x*w1 + c1 + c2, dat))
summary(lm_m2 <- lm(m2 ~ m1 + x + w1 + c1 + c2, dat))
summary(lm_y <- lm(y ~ m2*w2 + m1 + x + w1 + c1 + c2, dat))

Sample Dataset: Serial-Parallel Mediation with Two Moderators

Description

A serial-parallel mediation model with some paths moderated.

Usage

data_med_mod_serial_parallel

Format

A data frame with 100 rows and 9 variables:

x: Predictor. Numeric.
w1: Moderator 1. Numeric.
w2: Moderator 2. Numeric.
m11: Mediator 1 in Path 1. Numeric.
m12: Mediator 2 in Path 2. Numeric.
m2: Mediator 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_med_mod_serial_parallel)
data_med_mod_serial_parallel$xw1 <-
 data_med_mod_serial_parallel$x *
 data_med_mod_serial_parallel$w1
data_med_mod_serial_parallel$m2w2 <-
 data_med_mod_serial_parallel$m2 *
 data_med_mod_serial_parallel$w2
mod <-
"
m11 ~ a1 * x + w1 + da11 * xw1 + c1 + c2
m12 ~ b11 * m11 + x + w1 + c1 + c2
m2 ~ a2 * x + c1 + c2
y ~ b12 * m12 + b2 * m2 + m11 + x + w1 + w2 + db2 * m2w2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
a1b11b22 := a1 * b11 * b12
a2b2 := a2 * b2
ab := a1b11b22 + a2b2
a1b11b12_w1lo := (a1 + da11 * (m_w1 - sqrt(v_w1))) * b11 * b12
a1b11b12_w1hi := (a1 + da11 * (m_w1 + sqrt(v_w1))) * b11 * b12
a2b2_w2lo := a2 * (b2 + db2 * (m_w2 - sqrt(v_w2)))
a2b2_w2hi := a2 * (b2 + db2 * (m_w2 + sqrt(v_w2)))
"
fit <- sem(mod, data_med_mod_serial_parallel,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[parameterEstimates(fit)$label != "", ]

Sample Dataset: Serial-Parallel Moderated Mediation with Two Categorical Moderators

Description

A serial-parallel mediation model with two categorical moderators.

Usage

data_med_mod_serial_parallel_cat

Format

A data frame with 300 rows and 8 variables:

x: Predictor. Numeric.
w1: Moderator. String. Values: "group1", "group2", "group3"
w2: Moderator. String. Values: "team1", "team2"
m11: Mediator 1 in Path 1. Numeric.
m12: Mediator 2 in Path 1. Numeric.
m2: Mediator in Path 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

data(data_med_mod_serial_parallel_cat)
dat <- data_med_mod_serial_parallel_cat
summary(lm_m11 <- lm(m11 ~ x*w1 + c1 + c2, dat))
summary(lm_m12 <- lm(m12 ~ m11 + x + w1 + c1 + c2, dat))
summary(lm_m2 <- lm(m2 ~ x + w1 + c1 + c2, dat))
summary(lm_y <- lm(y ~ m12 + m2*w2 + m12 + x + c1 + c2, dat))

Sample Dataset: One Moderator

Description

A one-moderator model.

Usage

data_mod

Format

A data frame with 100 rows and 5 variables:

x: Predictor. Numeric.
w: Moderator. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_mod)
data_mod$xw <- data_mod$x * data_mod$w
mod <-
"
y ~ a * x + w + d * xw + c1 + c2
w ~~ v_w * w
w ~ m_w * 1
a_lo := a + d * (m_w - sqrt(v_w))
a_hi := a + d * (m_w + sqrt(v_w))
"
fit <- sem(mod, data_mod, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 7, 24, 25), ]

Sample Dataset: Two Moderators

Description

A two-moderator model.

Usage

data_mod2

Format

A data frame with 100 rows and 6 variables:

x: Predictor. Numeric.
w1: Moderator 1. Numeric.
w2: Moderator 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_mod2)
data_mod2$xw1 <- data_mod2$x * data_mod2$w1
data_mod2$xw2 <- data_mod2$x * data_mod2$w2
mod <-
"
y ~ a * x + w1 + w2 + d1 * xw1 + d2 * xw2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
a_lolo := a + d1 * (m_w1 - sqrt(v_w1)) + d2 * (m_w2 - sqrt(v_w2))
a_lohi := a + d1 * (m_w1 - sqrt(v_w1)) + d2 * (m_w2 + sqrt(v_w2))
a_hilo := a + d1 * (m_w1 + sqrt(v_w1)) + d2 * (m_w2 - sqrt(v_w2))
a_hihi := a + d1 * (m_w1 + sqrt(v_w1)) + d2 * (m_w2 + sqrt(v_w2))
"
fit <- sem(mod, data_mod2, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 4, 5, 8:11, 34:37), ]

Sample Dataset: Moderation with One Categorical Moderator

Description

A moderation model with a categorical moderator.

Usage

data_mod_cat

Format

A data frame with 300 rows and 5 variables:

x: Predictor. Numeric.
w: Moderator. String. Values: "group1", "group2", "group3"
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

data(data_mod_cat)
dat <- data_mod_cat
summary(lm_y <- lm(y ~ x*w + c1 + c2, dat))

Sample Dataset: A Complicated Moderated-Mediation Model

Description

Generated from a complicated moderated-mediation model for demonstration.

Usage

data_mome_demo

Format

A data frame with 200 rows and 11 variables:

x1: Predictor 1. Numeric.
x2: Predictor 2. Numeric.
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
m3: Mediator 3. Numeric.
y1: Outcome Variable 1. Numeric.
y2: Outcome Variable 2. Numeric.
w1: Moderator 1. Numeric.
w2: Moderator 21. Numeric.
c1: Control Variable 1. Numeric.
c2: Control Variable 2. Numeric.

Details

The model:

# w1x1 <- x1 * w1
# w2m2 <- w2 * m2
m1 ~ x1 + w1 + w1x1 + x2 + c1 + c2
m2 ~ m1 + c1 + c2
m3 ~ x2 + x1 + c1 + c2
y1 ~ m2 + w2 + w2m2 + x1 + x2 + m3 + c1 + c2
y2 ~ m3 + x2 + x1 + m2 + c1 + c2
# Covariances excluded for brevity

Sample Dataset: A Complicated Moderated-Mediation Model With Missing Data

Description

Generated from a complicated moderated-mediation model for demonstration, with missing data

Usage

data_mome_demo_missing

Format

A data frame with 200 rows and 11 variables:

x1: Predictor 1. Numeric.
x2: Predictor 2. Numeric.
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
m3: Mediator 3. Numeric.
y1: Outcome Variable 1. Numeric.
y2: Outcome Variable 2. Numeric.
w1: Moderator 1. Numeric.
w2: Moderator 21. Numeric.
c1: Control Variable 1. Numeric.
c2: Control Variable 2. Numeric.

Details

A copy of data_mome_demo with some randomly selected cells changed to NA. The number of cases with no missing data is 169.

The model:

# w1x1 <- x1 * w1
# w2m2 <- w2 * m2
m1 ~ x1 + w1 + w1x1 + x2 + c1 + c2
m2 ~ m1 + c1 + c2
m3 ~ x2 + x1 + c1 + c2
y1 ~ m2 + w2 + w2m2 + x1 + x2 + m3 + c1 + c2
y2 ~ m3 + x2 + x1 + m2 + c1 + c2
# Covariances excluded for brevity

Sample Dataset: Parallel Mediation

Description

A parallel mediation model.

Usage

data_parallel

Format

A data frame with 100 rows and 6 variables:

x: Predictor. Numeric.
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_parallel)
mod <-
"
m1 ~ a1 * x + c1 + c2
m2 ~ a2 * x + c1 + c2
y ~ b2 * m2 + b1 * m1 + x + c1 + c2
indirect1 := a1 * b1
indirect2 := a2 * b2
indirect := a1 * b1 + a2 * b2
"
fit <- sem(mod, data_parallel,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 4, 7, 8, 27:29), ]

Sample Dataset: A Latent Variable Mediation Model With 4 Factors

Description

This data set is for testing functions in a four-factor structural model.

Usage

data_sem

Format

A data frame with 200 rows and 14 variables:

x01: Indicator. Numeric.
x02: Indicator. Numeric.
x03: Indicator. Numeric.
x04: Indicator. Numeric.
x05: Indicator. Numeric.
x06: Indicator. Numeric.
x07: Indicator. Numeric.
x08: Indicator. Numeric.
x09: Indicator. Numeric.
x10: Indicator. Numeric.
x11: Indicator. Numeric.
x12: Indicator. Numeric.
x13: Indicator. Numeric.
x14: Indicator. Numeric.

Examples

data(data_sem)
dat <- data_med_mod_b_mod
mod <-
  'f1 =~ x01 + x02 + x03
   f2 =~ x04 + x05 + x06 + x07
   f3 =~ x08 + x09 + x10
   f4 =~ x11 + x12 + x13 + x14
   f3 ~  a1*f1 + a2*f2
   f4 ~  b1*f1 + b3*f3
   a1b3 := a1 * b3
   a2b3 := a2 * b3
  '
fit <- lavaan::sem(model = mod, data = data_sem)
summary(fit)

Sample Dataset: Serial Mediation

Description

A serial mediation model.

Usage

data_serial

Format

A data frame with 100 rows and 6 variables:

x: Predictor. Numeric.
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_serial)
mod <-
"
m1 ~ a * x + c1 + c2
m2 ~ b1 * m1 + x + c1 + c2
y ~ b2 * m2 + m1 + x + c1 + c2
indirect := a * b1 * b2
"
fit <- sem(mod, data_serial,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 4, 8, 28), ]

Sample Dataset: Serial-Parallel Mediation

Description

A mediation model with both serial and parallel components.

Usage

data_serial_parallel

Format

A data frame with 100 rows and 7 variables:

x: Predictor. Numeric.
m11: Mediator 1 in Path 1. Numeric.
m12: Mediator 2 in Path 1. Numeric.
m2: Mediator in Path 2. Numeric.
y: Outcome variable. Numeric.
c1: Control variable. Numeric.
c2: Control variable. Numeric.

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ a11 * x + c1 + c2
m12 ~ b11 * m11 + x + c1 + c2
m2 ~ a2 * x + c1 + c2
y ~ b12 * m12 + b2 * m2 + m11 + x + c1 + c2
indirect1 := a11 * b11 * b12
indirect2 := a2 * b2
indirect := a11 * b11 * b12 + a2 * b2
"
fit <- sem(mod, data_serial_parallel,
           meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 4, 8, 11, 12, 34:36), ]

Sample Dataset: A Latent Mediation Model With Three Mediators

Description

Generated from a 3-mediator mediation model among eight latent factors, fx1, fx2, fm11, fm12, fy1, and fy2, each has three indicators.

Usage

data_serial_parallel_latent

Format

A data frame with 500 rows and 21 variables:

x1: Indicator of fx1. Numeric.
x2: Indicator of fx1. Numeric.
x3: Indicator of fx1. Numeric.
x4: Indicator of fx2. Numeric.
x5: Indicator of fx2. Numeric.
x6: Indicator of fx2. Numeric.
m11a: Indicator of fm11. Numeric.
m11b: Indicator of fm11. Numeric.
m11c: Indicator of fm11. Numeric.
m12a: Indicator of fm12. Numeric.
m12b: Indicator of fm12. Numeric.
m12c: Indicator of fm12. Numeric.
m2a: Indicator of fm2. Numeric.
m2b: Indicator of fm2. Numeric.
m2c: Indicator of fm2. Numeric.
y1: Indicator of fy1. Numeric.
y2: Indicator of fy1. Numeric.
y3: Indicator of fy1. Numeric.
y4: Indicator of fy2. Numeric.
y5: Indicator of fy2. Numeric.
y6: Indicator of fy2. Numeric.

Details

The model:

fx1 =~ x1 + x2 + x3
fx2 =~ x4 + x5 + x6
fm11 =~ m11a + m11b + m11c
fm12 =~ m12a + m12b + m12c
fm2  =~ m2a + m2b + m2c
fy1 =~ y1 + y2 + y3
fy2 =~ y3 + y4 + y5
fm11 ~ a1 * fx1
fm12 ~ b11 * fm11 + a2m * fx2
fm2 ~ a2 * fx2
fy1 ~ b12 * fm12 + b11y1 * fm11 + cp1 * fx1
fy2 ~ b2 * fm2 + cp2 * fx2
a1b11b12 := a1 * b11 * b12
a1b11y1 := a1 * b11y1
a2b2 := a2 * b2
a2mb12 := a2m * b12

Delta_Med by Liu, Yuan, and Li (2023)

Description

It computes the Delta_Med proposed by Liu, Yuan, and Li (2023), an R^2-like measure of indirect effect.

Usage

delta_med(
  x,
  y,
  m,
  fit,
  paths_to_remove = NULL,
  boot_out = NULL,
  level = 0.95,
  progress = TRUE,
  skip_check_single_x = FALSE,
  skip_check_m_between_x_y = FALSE,
  skip_check_x_to_y = FALSE,
  skip_check_latent_variables = FALSE,
  boot_type = c("perc", "bc")
)

Arguments

x

The name of the x variable. Must be supplied as a quoted string.

y

The name of the y variable. Must be supplied as a quoted string.

m

A vector of the variable names of the mediator(s). If more than one mediators, they do not have to be on the same path from x to y. Cannot be NULL for this function.

fit

The fit object. Must be a lavaan::lavaan object.

paths_to_remove

A character vector of paths users want to manually remove, specified in lavaan model syntax. For example, c("m2~x", "m3~m2") removes the path from x to m2 and the path from m2 to m3. The default is NULL, and the paths to remove will be determined using the method by Liu et al. (2023). If supplied, then only paths specified explicitly will be removed.

boot_out

The output of do_boot(). If supplied, the stored bootstrap estimates will be used to form the nonparametric percentile bootstrap confidence interval of Delta_Med.

level

The level of confidence of the bootstrap confidence interval. Default is .95.

progress

Logical. Display bootstrapping progress or not. Default is TRUE.

skip_check_single_x

Logical Check whether the model has one and only one x-variable. Default is TRUE.

skip_check_m_between_x_y

Logical. Check whether all m variables are along a path from x to y. Default is TRUE.

skip_check_x_to_y

Logical. Check whether there is a direct path from x to y. Default is TRUE.

skip_check_latent_variables

Logical. Check whether the model has any latent variables. Default is TRUE.

boot_type

Details

It computes Delta_Med, an R^2-like effect size measure for the indirect effect from one variable (the y-variable) to another variable (the x-variable) through one or more mediators (m, or m1, m2, etc. when there are more than one mediator).

The Delta_Med of one or more mediators was computed as the difference between two R^2s:

R^2_1, the R^2 when y is predicted by x and all mediators.
R^2_2, the R^2 when the mediator(s) of interest is/are removed from the models, while the error term(s) of the mediator(s) is/are kept.

Delta_Med is given by R^2_1 - R^2_2.

Please refer to Liu et al. (2023) for the technical details.

The function can also form a nonparametric percentile bootstrap confidence of Delta_Med.

Value

A delta_med class object. It is a list-like object with these major elements:

delta_med: The Delta_Med.
x: The name of the x-variable.
y: The name of the y-variable.
m: A character vector of the mediator(s) along a path. The path runs from the first element to the last element.

This class has a print method, a coef method, and a confint method. See print.delta_med(), coef.delta_med(), and confint.delta_med().

Implementation

The function identifies all the path(s) pointing to the mediator(s) of concern and fixes the path(s) to zero, effectively removing the mediator(s). However, the model is not refitted, hence keeping the estimates of all other parameters unchanged. It then uses lavaan::lav_model_set_parameters() to update the parameters, lavaan::lav_model_implied() to update the implied statistics, and then calls lavaan::lavInspect() to retrieve the implied variance of the predicted values of y for computing the R^2_2. Subtracting this R^2_2 from R^2_1 of y can then yield Delta_Med.

Model Requirements

For now, by default, it only computes Delta_Med for the types of models discussed in Liu et al. (2023):

Having one predictor (the x-variable).
Having one or more mediators, the m-variables, with arbitrary way to mediate the effect of x on the outcome variable (y-variable).
Having one or more outcome variables. Although their models only have outcome variables, the computation of the Delta_Med is not affected by the presence of other outcome variables.
Having no control variables.
The mediator(s), m, and the y-variable are continuous.
x can be continuous or categorical. If categorical, it needs to be handle appropriately when fitting the model.
x has a direct path to y.
All the mediators listed in the argument m is present in at least one path from x to y.
None of the paths from x to y are moderated.

It can be used for other kinds of models but support for them is disabled by default. To use this function for cases not discussed in Liu et al. (2023), please disable relevant requirements stated above using the relevant ⁠skip_check_*⁠ arguments. An error will be raised if the models failed any of the checks not skipped by users.

References

Examples


library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)
dm <- delta_med(x = "x",
                y = "y",
                m = "m",
                fit = fit)
dm
print(dm, full = TRUE)

# Call do_boot() to generate
# bootstrap estimates
# Use 2000 or even 5000 for R in real studies
# Set parallel to TRUE in real studies for faster bootstrapping
boot_out <- do_boot(fit,
                    R = 45,
                    seed = 879,
                    parallel = FALSE,
                    progress = FALSE)
# Remove 'progress = FALSE' in practice
dm_boot <- delta_med(x = "x",
                     y = "y",
                     m = "m",
                     fit = fit,
                     boot_out = boot_out,
                     progress = FALSE)
dm_boot
confint(dm_boot)

Bootstrap Estimates for 'indirect_effects' and 'cond_indirect_effects'

Description

Generate bootstrap estimates to be used by cond_indirect_effects(), indirect_effect(), and cond_indirect(),

Usage

do_boot(
  fit,
  R = 100,
  seed = NULL,
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  make_cluster_args = list(),
  progress = TRUE,
  compute_implied_stats = TRUE
)

Arguments

fit

It can be (a) a list of lm class objects, or the output of lm2list() (i.e., an lm_list-class object), or (b) the output of lavaan::sem(). If it is a single model fitted by lm(), it will be automatically converted to a list by lm2list().

R

The number of bootstrap samples. Default is 100.

seed

The seed for the bootstrapping. Default is NULL and seed is not set.

parallel

Logical. Whether parallel processing will be used. Default is TRUE.

ncores

make_cluster_args

A named list of additional arguments to be passed to parallel::makeCluster(). For advanced users. See parallel::makeCluster() for details. Default is list(), no additional arguments.

progress

Logical. Display progress or not. Default is TRUE.

compute_implied_stats

If TRUE, default, implied statistics will be computed for each bootstrap sample. Letting users to disable this is an experimental features to let the process run faster.

Details

It does nonparametric bootstrapping to generate bootstrap estimates of the parameter estimates in a model fitted either by lavaan::sem() or by a sequence of calls to lm(). The stored estimates can then be used by cond_indirect_effects(), indirect_effect(), and cond_indirect() to form bootstrapping confidence intervals.

This approach removes the need to repeat bootstrapping in each call to cond_indirect_effects(), indirect_effect(), and cond_indirect(). It also ensures that the same set of bootstrap samples is used in all subsequent analysis.

It determines the type of the fit object automatically and then calls lm2boot_out(), fit2boot_out(), or fit2boot_out_do_boot().

Multigroup Models

Since Version 0.1.14.2, support for multigroup models has been added for models fitted by lavaan. The implementation of bootstrapping is identical to that used by lavaan, with resampling done within each group.

Value

A boot_out-class object that can be used for the boot_out argument of cond_indirect_effects(), indirect_effect(), and cond_indirect() for forming bootstrap confidence intervals. The object is a list with the number of elements equal to the number of bootstrap samples. Each element is a list of the parameter estimates and sample variances and covariances of the variables in each bootstrap sample.

Examples

data(data_med_mod_ab1)
dat <- data_med_mod_ab1
lm_m <- lm(m ~ x*w + c1 + c2, dat)
lm_y <- lm(y ~ m*w + x + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
# In real research, R should be 2000 or even 5000
# In real research, no need to set parallel and progress to FALSE
# Parallel processing is enabled by default and
# progress is displayed by default.
lm_boot_out <- do_boot(lm_out, R = 50, seed = 1234,
                       parallel = FALSE,
                       progress = FALSE)
wlevels <- mod_levels(w = "w", fit = lm_out)
wlevels
out <- cond_indirect_effects(wlevels = wlevels,
                             x = "x",
                             y = "y",
                             m = "m",
                             fit = lm_out,
                             boot_ci = TRUE,
                             boot_out = lm_boot_out)
out

Monte Carlo Estimates for 'indirect_effects' and 'cond_indirect_effects'

Description

Generate Monte Carlo estimates to be used by cond_indirect_effects(), indirect_effect(), and cond_indirect(),

Usage

do_mc(
  fit,
  R = 100,
  seed = NULL,
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  make_cluster_args = list(),
  progress = TRUE,
  compute_implied_stats = TRUE
)

gen_mc_est(fit, R = 100, seed = NULL)

Arguments

fit

The output of lavaan::sem(). It can also be a lavaan.mi object returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi(). The output of stats::lm() is not supported.

R

The number of replications. Default is 100.

seed

The seed for the generating Monte Carlo estimates. Default is NULL and seed is not set.

parallel

Not used. Kept for compatibility with do_boot().

ncores

Not used. Kept for compatibility with do_boot().

make_cluster_args

Not used. Kept for compatibility with do_boot().

progress

Logical. Display progress or not. Default is TRUE.

compute_implied_stats

If TRUE, default, implied statistics will be computed for each replication. Letting users to disable this is an experimental features to let the process run faster.

Details

It uses the parameter estimates and their variance-covariance matrix to generate Monte Carlo estimates of the parameter estimates in a model fitted by lavaan::sem(). The stored estimates can then be used by cond_indirect_effects(), indirect_effect(), and cond_indirect() to form Monte Carlo confidence intervals.

It also supports a model estimated by multiple imputation using lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi(). The pooled estimates and their variance-covariance matrix will be used to generate the Monte Carlo estimates.

This approach removes the need to repeat Monte Carlo simulation in each call to cond_indirect_effects(), indirect_effect(), and cond_indirect(). It also ensures that the same set of Monte Carlo estimates is used in all subsequent analysis.

Multigroup Models

Since Version 0.1.14.2, support for multigroup models has been added for models fitted by lavaan.

Value

A mc_out-class object that can be used for the mc_out argument of cond_indirect_effects(), indirect_effect(), and cond_indirect() for forming Monte Carlo confidence intervals. The object is a list with the number of elements equal to the number of Monte Carlo replications. Each element is a list of the parameter estimates and sample variances and covariances of the variables in each Monte Carlo replication.

Functions

do_mc(): A general purpose function for creating Monte Carlo estimates to be reused by other functions. It returns a mc_out-class object.
gen_mc_est(): Generate Monte Carlo estimates and store them in the external slot: external$manymome$mc. For advanced users.

Examples


library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"
fit <- sem(mod, dat)
# In real research, R should be 5000 or even 10000
mc_out <- do_mc(fit, R = 100, seed = 1234)
wlevels <- mod_levels(w = "w", fit = fit)
wlevels
out <- cond_indirect_effects(wlevels = wlevels,
                             x = "x",
                             y = "y",
                             m = "m",
                             fit = fit,
                             mc_ci = TRUE,
                             mc_out = mc_out)
out

Create Dummy Variables

Description

Create dummy variables from a categorical variable.

Usage

factor2var(
  x_value,
  x_contrasts = "contr.treatment",
  prefix = "",
  add_rownames = TRUE
)

Arguments

x_value

The vector of categorical variable.

x_contrasts

The contrast to be used. Default is "constr.treatment".

prefix

The prefix to be added to the variables to be created. Default is "".

add_rownames

Whether row names will be added to the output. Default is TRUE.

Details

Its main use is for creating dummy variables (indicator variables) from a categorical variable, to be used in lavaan::sem().

Optionally, the other contrasts can be used through the argument x_contrasts.

Value

It always returns a matrix with the number of rows equal to the length of the vector (x_value). If the categorical has only two categories and so only one dummy variable is needed, the output is still a one-column "matrix" in R.

Examples

dat <- data_mod_cat
dat <- data.frame(dat,
                  factor2var(dat$w, prefix = "gp", add_rownames = FALSE))
head(dat[, c("w", "gpgroup2", "gpgroup3")], 15)

Bootstrap Estimates for a `lavaan` Output

Description

Generate bootstrap estimates from the output of lavaan::sem().

Usage

fit2boot_out(fit, compute_implied_stats = TRUE)

fit2boot_out_do_boot(
  fit,
  R = 100,
  seed = NULL,
  parallel = FALSE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  make_cluster_args = list(),
  progress = TRUE,
  compute_implied_stats = TRUE,
  compute_rsquare = FALSE,
  internal = list()
)

Arguments

fit

The fit object. This function only supports a lavaan::lavaan object.

compute_implied_stats

If TRUE, default, implied statistics will be computed for each bootstrap sample. Letting users to disable this is an experimental features to let the process run faster.

R

The number of bootstrap samples. Default is 100.

seed

The seed for the random resampling. Default is NULL.

parallel

Logical. Whether parallel processing will be used. Default is NULL.

ncores

make_cluster_args

A named list of additional arguments to be passed to parallel::makeCluster(). For advanced users. See parallel::makeCluster() for details. Default is list().

progress

Logical. Display progress or not. Default is TRUE.

compute_rsquare

If TRUE, R-squares will be computed for each bootstrap sample (given by lavaan::parameterEstimates()). Default is FALSE because it is rarely necessary, and enabling it slows down the computation.

internal

A list of arguments to be used internally for debugging. Default is list().

Details

This function is for advanced users. do_boot() is a function users should try first because do_boot() has a general interface for input-specific functions like this one.

If bootstrapping confidence intervals was requested when calling lavaan::sem() by setting se = "boot", fit2boot_out() can be used to extract the stored bootstrap estimates so that they can be reused by indirect_effect(), cond_indirect_effects() and related functions to form bootstrapping confidence intervals for effects such as indirect effects and conditional indirect effects.

If bootstrapping confidence was not requested when fitting the model by lavaan::sem(), fit2boot_out_do_boot() can be used to generate nonparametric bootstrap estimates from the output of lavaan::sem() and store them for use by indirect_effect(), cond_indirect_effects(), and related functions.

This approach removes the need to repeat bootstrapping in each call to indirect_effect(), cond_indirect_effects(), and related functions. It also ensures that the same set of bootstrap samples is used in all subsequent analyses.

Value

A boot_out-class object that can be used for the boot_out argument of indirect_effect(), cond_indirect_effects(), and related functions for forming bootstrapping confidence intervals.

The object is a list with the number of elements equal to the number of bootstrap samples. Each element is a list of the parameter estimates and sample variances and covariances of the variables in each bootstrap sample.

Functions

fit2boot_out(): Process stored bootstrap estimates for functions such as cond_indirect_effects().
fit2boot_out_do_boot(): Do bootstrapping and store information to be used by cond_indirect_effects() and related functions. Support parallel processing.

Examples


library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
dat$"x:w" <- dat$x * dat$w
dat$"m:w" <- dat$m * dat$w
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"

# Bootstrapping not requested in calling lavaan::sem()
fit <- sem(model = mod, data = dat, fixed.x = FALSE,
           se = "none", baseline = FALSE)
fit_boot_out <- fit2boot_out_do_boot(fit = fit,
                                     R = 40,
                                     seed = 1234,
                                     progress = FALSE)
out <- cond_indirect_effects(wlevels = "w",
                             x = "x",
                             y = "y",
                             m = "m",
                             fit = fit,
                             boot_ci = TRUE,
                             boot_out = fit_boot_out)
out

Monte Carlo Estimates for a `lavaan` Output

Description

Generate Monte Carlo estimates from the output of lavaan::sem().

Usage

fit2mc_out(fit, progress = TRUE, compute_implied_stats = TRUE)

Arguments

fit

The fit object. This function only supports a lavaan::lavaan object. It can also be a lavaan.mi object returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi().

progress

Logical. Display progress or not. Default is TRUE.

compute_implied_stats

If TRUE, default, implied statistics will be computed for each replication. Letting users to disable this is an experimental features to let the process run faster.

Details

This function is for advanced users. do_mc() is a function users should try first because do_mc() has a general interface for input-specific functions like this one.

fit2mc_out() can be used to extract the stored Monte Carlo estimates so that they can be reused by indirect_effect(), cond_indirect_effects() and related functions to form Monte Carlo confidence intervals for effects such as indirect effects and conditional indirect effects.

This approach removes the need to repeat Monte Carlo simulation in each call to indirect_effect(), cond_indirect_effects(), and related functions. It also ensures that the same set of Monte Carlo estimates is used in all subsequent analyses.

Value

A mc_out-class object that can be used for the mc_out argument of indirect_effect(), cond_indirect_effects(), and related functions for forming Monte Carlo confidence intervals.

The object is a list with the number of elements equal to the number of Monte Carlo replications. Each element is a list of the parameter estimates and sample variances and covariances of the variables in each Monte Carlo replication.

Examples


library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
dat$"x:w" <- dat$x * dat$w
dat$"m:w" <- dat$m * dat$w
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"

fit <- sem(model = mod, data = dat, fixed.x = FALSE,
           baseline = FALSE)
# In real research, R should be 5000 or even 10000.
fit <- gen_mc_est(fit, R = 100, seed = 453253)
fit_mc_out <- fit2mc_out(fit)
out <- cond_indirect_effects(wlevels = "w",
                             x = "x",
                             y = "y",
                             m = "m",
                             fit = fit,
                             mc_ci = TRUE,
                             mc_out = fit_mc_out)
out

Get The Conditional Indirect Effect for One Row of 'cond_indirect_effects' Output

Description

Return the conditional indirect effect of one row of the output of cond_indirect_effects().

Usage

get_one_cond_indirect_effect(object, row)

get_one_cond_effect(object, row)

print_all_cond_indirect_effects(object, ...)

print_all_cond_effects(object, ...)

Arguments

object

The output of cond_indirect_effects().

row

The row number of the row to be retrieved.

...

Optional arguments to be passed to teh print method of the output of indirect_effect() and cond_indirect()

Details

get_one_cond_indirect_effect() extracts the corresponding output of cond_indirect() from the requested row.

get_one_cond_effect() is an alias of get_one_cond_indirect_effect().

print_all_cond_indirect_effects() loops over the conditional effects and print all of them.

print_all_cond_effects() is an alias of print_all_cond_indirect_effects().

Value

get_one_cond_indirect_effect() returns an indirect-class object, similar to the output of indirect_effect() and cond_indirect(). See indirect_effect() and cond_indirect() for details on these classes.

print_all_cond_indirect_effects() returns the object invisibly. Called for its side effect.

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x  + w1 + x:w1
m2 ~ m1
y  ~ m2 + x + w4 + m2:w4
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Examples for cond_indirect():

# Conditional effects from x to m1
# when w1 is equal to each of the default levels
out1 <- cond_indirect_effects(x = "x", y = "m1",
                              wlevels = c("w1", "w4"), fit = fit)
get_one_cond_indirect_effect(out1, 3)

# Conditional Indirect effect from x1 through m1 to y,
# when w1 is equal to each of the levels
out2 <- cond_indirect_effects(x = "x", y = "y", m = c("m1", "m2"),
                              wlevels = c("w1", "w4"), fit = fit)
get_one_cond_indirect_effect(out2, 4)


print_all_cond_indirect_effects(out2, digits = 2)

Product Terms (if Any) Along a Path

Description

Identify the product term(s), if any, along a path in a model and return the term(s), with the variables involved and the coefficient(s) of the term(s).

Usage

get_prod(
  x,
  y,
  operator = ":",
  fit = NULL,
  est = NULL,
  data = NULL,
  expand = FALSE
)

Arguments

x

Character. Variable name.

y

Character. Variable name.

operator

Character. The string used to indicate a product term. Default is ":", used in both lm() and lavaan::sem() for observed variables.

fit

The fit object. Currently only supports a lavaan::lavaan object. It can also be a lavaan.mi object returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi().

est

The output of lavaan::parameterEstimates(). If NULL, the default, it will be generated from fit. If supplied, fit will ge ignored.

data

Data frame (optional). If supplied, it will be used to identify the product terms.

expand

Whether products of more than two terms will be searched. FALSE by default.

Details

This function is used by several functions in manymome to identify product terms along a path. If possible, this is done by numerically checking whether a column in a dataset is the product of two other columns. If not possible (e.g., the "product term" is the "product" of two latent variables, formed by the products of indicators), then it requires the user to specify an operator.

The detailed workflow of this function can be found in the article https://sfcheung.github.io/manymome/articles/get_prod.html

This function is not intended to be used by users. It is exported such that advanced users or developers can use it.

Value

If at least one product term is found, it returns a list with these elements:

prod: The names of the product terms found.
b: The coefficients of these product terms.
w: The variable, other than x, in each product term.
x: The x-variable, that is, where the path starts.
y: The y-variable, that is, where the path ends.

It returns NA if no product term is found along the path.

Examples


dat <- modmed_x1m3w4y1
library(lavaan)
mod <-
"
m1 ~ x   + w1 + x:w1
m2 ~ m1  + w2 + m1:w2
m3 ~ m2
y  ~ m3  + w4 + m3:w4 + x + w3 + x:w3 + x:w4
"
fit <- sem(model = mod,
           data = dat,
           meanstructure = TRUE,
           fixed.x = FALSE)

# One product term
get_prod(x = "x", y = "m1", fit = fit)
# Two product terms
get_prod(x = "x", y = "y", fit = fit)
# No product term
get_prod(x = "m2", y = "m3", fit = fit)

Index of Moderated Mediation and Index of Moderated Moderated Mediation

Description

It computes the index of moderated mediation and the index of moderated moderated mediation proposed by Hayes (2015, 2018).

Usage

index_of_mome(
  x,
  y,
  m = NULL,
  w = NULL,
  fit = NULL,
  boot_ci = FALSE,
  level = 0.95,
  boot_out = NULL,
  R = 100,
  seed = NULL,
  progress = TRUE,
  mc_ci = FALSE,
  mc_out = NULL,
  ci_type = NULL,
  ci_out = NULL,
  boot_type = c("perc", "bc"),
  ...
)

index_of_momome(
  x,
  y,
  m = NULL,
  w = NULL,
  z = NULL,
  fit = NULL,
  boot_ci = FALSE,
  level = 0.95,
  boot_out = NULL,
  R = 100,
  seed = NULL,
  progress = TRUE,
  mc_ci = FALSE,
  mc_out = NULL,
  ci_type = NULL,
  ci_out = NULL,
  boot_type = c("perc", "bc"),
  ...
)

Arguments

x

Character. The name of the predictor at the start of the path.

y

Character. The name of the outcome variable at the end of the path.

m

A vector of the variable names of the mediator(s). The path goes from the first mediator successively to the last mediator. If NULL, the default, the path goes from x to y.

w

Character. The name of the moderator.

fit

The fit object. Can be a lavaan::lavaan-class object, a list of lm() outputs, or an object created by lm2list(). It can also be a lavaan.mi object returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi().

boot_ci

Logical. Whether bootstrap confidence interval will be formed. Default is FALSE.

level

The level of confidence for the bootstrap confidence interval. Default is .95.

boot_out

R

Integer. If boot_ci is TRUE, boot_out is NULL, and bootstrap standard errors not requested if fit is a lavaan-class object, this function will do bootstrapping on fit. R is the number of bootstrap samples. Default is 100. For Monte Carlo simulation, this is the number of replications.

seed

If bootstrapping or Monte Carlo simulation is conducted, this is the seed for the bootstrapping or simulation. Default is NULL and seed is not set.

progress

Logical. Display bootstrapping progress or not. Default is TRUE.

mc_ci

Logical. Whether Monte Carlo confidence interval will be formed. Default is FALSE.

mc_out

ci_type

ci_out

If ci_type is supplied, this is the corresponding argument. If ci_type is "boot", this argument will be used as boot_out. If ci_type is "mc", this argument will be used as mc_out.

boot_type

...

Arguments to be passed to cond_indirect_effects()

z

Character. The name of the second moderator, for computing the index of moderated moderated mediation.

Details

The function index_of_mome() computes the index of moderated mediation proposed by Hayes (2015). It supports any path in a model with one (and only one) component path moderated. For example, x->m1->m2->y with x->m1 moderated by w. It measures the change in indirect effect when the moderator increases by one unit.

The function index_of_momome() computes the index of moderated moderated mediation proposed by Hayes (2018). It supports any path in a model, with two component paths moderated, each by one moderator. For example, x->m1->m2->y with x->m1 moderated by w and m2->y moderated by z. It measures the change in the index of moderated mediation of one moderator when the other moderator increases by one unit.

Value

It returns a cond_indirect_diff-class object. This class has a print method (print.cond_indirect_diff()), a coef method for extracting the index (coef.cond_indirect_diff()), and a confint method for extracting the confidence interval if available (confint.cond_indirect_diff()).

Functions

index_of_mome(): Compute the index of moderated mediation.
index_of_momome(): Compute the index of moderated moderated mediation.

References

Hayes, A. F. (2015). An index and test of linear moderated mediation. Multivariate Behavioral Research, 50(1), 1-22. doi:10.1080/00273171.2014.962683

Hayes, A. F. (2018). Partial, conditional, and moderated moderated mediation: Quantification, inference, and interpretation. Communication Monographs, 85(1), 4-40. doi:10.1080/03637751.2017.1352100

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
dat$xw1 <- dat$x * dat$w1
mod <-
"
m1 ~ a * x  + f * w1 + d * xw1
y  ~ b * m1 + cp * x
ind_mome := d * b
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# R should be at least 2000 or even 5000 in real research.
# parallel is set to TRUE by default.
# Therefore, in research, the argument parallel can be omitted.
out_mome <- index_of_mome(x = "x", y = "y", m = "m1", w = "w1",
                          fit = fit,
                          boot_ci = TRUE,
                          R = 42,
                          seed = 4314,
                          parallel = FALSE,
                          progress = FALSE)
out_mome
coef(out_mome)
# From lavaan
print(est[19, ], nd = 8)
confint(out_mome)



library(lavaan)
dat <- modmed_x1m3w4y1
dat$xw1 <- dat$x * dat$w1
dat$m1w4 <- dat$m1 * dat$w4
mod <-
"
m1 ~ a * x  + f1 * w1 + d1 * xw1
y  ~ b * m1 + f4 * w4 + d4 * m1w4 + cp * x
ind_momome := d1 * d4
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# See the example of index_of_mome on how to request
# bootstrap confidence interval.
out_momome <- index_of_momome(x = "x", y = "y", m = "m1",
                              w = "w1", z = "w4",
                              fit = fit)
out_momome
coef(out_momome)
print(est[32, ], nd = 8)

Coefficient Table of an 'indirect_list' Class Object

Description

Create a coefficient table for the point estimates and confidence intervals (if available) in the output of many_indirect_effects().

Usage

indirect_effects_from_list(object, add_sig = TRUE, pvalue = FALSE, se = FALSE)

Arguments

object

The output of many_indirect_effects() or other functions that return an object of the class indirect_list.

add_sig

Whether a column of significance test results will be added. Default is TRUE.

pvalue

Logical. If TRUE, asymmetric p-values based on bootstrapping will be added available. Default is FALSE.

se

Logical. If TRUE and confidence intervals are available, the standard errors of the estimates are also added. They are simply the standard deviations of the bootstrap estimates or Monte Carlo simulated values, depending on the method used to form the confidence intervals.

Details

If bootstrapping confidence interval was requested, this method has the option to add p-values computed by the method presented in Asparouhov and Muthén (2021). Note that these p-values is asymmetric bootstrap p-values based on the distribution of the bootstrap estimates. They are not computed based on the distribution under the null hypothesis.

For a p-value of a, it means that a 100(1 - a)% bootstrapping confidence interval will have one of its limits equal to 0. A confidence interval with a higher confidence level will include zero, while a confidence interval with a lower confidence level will exclude zero.

Value

A data frame with the indirect effect estimates and confidence intervals (if available). It also has A string column, "Sig", for #' significant test results if add_sig is TRUE and confidence intervals are available.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

Examples


library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
           fixed.x = FALSE)

# All indirect paths from x to y
paths <- all_indirect_paths(fit,
                           x = "x",
                           y = "y")
paths

# Indirect effect estimates
out <- many_indirect_effects(paths,
                             fit = fit)
out

# Create a data frame of the indirect effect estimates

out_df <- indirect_effects_from_list(out)
out_df

Indirect Effect (No Bootstrapping)

Description

It computes an indirect effect, optionally conditional on the value(s) of moderator(s) if present.

Usage

indirect_i(
  x,
  y,
  m = NULL,
  fit = NULL,
  est = NULL,
  implied_stats = NULL,
  wvalues = NULL,
  standardized_x = FALSE,
  standardized_y = FALSE,
  computation_digits = 5,
  prods = NULL,
  get_prods_only = FALSE,
  data = NULL,
  expand = TRUE,
  warn = TRUE,
  allow_mixing_lav_and_obs = TRUE,
  group = NULL,
  est_vcov = NULL,
  df_residual = NULL
)

Arguments

x

Character. The name of the predictor at the start of the path.

y

Character. The name of the outcome variable at the end of the path.

m

A vector of the variable names of the mediator(s). The path goes from the first mediator successively to the last mediator. If NULL, the default, the path goes from x to y.

fit

The fit object. Currently only supports lavaan::lavaan objects. Support for lists of lm() output is implemented by high level functions such as indirect_effect() and cond_indirect_effects(). It can also be a lavaan.mi object returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi().

est

The output of lavaan::parameterEstimates(). If NULL, the default, it will be generated from fit. If supplied, fit will be ignored.

implied_stats

Implied means, variances, and covariances of observed variables and latent variables (if any), of the form of the output of lavaan::lavInspect() with what set to "implied", but with means extracted with what set to "mean.ov" and "mean.lv". The standard deviations are extracted from this object for standardization. Default is NULL, and implied statistics will be computed from fit if required.

wvalues

A numeric vector of named elements. The names are the variable names of the moderators, and the values are the values to which the moderators will be set to. Default is NULL.

standardized_x

Logical. Whether x will be standardized. Default is FALSE.

standardized_y

Logical. Whether y will be standardized. Default is FALSE.

computation_digits

The number of digits in storing the computation in text. Default is 3.

prods

The product terms found. For internal use.

get_prods_only

IF TRUE, will quit early and return the product terms found. The results can be passed to the prod argument when calling this function. Default is FALSE. For internal use.

data

Data frame (optional). If supplied, it will be used to identify the product terms. For internal use.

expand

Whether products of more than two terms will be searched. TRUE by default. For internal use.

warn

If TRUE, the default, the function will warn against possible misspecification, such as not setting the value of a moderator which moderate one of the component path. Set this to FALSE will suppress these warnings. Suppress them only when the moderators are omitted intentionally.

allow_mixing_lav_and_obs

If TRUE, it accepts a path with both latent variables and observed variables. Default is TRUE.

group

Either the group number as appeared in the summary() or lavaan::parameterEstimates() output of an lavaan-class object, or the group label as used in the lavaan-class object. Used only when the number of groups is greater than one. Default is NULL.

est_vcov

A list of variance-covariance matrix of estimates, one for each response variable (y-variable). Used only for models fitted by stats::lm() for now. It is used to compute the standard error for a path with no mediator, and both x and y are not standardized.

df_residual

A numeric vector of the residual degrees of freedom for the model of each response variable (y-variable). Used only for models fitted by stats::lm() for now. It is used to compute the p-value and confidence interval for a path with no mediator and both x and y are not standardized.

Details

This function is a low-level function called by indirect_effect(), cond_indirect_effects(), and cond_indirect(), which call this function multiple times if bootstrap confidence interval is requested.

This function usually should not be used directly. It is exported for advanced users and developers

Value

It returns an indirect-class object. This class has the following methods: coef.indirect(), print.indirect(). The confint.indirect() method is used only when called by cond_indirect() or cond_indirect_effects().

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x   + b1 * w1 + d1 * x:w1
m2 ~ a2 * m1  + b2 * w2 + d2 * m1:w2
m3 ~ a3 * m2  + b3 * w3 + d3 * m2:w3
y  ~ a4 * m3  + b4 * w4 + d4 * m3:w4
"
fit <- sem(mod, dat, meanstructure = TRUE,
           fixed.x = FALSE, se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

wvalues <- c(w1 = 5, w2 = 4, w3 = 2, w4 = 3)

# Compute the conditional indirect effect by indirect_i()
indirect_1 <- indirect_i(x = "x", y = "y", m = c("m1", "m2", "m3"), fit = fit,
                       wvalues = wvalues)

# Manually compute the conditional indirect effect
indirect_2 <- (est[est$label == "a1", "est"] +
                wvalues["w1"] * est[est$label == "d1", "est"]) *
              (est[est$label == "a2", "est"] +
                wvalues["w2"] * est[est$label == "d2", "est"]) *
              (est[est$label == "a3", "est"] +
                wvalues["w3"] * est[est$label == "d3", "est"]) *
              (est[est$label == "a4", "est"] +
                wvalues["w4"] * est[est$label == "d4", "est"])
# They should be the same
coef(indirect_1)
indirect_2

Proportion of Effect Mediated

Description

It computes the proportion of effect mediated along a pathway.

Usage

indirect_proportion(x, y, m = NULL, fit = NULL)

Arguments

x

The name of the x variable. Must be supplied as a quoted string.

y

The name of the y variable. Must be supplied as a quoted string.

m

A vector of the variable names of the mediator(s). The path goes from the first mediator successively to the last mediator. Cannot be NULL for this function.

fit

The fit object. Can be a lavaan::lavaan object or a list of lm() outputs. It can also be a lavaan.mi object returned by lavaan.mi::lavaan.mi() or its wrapper, such as lavaan.mi::sem.mi().

Details

The proportion of effect mediated along a path from x to y is the indirect effect along this path divided by the total effect from x to y (Alwin & Hauser, 1975). This total effect is equal to the sum of all indirect effects from x to y and the direct effect from x to y.

To ensure that the proportion can indeed be interpreted as a proportion, this function computes the the proportion only if the signs of all the indirect and direct effects from x to y are same (i.e., all effects positive or all effects negative).

Value

An indirect_proportion class object. It is a list-like object with these major elements:

proportion: The proportion of effect mediated.
x: The name of the x-variable.
y: The name of the y-variable.
m: A character vector of the mediator(s) along a path. The path runs from the first element to the last element.

This class has a print method and a coef method.

References

Alwin, D. F., & Hauser, R. M. (1975). The decomposition of effects in path analysis. American Sociological Review, 40(1), 37. doi:10.2307/2094445

Examples


library(lavaan)
dat <- data_med
head(dat)
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, fixed.x = FALSE)
out <- indirect_proportion(x = "x",
                           y = "y",
                           m = "m",
                           fit = fit)
out

Bootstrap Estimates for `lm` Outputs

Description

Generate bootstrap estimates for models in a list of 'lm' outputs.

Usage

lm2boot_out(
  outputs,
  R = 100,
  seed = NULL,
  progress = TRUE,
  compute_implied_stats = TRUE
)

lm2boot_out_parallel(
  outputs,
  R = 100,
  seed = NULL,
  parallel = FALSE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  make_cluster_args = list(),
  progress = TRUE,
  compute_implied_stats = TRUE
)

Arguments

outputs

A list of lm class objects, or the output of lm2list() (i.e., an lm_list-class object).

R

The number of bootstrap samples. Default is 100.

seed

The seed for the random resampling. Default is NULL.

progress

Logical. Display progress or not. Default is TRUE.

compute_implied_stats

If TRUE, default, implied statistics will be computed for each bootstrap sample. Letting users to disable this is an experimental features to let the process run faster.

parallel

Logical. Whether parallel processing will be used. Default is NULL.

ncores

make_cluster_args

A named list of additional arguments to be passed to parallel::makeCluster(). For advanced users. See parallel::makeCluster() for details. Default is list().

Details

This function is for advanced users. do_boot() is a function users should try first because do_boot() has a general interface for input-specific functions like this one.

It does nonparametric bootstrapping to generate bootstrap estimates of the regression coefficients in the regression models of a list of lm() outputs, or an lm_list-class object created by lm2list(). The stored estimates can be used by indirect_effect(), cond_indirect_effects(), and related functions in forming bootstrapping confidence intervals for effects such as indirect effect and conditional indirect effects.

Value

A boot_out-class object that can be used for the boot_out argument of indirect_effect(), cond_indirect_effects(), and related functions for forming bootstrapping confidence intervals. The object is a list with the number of elements equal to the number of bootstrap samples. Each element is a list of the parameter estimates and sample variances and covariances of the variables in each bootstrap sample.

Functions

lm2boot_out(): Generate bootstrap estimates using one process (serial, without parallelization).
lm2boot_out_parallel(): Generate bootstrap estimates using parallel processing.

Examples


data(data_med_mod_ab1)
dat <- data_med_mod_ab1
lm_m <- lm(m ~ x*w + c1 + c2, dat)
lm_y <- lm(y ~ m*w + x + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
# In real research, R should be 2000 or even 5000
# In real research, no need to set progress to FALSE
# Progress is displayed by default.
lm_boot_out <- lm2boot_out(lm_out, R = 100, seed = 1234,
                           progress = FALSE)
out <- cond_indirect_effects(wlevels = "w",
                             x = "x",
                             y = "y",
                             m = "m",
                             fit = lm_out,
                             boot_ci = TRUE,
                             boot_out = lm_boot_out)
out

Join 'lm()' Output to Form an 'lm_list'-Class Object

Description

The resulting model can be used by indirect_effect(), cond_indirect_effects(), or cond_indirect() as a path method, as if fitted by lavaan::sem().

Usage

lm2list(...)

Arguments

...

The lm() outputs to be grouped in a list.

Details

If a path model with mediation and/or moderation is fitted by a set of regression models using lm(), this function can combine them to an object of the class lm_list that represents a path model, as one fitted by structural equation model functions such as lavaan::sem(). This class of object can be used by some functions, such as indirect_effect(), cond_indirect_effects(), and cond_indirect() as if they were the output of fitting a path model, with the regression coefficients treated as path coefficients.

The regression outputs to be combined need to meet the following requirements:

All models must be connected to at least one another model. That is, a regression model must either have (a) at least on predictor that is the outcome variable of another model, or (b) its outcome variable the predictor of another model.
All models must be fitted to the same sample. This implies that the sample size must be the same in all analysis.

Value

It returns an lm_list-class object that forms a path model represented by a set of regression models. This class has a summary method that shows the summary of each regression model stored (see summary.lm_list()), and a print method that prints the models stored (see print.lm_list()).

Examples




data(data_serial_parallel)
lm_m11 <- lm(m11 ~ x + c1 + c2, data_serial_parallel)
lm_m12 <- lm(m12 ~ m11 + x + c1 + c2, data_serial_parallel)
lm_m2 <- lm(m2 ~ x + c1 + c2, data_serial_parallel)
lm_y <- lm(y ~ m11 + m12 + m2 + x + c1 + c2, data_serial_parallel)
# Join them to form a lm_list-class object
lm_serial_parallel <- lm2list(lm_m11, lm_m12, lm_m2, lm_y)
lm_serial_parallel
summary(lm_serial_parallel)

# Compute indirect effect from x to y through m11 and m12
outm11m12 <- cond_indirect(x = "x", y = "y",
                           m = c("m11", "m12"),
                           fit = lm_serial_parallel)
outm11m12
# Compute indirect effect from x to y
# through m11 and m12 with bootstrapping CI
# R should be at least 2000 or even 5000 in read study.
# In real research, parallel and progress can be omitted.
# They are est to TRUE by default.
outm11m12 <- cond_indirect(x = "x", y = "y",
                           m = c("m11", "m12"),
                           fit = lm_serial_parallel,
                           boot_ci = TRUE,
                           R = 100,
                           seed = 1234,
                           parallel = FALSE,
                           progress = FALSE)
outm11m12

'lavaan'-class to 'lm_from_lavaan_list'-Class

Description

Converts the regression models in a lavaan-class model to an lm_from_lavaan_list-class object.

Usage

lm_from_lavaan_list(fit)

Arguments

fit

A lavaan-class object, usually the output of lavaan::lavaan() or its wrappers.

Details

It identifies all dependent variables in a lavaan model and creates an lm_from_lavaan-class object for each of them.

This is an advanced helper used by plot.cond_indirect_effects(). Exported for advanced users and developers.

Value

An lm_from_lavaan_list-class object, which is a list of lm_from_lavaan objects. It has a predict-method (predict.lm_from_lavaan_list()) for computing the predicted values from one variable to another.

Examples

library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
tmp <- data.frame(x = 1, c1 = 2, c2 = 3, m = 4)
predict(fit_list, x = "x", y = "y", m = "m", newdata = tmp)

Math Operators for 'indirect'-Class Objects

Description

Mathematic operators for 'indirect'-class object, the output of indirect_effect() and cond_indirect().

Usage

## S3 method for class 'indirect'
e1 + e2

## S3 method for class 'indirect'
e1 - e2

Arguments

e1

An 'indirect'-class object.

e2

An 'indirect'-class object.

Details

For now, only + operator and - operator are supported. These operators can be used to estimate and test a function of effects between the same pair of variables.

For example, they can be used to compute and test the total effects along different paths. They can also be used to compute and test the difference between the effects along two paths.

The operators will check whether an operation is valid. An operation is not valid if

the two paths do not start from the same variable,
the two paths do not end at the same variable,
moderators are involved but they are not set to the same values in both objects, and
bootstrap estimates stored in boot_out, if any, are not identical.
Monte Carlo simulated estimates stored in mc_out, if any, are not identical.

If bootstrap estimates are stored and both objects used the same type of bootstrap confidence interval, that type will be used. Otherwise, percentile bootstrap confidence interval, the recommended method, will be used.

Multigroup Models

Since Version 0.1.14.2, support for multigroup models has been added for models fitted by lavaan. Both bootstrapping and Monte Carlo confidence intervals are supported. These operators can be used to compute and test the difference of an indirect effect between two groups. This can also be used to compute and test the difference between a function of effects between groups, for example, the total indirect effects between two groups.

The operators are flexible and allow users to do many possible computations. Therefore, users need to make sure that the function of effects is meaningful.

Value

An 'indirect'-class object with a list of effects stored. See indirect_effect() on details for this class.

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x  + d1 * w1 + e1 * x:w1
m2 ~ m1 + a2 * x
y  ~ b1 * m1 + b2 * m2 + cp * x
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)
hi_w1 <- mean(dat$w1) + sd(dat$w1)

# Examples for cond_indirect():

# Conditional effect from x to m1 when w1 is 1 SD above mean
out1 <- cond_indirect(x = "x", y = "y", m = c("m1", "m2"),
              wvalues = c(w1 = hi_w1), fit = fit)
out2 <- cond_indirect(x = "x", y = "y", m = c("m2"),
              wvalues = c(w1 = hi_w1), fit = fit)
out3 <- cond_indirect(x = "x", y = "y",
              wvalues = c(w1 = hi_w1), fit = fit)

out12 <- out1 + out2
out12
out123 <- out1 + out2 + out3
out123
coef(out1) + coef(out2) + coef(out3)

# Multigroup model with indirect effects

dat <- data_med_mg
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE,
           group = "group")

# If a model has more than one group,
# the argument 'group' must be set.
ind1 <- indirect_effect(x = "x",
                        y = "y",
                        m = "m",
                        fit = fit,
                        group = "Group A")
ind1
ind2 <- indirect_effect(x = "x",
                        y = "y",
                        m = "m",
                        fit = fit,
                        group = 2)
ind2

# Compute the difference in indirect effects between groups
ind2 - ind1

Merge the Generated Levels of Moderators

Description

Merge the levels of moderators generated by mod_levels() into a data frame.

Usage

merge_mod_levels(...)

Arguments

...

The output from mod_levels(), or a list of levels generated by mod_levels_list().

Details

It merges the levels of moderators generated by mod_levels() into a data frame, with each row represents a combination of the levels. The output is to be used by cond_indirect_effects().

Users usually do not need to use this function because cond_indirect_effects() will merge the levels internally if necessary. This function is used when users need to customize the levels for each moderator and so cannot use mod_levels_list() or the default levels in cond_indirect_effects().

Value

A wlevels-class object, which is a data frame of the combinations of levels, with additional attributes about the levels.

Examples


data(data_med_mod_ab)
dat <- data_med_mod_ab
# Form the levels from a list of lm() outputs
lm_m <- lm(m ~ x*w1 + c1 + c2, dat)
lm_y <- lm(y ~ m*w2 + x + w1 + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
w1_levels <- mod_levels(lm_out, w = "w1")
w1_levels
w2_levels <- mod_levels(lm_out, w = "w2")
w2_levels
merge_mod_levels(w1_levels, w2_levels)

Create Levels of Moderators

Description

Create levels of moderators to be used by indirect_effect(), cond_indirect_effects(), and cond_indirect().

Usage

mod_levels(
  w,
  fit,
  w_type = c("auto", "numeric", "categorical"),
  w_method = c("sd", "percentile"),
  sd_from_mean = c(-1, 0, 1),
  percentiles = c(0.16, 0.5, 0.84),
  extract_gp_names = TRUE,
  prefix = NULL,
  values = NULL,
  reference_group_label = NULL,
  descending = TRUE
)

mod_levels_list(
  ...,
  fit,
  w_type = "auto",
  w_method = "sd",
  sd_from_mean = NULL,
  percentiles = NULL,
  extract_gp_names = TRUE,
  prefix = NULL,
  descending = TRUE,
  merge = FALSE
)

Arguments

w

Character. The names of the moderator. If the moderator is categorical with 3 or more groups, this is the vector of the indicator variables.

fit

w_type

Character. Whether the moderator is a "numeric" variable or a "categorical" variable. If "auto", the function will try to determine the type automatically.

w_method

Character, either "sd" or "percentile". If "sd", the levels are defined by the distance from the mean in terms of standard deviation. if "percentile", the levels are defined in percentiles.

sd_from_mean

A numeric vector. Specify the distance in standard deviation from the mean for each level. Default is c(-1, 0, 1) for mod_levels(). For mod_levels_list(), the default is c(-1, 0, 1) when there is only one moderator, and c(-1, 1) when there are more than one moderator. Ignored if w_method is not equal to "sd".

percentiles

A numeric vector. Specify the percentile (in proportion) for each level. Default is c(.16, .50, .84) for mod_levels(), corresponding approximately to one standard deviation below mean, mean, and one standard deviation above mean in a normal distribution. For mod_levels_list(), default is c(.16, .50, .84) if there is one moderator, and c(.16, .84) when there are more than one moderator. Ignored if w_method is not equal to "percentile".

extract_gp_names

Logical. If TRUE, the default, the function will try to determine the name of each group from the variable names.

prefix

Character. If extract_gp_names is TRUE and prefix is supplied, it will be removed from the variable names to create the group names. Default is NULL, and the function will try to determine the prefix automatically.

values

For numeric moderators, a numeric vector. These are the values to be used and will override other options. For categorical moderators, a named list of numeric vector, each vector has length equal to the number of indicator variables. If the vector is named, the names will be used to label the values. For example, if set to ⁠list(gp1 = c(0, 0), gp3 = c(0, 1)⁠, two levels will be returned, one named gp1 with the indicator variables equal to 0 and 0, the other named gp3 with the indicator variables equal to 0 and 1. Default is NULL.

reference_group_label

For categorical moderator, if the label for the reference group (group with all indicators equal to zero) cannot be determined, the default label is "Reference". To change it, set reference_group_label to the desired label. Ignored if values is set.

descending

If TRUE (default), the rows are sorted in descending order for numerical moderators: The highest value on the first row and the lowest values on the last row. For user supplied values, the first value is on the last row and the last value is on the first row. If FALSE, the rows are sorted in ascending order.

...

The names of moderators variables. For a categorical variable, it should be a vector of variable names.

merge

If TRUE, mod_levels_list() will call merge_mod_levels() and return the merged levels. Default is FALSE.

Details

It creates values of a moderator that can be used to compute conditional effect or conditional indirect effect. By default, for a numeric moderator, it uses one standard deviation below mean, mean, and one standard deviation above mean. The percentiles of these three levels in a normal distribution (16th, 50th, and 84th) can also be used. For categorical variable, it will simply collect the unique categories in the data.

The generated levels are then used by cond_indirect() and cond_indirect_effects().

If a model has more than one moderator, mod_levels_list() can be used to generate combinations of levels. The output can then passed to cond_indirect_effects() to compute the conditional effects or conditional indirect effects for all the combinations.

Value

mod_levels() returns a wlevels-class object which is a data frame with additional attributes about the levels.

mod_levels_list() returns a list of wlevels-class objects, or a wlevels-class object which is a data frame of the merged levels if merge = TRUE.

Functions

mod_levels(): Generate levels for one moderator.
mod_levels_list(): Generate levels for several moderators.

Examples


library(lavaan)
data(data_med_mod_ab)
dat <- data_med_mod_ab
# Form the levels from a list of lm() outputs
lm_m <- lm(m ~ x*w1 + c1 + c2, dat)
lm_y <- lm(y ~ m*w2 + x + w1 + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
w1_levels <- mod_levels(lm_out, w = "w1")
w1_levels
w2_levels <- mod_levels(lm_out, w = "w2")
w2_levels
# Indirect effect from x to y through m, at the first levels of w1 and w2
cond_indirect(x = "x", y = "y", m = "m",
              fit = lm_out,
              wvalues = c(w1 = w1_levels$w1[1],
                          w2 = w2_levels$w2[1]))
# Can form the levels based on percentiles
w1_levels2 <- mod_levels(lm_out, w = "w1", w_method = "percentile")
w1_levels2
# Form the levels from a lavaan output
# Compute the product terms before fitting the model
dat$mw2 <- dat$m * dat$w2
mod <-
"
m ~ x + w1 + x:w1 + c1 + c2
y ~ m + x + w1 + w2 + mw2 + c1 + c2
"
fit <- sem(mod, dat, fixed.x = FALSE)
cond_indirect(x = "x", y = "y", m = "m",
              fit = fit,
              wvalues = c(w1 = w1_levels$w1[1],
                          w2 = w2_levels$w2[1]))
# Can pass all levels to cond_indirect_effects()
# First merge the levels by merge_mod_levels()
w1w2_levels <- merge_mod_levels(w1_levels, w2_levels)
cond_indirect_effects(x = "x", y = "y", m = "m",
                      fit = fit,
                      wlevels = w1w2_levels)




# mod_levels_list() forms a combinations of levels in one call
# It returns a list, by default.
# Form the levels from a list of lm() outputs
# "merge = TRUE" is optional. cond_indirect_effects will merge the levels
# automatically.
w1w2_levels <- mod_levels_list("w1", "w2", fit = fit, merge = TRUE)
w1w2_levels
cond_indirect_effects(x = "x", y = "y", m = "m",
                      fit = fit, wlevels = w1w2_levels)
# Can work without merge = TRUE:
w1w2_levels <- mod_levels_list("w1", "w2", fit = fit)
w1w2_levels
cond_indirect_effects(x = "x", y = "y", m = "m",
                      fit = fit, wlevels = w1w2_levels)

Sample Dataset: Moderated Serial Mediation

Description

Generated from a serial mediation model with one predictor, three mediators, and one outcome variable, with one moderator in each stage.

Usage

modmed_x1m3w4y1

Format

A data frame with 200 rows and 11 variables:

x: Predictor. Numeric.
w1: Moderator 1. Numeric.
w2: Moderator 2. Numeric.
w3: Moderator 3. Numeric.
w4: Moderator 4. Numeric.
m1: Mediator 1. Numeric.
m2: Mediator 2. Numeric.
m3: Mediator 3. Numeric.
y: Outcome variable. Numeric.
gp: Three values: "earth", "mars", "venus". String.
city: Four values: "alpha", "beta", "gamma", "sigma". String.

Plot Conditional Effects

Description

Plot the conditional effects for different levels of moderators.

Usage

## S3 method for class 'cond_indirect_effects'
plot(
  x,
  x_label,
  w_label = "Moderator(s)",
  y_label,
  title,
  x_from_mean_in_sd = 1,
  x_method = c("sd", "percentile"),
  x_percentiles = c(0.16, 0.84),
  x_sd_to_percentiles = NA,
  note_standardized = TRUE,
  no_title = FALSE,
  line_width = 1,
  point_size = 5,
  graph_type = c("default", "tumble"),
  use_implied_stats = TRUE,
  facet_grid_cols = NULL,
  facet_grid_rows = NULL,
  facet_grid_args = list(as.table = FALSE, labeller = "label_both"),
  digits = 4,
  ...
)

Arguments

x

The output of cond_indirect_effects(). (Named x because it is required in the naming of arguments of the plot generic function.)

x_label

The label for the X-axis. Default is the value of the predictor in the output of cond_indirect_effects().

w_label

The label for the legend for the lines. Default is "Moderator(s)".

y_label

The label for the Y-axis. Default is the name of the response variable in the model.

title

The title of the graph. If not supplied, it will be generated from the variable names or labels (in x_label, y_label, and w_label). If "", no title will be printed. This can be used when the plot is for manuscript submission and figures are required to have no titles.

x_from_mean_in_sd

How many SD from mean is used to define "low" and "high" for the focal variable. Default is 1.

x_method

How to define "high" and "low" for the focal variable levels. Default is in terms of the standard deviation of the focal variable, "sd". If equal to "percentile", then the percentiles of the focal variable in the dataset is used. If the focal variable is a latent variable, only "sd" can be used.

x_percentiles

If x_method is "percentile", then this argument specifies the two percentiles to be used, divided by 100. It must be a vector of two numbers. The default is c(.16, .84), the 16th and 84th percentiles, which corresponds approximately to one SD below and above mean for a normal distribution, respectively.

x_sd_to_percentiles

If x_method is "percentile" and this argument is set to a number, this number will be used to determine the percentiles to be used. The lower percentile is the percentile in a normal distribution that is x_sd_to_percentiles SD below the mean. The upper percentile is the percentile in a normal distribution that is x_sd_to_percentiles SD above the mean. Therefore, if x_sd_to_percentiles is set to 1, then the lower and upper percentiles are 16th and 84th, respectively. Default is NA.

note_standardized

If TRUE, will check whether a variable has SD nearly equal to one. If yes, will report this in the plot. Default is TRUE.

no_title

If TRUE, title will be suppressed. Default is FALSE.

line_width

The width of the lines as used in ggplot2::geom_segment(). Default is 1.

point_size

The size of the points as used in ggplot2::geom_point(). Default is 5.

graph_type

If "default", the typical line-graph with equal end-points will be plotted. If "tumble", then the tumble graph proposed by Bodner (2016) will be plotted. Default is "default" for single-group models, and "tumble" for multigroup models.

use_implied_stats

For a multigroup model, if TRUE, the default, model implied statistics will be used in computing the means and SDs, which take into equality constraints, if any. If FALSE, then the raw data is used to compute the means and SDs. For latent variables, model implied statistics are always used.

facet_grid_cols, facet_grid_rows

If either or both of them are set to character vector(s) of moderator names, then ggplot2::facet_grid() will be used to plot the graph, with facet_grid_cols used as cols and facet_grid_rows used as rows when calling ggplot2::facet_grid().

facet_grid_args

The list of arguments to be used in calling ggplot2::facet_grid(). Ignored if ggplot2::facet_grid() is not used.

digits

The number of decimal places to be printed for numerical moderators when facet_grid is used. Default is 4.

...

Additional arguments. Ignored.

Details

This function is a plot method of the output of cond_indirect_effects(). It will use the levels of moderators in the output.

It plots the conditional effect from x to y in a model for different levels of the moderators. For multigroup models, the group will be the 'moderator' and one line is drawn for each group.

It does not support conditional indirect effects. If there is one or more mediators in x, it will raise an error.

Multigroup Models

Since Version 0.1.14.2, support for multigroup models has been added for models fitted by lavaan. If the effect for each group is drawn, the graph_type is automatically switched to "tumble" and the means and SDs in each group will be used to determine the locations of the points.

If the multigroup model has any equality constraints, the implied means and/or SDs may be different from those of the raw data. For example, the mean of the x-variable may be constrained to be equal in this model. To plot the tumble graph using the model implied means and SDs, set use_implied_stats to TRUE.

Latent Variables

A path that involves a latent x-variable and/or a latent y-variable can be plotted. Because the latent variables have no observed data, the model implied statistics will always be used to get the means and SDs to compute values such as the low and high points of the x-variable.

Value

A ggplot2 graph. Plotted if not assigned to a name. It can be further modified like a usual ggplot2 graph.

References

Bodner, T. E. (2016). Tumble graphs: Avoiding misleading end point extrapolation when graphing interactions from a moderated multiple regression analysis. Journal of Educational and Behavioral Statistics, 41(6), 593-604. doi:10.3102/1076998616657080

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
n <- nrow(dat)
set.seed(860314)
dat$gp <- sample(c("gp1", "gp2", "gp3"), n, replace = TRUE)
dat <- cbind(dat, factor2var(dat$gp, prefix = "gp", add_rownames = FALSE))

# Categorical moderator

mod <-
"
m3 ~ m1 + x + gpgp2 + gpgp3 + x:gpgp2 + x:gpgp3
y ~ m2 + m3 + x
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE)
out_mm_1 <- mod_levels(c("gpgp2", "gpgp3"),
                       sd_from_mean = c(-1, 1),
                       fit = fit)
out_1 <- cond_indirect_effects(wlevels = out_mm_1, x = "x", y = "m3", fit = fit)
plot(out_1)
plot(out_1, graph_type = "tumble")

# Numeric moderator

dat <- modmed_x1m3w4y1
mod2 <-
"
m3 ~ m1 + x + w1 + x:w1
y ~ m3 + x
"
fit2 <- sem(mod2, dat, meanstructure = TRUE, fixed.x = FALSE)
out_mm_2 <- mod_levels("w1",
                       w_method = "percentile",
                       percentiles = c(.16, .84),
                       fit = fit2)
out_mm_2
out_2 <- cond_indirect_effects(wlevels = out_mm_2, x = "x", y = "m3", fit = fit2)
plot(out_2)
plot(out_2, graph_type = "tumble")

# Multigroup models

dat <- data_med_mg
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE,
           group = "group")

# For a multigroup model, group will be used as
# a moderator
out <- cond_indirect_effects(x = "m",
                             y = "y",
                             fit = fit)
out
plot(out)

Plot an Effect Against a Moderator

Description

It plots an effect, direct or indirect, against a moderator, with confidence band if available.

Usage

plot_effect_vs_w(
  object,
  w = NULL,
  w_label = NULL,
  effect_label = NULL,
  add_zero_line = TRUE,
  always_draw_zero_line = FALSE,
  line_linewidth = 1,
  line_color = "blue",
  shade_the_band = TRUE,
  draw_the_intervals = TRUE,
  band_fill_color = "lightgrey",
  band_alpha = 0.5,
  intervals_color = "black",
  intervals_linetype = "longdash",
  intervals_linewidth = 1,
  zero_line_color = "grey",
  zero_line_linewidth = 1,
  zero_line_linetype = "solid",
  line_args = list(),
  band_args = list(),
  intervals_args = list(),
  zero_line_args = list(),
  level = 0.95
)

fill_wlevels(to_fill, cond_out = NULL, k = 21)

Arguments

object

The output of cond_indirect_effects().

w

The name of the moderator. Must be present in object. If NULL, the default, and object has only one moderator, then it will be set to that moderator. Because this function currently only supports a path with only one moderator, this argument can be left as NULL for now.

w_label

The label of the horizontal axis. If NULL, the default, it will be paste0("Moderator: ", w).

effect_label

The label of the vertical axis. If NULL, the default, it will be generated from the path.

add_zero_line

Whether a horizontal line at zero will be drawn. Default is TRUE.

always_draw_zero_line

If FALSE, the default, then the line at zero, if requested will be drawn only if zero is within the range of the plot. If TRUE, then the line at zero will always be drawn.

line_linewidth

The width of the line of the effect for each level of the moderator, to be used by ggplot2::geom_line(). Default is 1. Always overrides the value of line_args.

line_color

The color of the line of the effect for each level of the moderator, to be used by ggplot2::geom_line(). Default is "blue". Always overrides the value of line_args.

shade_the_band

If TRUE, the default, a confidence band will be drawn as a region along the line if confidence intervals can be retrieved from object.

draw_the_intervals

If TRUE, the default, two lines will be drawn for the confidence intervals along the line if they can be retrieved from object.

band_fill_color

The color of of the confidence band, to be used by ggplot2::geom_ribbon(). Default is "lightgrey". Always overrides the value of band_args.

band_alpha

A number from 0 to 1 for the level of transparency of the confidence band, to be used by ggplot2::geom_ribbon(). Default is .50. Always overrides the value of band_args.

intervals_color

The color of the lines of the confidence intervals, to be used by ggplot2::geom_line(). Default is "black". Always overrides the value of intervals_args.

intervals_linetype

The line type of the lines of the confidence intervals, to be used by ggplot2::geom_line(). Default is "longdash". Always overrides the value of intervals_args.

intervals_linewidth

The line width of the lines of the confidence intervals, to be used by ggplot2::geom_line(). Default is 1. Always overrides the value of intervals_args.

zero_line_color

The color of the line at zero, to be used by ggplot2::geom_line(). Default is "grey". Always overrides the value of zero_line_args.

zero_line_linewidth

The line width of the line at zero, to be used by ggplot2::geom_line(). Default is 1. Always overrides the value of zero_line_args.

zero_line_linetype

The line type of the line at zero, to be used by ggplot2::geom_line(). Default is "solid". Always overrides the value of zero_line_args.

line_args

A named list of additional arguments to be passed to ggplot2::geom_line() for the line of the effect against moderator. Default is list().

band_args

A named list of additional arguments to be passed to ggplot2::geom_ribbon() for the confidence band. Default is list().

intervals_args

A named list of additional arguments to be passed to ggplot2::geom_line() for the lines of confidence intervals. Default is list().

zero_line_args

A named list of additional arguments to be passed to ggplot2::geom_line() for the line at zero. Default is list().

level

The level of confidence for the confidence intervals computed from the original standard errors. Used only for paths without mediators and both x- and y-variables are not standardized.

to_fill

The output of cond_indirect_effects() or pseudo_johnson_neyman(), for which additional levels of the moderator will be added.

cond_out

If to_fill is the output of pseudo_johnson_neyman(), the original output of cond_indirect_effects() used in the call to pseudo_johnson_neyman() need to be supplied through this argument.

k

The desired number of levels of the moderator.

Details

It receives an output of cond_indirect_effects() and plot the effect against the moderator. The effect can be an indirect effect or a direct effect.

It uses the levels of the moderator stored in the output of cond_indirect_effects(). Therefore, the desired levels of the moderator to be plotted needs to be specified when calling cond_indirect_effects(), as illustrated in the example.

Currently, this function only supports a path with exactly one moderator, and the moderator is a numeric variable.

Using Original Standard Errors

If the following conditions are met, the stored standard errors, if available, will be used to form the confidence intervals:

Confidence intervals have not been formed (e.g., by bootstrapping or Monte Carlo).
The path has no mediators.
The model has only one group.
The path is moderated by one or more moderator.
Both the x-variable and the y-variable are not standardized.

If the model is fitted by structural equation modeling using lavaan, then the variance-covariance computed by lavaan will be used, and confidence intervals are computed from the z statistic.

Caution

The function fill_wlevels() is a helper to automatically fill in additional levels of the moderators, to plot a graph with smooth confidence band. It accepts the output of cond_indirect_effects() or pseudo_johnson_neyman(), finds the range of the values of the moderator, and returns an output of cond_indirect_effects() with the desired number of levels within this range. It is intended to be a helper. If it does not work, users can still get the desired number of levels by setting the values manually when calling cond_indirect_effects().

Value

plot_effect_vs_w() returns a ggplot2 graph. Plotted if not assigned to a name. It can be further modified like a usual ggplot2 graph.

fill_wlevels() returns an updated output of cond_indirect_effects() with the desired number of levels of the moderator.

Examples


dat <- data_med_mod_a
lm_m <- lm(m ~ x*w + c1 + c2, dat)
lm_y <- lm(y ~ m + x + c1 + c2, dat)
fit_lm <- lm2list(lm_m, lm_y)
# Set R to a large value in real research.
boot_out_lm <- do_boot(fit_lm,
                       R = 50,
                       seed = 54532,
                       parallel = FALSE,
                       progress = FALSE)

# Compute the conditional indirect effects
# from 2 SD below mean to 2 SD above mean of the moderator,
# by setting sd_from_mean of cond_indirect_effects().
# Set length.out to a larger number for a smooth graph.
out_lm <- cond_indirect_effects(wlevels = "w",
                                x = "x",
                                y = "y",
                                m = "m",
                                fit = fit_lm,
                                sd_from_mean = seq(-2, 2, length.out = 10),
                                boot_ci = TRUE,
                                boot_out = boot_out_lm)
p <- plot_effect_vs_w(out_lm)
p
# The output is a ggplot2 graph and so can be further customized
library(ggplot2)
# Add the line for the mean of w, the moderator
p2 <- p + geom_vline(xintercept = mean(dat$w),
                     color = "red")
p2


# Use fill_wlevels to add moderator levels:

dat <- data_med_mod_a
lm_m <- lm(m ~ x*w + c1 + c2, dat)
lm_y <- lm(y ~ m + x + c1 + c2, dat)
fit_lm <- lm2list(lm_m, lm_y)
wlevels <- mod_levels(w = "w",
                      sd_from_mean = c(-3, 0, 3),
                      fit = fit_lm)
wlevels
cond_out <- cond_indirect_effects(wlevels = wlevels,
                                  x = "x",
                                  y = "m",
                                  fit = fit_lm)
cond_out
# Only 3 points
p1 <- plot_effect_vs_w(cond_out)
p1
# Increase the number of levels to 15
cond_out_filled <- fill_wlevels(cond_out,
                                k = 15)
cond_out_filled
p2 <- plot_effect_vs_w(cond_out_filled)
p2

Predicted Values of a 'lm_from_lavaan'-Class Object

Description

Compute the predicted values based on the model stored in a 'lm_from_lavaan'-class object.

Usage

## S3 method for class 'lm_from_lavaan'
predict(object, newdata, ...)

Arguments

object

A 'lm_from_lavaan'-class object.

newdata

Required. A data frame of the new data. It must be a data frame.

...

Additional arguments. Ignored.

Details

An lm_from_lavaan-class method that converts a regression model for a variable in a lavaan model to a formula object. This function uses the stored model to compute predicted values using user-supplied data.

This is an advanced helper used by plot.cond_indirect_effects(). Exported for advanced users and developers.

Value

A numeric vector of the predicted values, with length equal to the number of rows of user-supplied data.

Examples

library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
tmp <- data.frame(x = 1, c1 = 2, c2 = 3, m = 4)
predict(fit_list$m, newdata = tmp)
predict(fit_list$y, newdata = tmp)

Predicted Values of an 'lm_from_lavaan_list'-Class Object

Description

It computes the predicted values based on the models stored in an 'lm_from_lavaan_list'-class object.

Usage

## S3 method for class 'lm_from_lavaan_list'
predict(object, x = NULL, y = NULL, m = NULL, newdata, ...)

Arguments

object

A 'lm_from_lavaan'-class object.

x

The variable name at the start of a path.

y

The variable name at the end of a path.

m

Optional. The mediator(s) from x to y. A numeric vector of the names of the mediators. The path goes from the first element to the last element. For example, if m = c("m1", "m2"), then the path is x -> m1 -> m2 -> y.

newdata

Required. A data frame of the new data. It must be a data frame.

...

Additional arguments. Ignored.

Details

An lm_from_lavaan_list-class object is a list of lm_from_lavaan-class objects.

This is an advanced helper used by plot.cond_indirect_effects(). Exported for advanced users and developers.

Value

A numeric vector of the predicted values, with length equal to the number of rows of user-supplied data.

Examples

library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
tmp <- data.frame(x = 1, c1 = 2, c2 = 3, m = 4)
predict(fit_list, x = "x", y = "y", m = "m", newdata = tmp)

Predicted Values of an 'lm_list'-Class Object

Description

Compute the predicted values based on the models stored in an 'lm_list'-class object.

Usage

## S3 method for class 'lm_list'
predict(object, x = NULL, y = NULL, m = NULL, newdata, ...)

Arguments

object

An 'lm_list'-class object.

x

The variable name at the start of a path.

y

The variable name at the end of a path.

m

newdata

Required. A data frame of the new data. It must be a data frame.

...

Additional arguments. Ignored.

Details

An lm_list-class object is a list of lm-class objects, this function is similar to the stats::predict() method of lm() but it works on a system defined by a list of regression models.

This is an advanced helper used by some functions in this package. Exported for advanced users.

Value

A numeric vector of the predicted values, with length equal to the number of rows of user-supplied data.

Examples

data(data_serial_parallel)
lm_m11 <- lm(m11 ~ x + c1 + c2, data_serial_parallel)
lm_m12 <- lm(m12 ~ m11 + x + c1 + c2, data_serial_parallel)
lm_m2 <- lm(m2 ~ x + c1 + c2, data_serial_parallel)
lm_y <- lm(y ~ m11 + m12 + m2 + x + c1 + c2, data_serial_parallel)
# Join them to form a lm_list-class object
lm_serial_parallel <- lm2list(lm_m11, lm_m12, lm_m2, lm_y)
lm_serial_parallel
summary(lm_serial_parallel)
newdat <- data_serial_parallel[3:5, ]
predict(lm_serial_parallel,
        x = "x",
        y = "y",
        m = "m2",
        newdata = newdat)

Print 'all_paths' Class Object

Description

Print the content of 'all_paths'-class object, which can be generated by all_indirect_paths().

Usage

## S3 method for class 'all_paths'
print(x, ...)

Arguments

x

A 'all_paths'-class object.

...

Optional arguments.

Details

This function is used to print the paths identified in a readable format.

Value

x is returned invisibly. Called for its side effect.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
           fixed.x = FALSE)
# All indirect paths
out1 <- all_indirect_paths(fit)
out1

Print a `boot_out`-Class Object

Description

Print the content of the output of do_boot() or related functions.

Usage

## S3 method for class 'boot_out'
print(x, ...)

Arguments

x

The output of do_boot(), or any boot_out-class object returned by similar functions.

...

Other arguments. Not used.

Value

x is returned invisibly. Called for its side effect.

Examples


data(data_med_mod_ab1)
dat <- data_med_mod_ab1
lm_m <- lm(m ~ x*w + c1 + c2, dat)
lm_y <- lm(y ~ m*w + x + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
# In real research, R should be 2000 or even 5000
# In real research, no need to set parallel to FALSE
# In real research, no need to set progress to FALSE
# Progress is displayed by default.
lm_boot_out <- do_boot(lm_out, R = 100,
                       seed = 1234,
                       progress = FALSE,
                       parallel = FALSE)
# Print the output of do_boot()
lm_boot_out

library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
dat$"x:w" <- dat$x * dat$w
dat$"m:w" <- dat$m * dat$w
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"
fit <- sem(model = mod, data = dat, fixed.x = FALSE,
           se = "none", baseline = FALSE)
# In real research, R should be 2000 or even 5000
# In real research, no need to set progress to FALSE
# In real research, no need to set parallel to FALSE
# Progress is displayed by default.
fit_boot_out <- do_boot(fit = fit,
                        R = 40,
                        seed = 1234,
                        parallel = FALSE,
                        progress = FALSE)
# Print the output of do_boot()
fit_boot_out

Print the Output of 'cond_indirect_diff'

Description

Print the output of cond_indirect_diff().

Usage

## S3 method for class 'cond_indirect_diff'
print(x, digits = 3, pvalue = FALSE, pvalue_digits = 3, se = FALSE, ...)

Arguments

x

The output of cond_indirect_diff().

digits

The number of decimal places in the printout.

pvalue

Logical. If TRUE, asymmetric p-value based on bootstrapping will be printed if available. Default is FALSE.

pvalue_digits

Number of decimal places to display for the p-value. Default is 3.

se

...

Optional arguments. Ignored.

Details

The print method of the cond_indirect_diff-class object.

If bootstrapping confidence interval was requested, this method has the option to print a p-value computed by the method presented in Asparouhov and Muthén (2021). Note that this p-value is asymmetric bootstrap p-value based on the distribution of the bootstrap estimates. It is not computed based on the distribution under the null hypothesis.

Value

It returns x invisibly. Called for its side effect.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

Print a 'cond_indirect_effects' Class Object

Description

Print the content of the output of cond_indirect_effects()

Usage

## S3 method for class 'cond_indirect_effects'
print(
  x,
  digits = 3,
  annotation = TRUE,
  pvalue = NULL,
  pvalue_digits = 3,
  se = NULL,
  level = 0.95,
  se_ci = TRUE,
  ...
)

## S3 method for class 'cond_indirect_effects'
as.data.frame(
  x,
  row.names = NULL,
  optional = NULL,
  digits = 3,
  add_sig = TRUE,
  pvalue = NULL,
  pvalue_digits = 3,
  se = NULL,
  level = 0.95,
  se_ci = TRUE,
  to_string = FALSE,
  ...
)

Arguments

x

The output of cond_indirect_effects().

digits

Number of digits to display. Default is 3.

annotation

Logical. Whether the annotation after the table of effects is to be printed. Default is TRUE.

pvalue

Logical. If TRUE, asymmetric p-values based on bootstrapping will be printed if available. Default to FALSE if confidence intervals have already computed. Default to TRUE if no confidence intervals have been computed and the original standard errors are to be used. See Details on when the original standard errors will be used by default.

pvalue_digits

Number of decimal places to display for the p-values. Default is 3.

se

Logical. If TRUE and confidence intervals are available, the standard errors of the estimates are also printed. They are simply the standard deviations of the bootstrap estimates or Monte Carlo simulated values, depending on the method used to form the confidence intervals. Default to FALSE if confidence intervals are available. Default to TRUE if no confidence intervals have been computed and the original standard errors are to be used. See Details on when the original standard errors will be used by default.

level

The level of confidence for the confidence intervals computed from the original standard errors. Used only for paths without mediators and both x- and y-variables are not standardized.

se_ci

Logical. If TRUE and confidence interval has not been computed, the function will try to compute them from stored standard errors if the original standard errors are to be used. Ignored if confidence intervals have already been computed. Default to TRUE.

...

Other arguments. Not used.

row.names

Not used. Included to be compatible with the generic method.

optional

Not used. Included to be compatible with the generic method.

add_sig

Whether a column of significance test results will be added. Default is TRUE.

to_string

If TRUE, numeric columns will be converted to string columns, formatted based on digits and pvalue_digits. For printing. Default is FALSE.

Details

The print method of the cond_indirect_effects-class object.

If bootstrapping confidence intervals were requested, this method has the option to print p-values computed by the method presented in Asparouhov and Muthén (2021). Note that these p-values are asymmetric bootstrap p-values based on the distribution of the bootstrap estimates. They not computed based on the distribution under the null hypothesis.

Using Original Standard Errors

If these conditions are met, the stored standard errors, if available, will be used test an effect and form it confidence interval:

Confidence intervals have not been formed (e.g., by bootstrapping or Monte Carlo).
The path has no mediators.
The model has only one group.
The path is moderated by one or more moderator.
Both the x-variable and the y-variable are not standardized.

If the model is fitted by OLS regression (e.g., using stats::lm()), then the variance-covariance matrix of the coefficient estimates will be used, and the p-value and confidence intervals are computed from the t statistic.

If the model is fitted by structural equation modeling using lavaan, then the variance-covariance computed by lavaan will be used, and the p-value and confidence intervals are computed from the z statistic.

Caution

The method as.data.frame() for cond_indirect_effects objects is used to convert this class of objects to data frames. Used internally by the print method but can also be used for getting a data frame with columns such as p-values and standard errors added.

Value

The print-method returns x invisibly. Called for its side effect.

The as.data.frame-method returns a data frame with the conditional effects and confidence intervals (if available), as well as other columns requested.

Functions

as.data.frame(cond_indirect_effects): The as.data.frame-method for cond_indirect_effects objects. Used internally by the print-method but can also be used directly.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x  + d1 * w1 + e1 * x:w1
m2 ~ a2 * x
y  ~ b1 * m1 + b2 * m2 + cp * x
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE)

# Conditional effects from x to m1 when w1 is equal to each of the default levels
cond_indirect_effects(x = "x", y = "m1",
                      wlevels = "w1", fit = fit)

# Conditional Indirect effect from x1 through m1 to y,
# when w1 is equal to each of the default levels
out <- cond_indirect_effects(x = "x", y = "y", m = "m1",
                      wlevels = "w1", fit = fit)
out

print(out, digits = 5)

print(out, annotation = FALSE)



# Convert to data frames

as.data.frame(out)

as.data.frame(out, to_string = TRUE)

Print a 'delta_med' Class Object

Description

Print the content of a delta_med-class object.

Usage

## S3 method for class 'delta_med'
print(x, digits = 3, level = NULL, full = FALSE, boot_type, ...)

Arguments

x

A delta_med-class object.

digits

The number of digits after the decimal. Default is 3.

level

The level of confidence of bootstrap confidence interval, if requested when created. If NULL, the default, the level requested when calling delta_med() is used. If not null, then this level will be used.

full

Logical. Whether additional information will be printed. Default is FALSE.

boot_type

...

Optional arguments. Ignored.

Details

It prints the output of delta_med(), which is a delta_med-class object.

Value

x is returned invisibly. Called for its side effect.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

Examples


library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)
dm <- delta_med(x = "x",
                y = "y",
                m = "m",
                fit = fit)
dm
print(dm, full = TRUE)

# Call do_boot() to generate
# bootstrap estimates
# Use 2000 or even 5000 for R in real studies
# Set parallel to TRUE in real studies for faster bootstrapping
boot_out <- do_boot(fit,
                    R = 45,
                    seed = 879,
                    parallel = FALSE,
                    progress = FALSE)
# Remove 'progress = FALSE' in practice
dm_boot <- delta_med(x = "x",
                     y = "y",
                     m = "m",
                     fit = fit,
                     boot_out = boot_out,
                     progress = FALSE)
dm_boot
confint(dm_boot)
confint(dm_boot,
        level = .90)

Print an 'indirect' Class Object

Description

Print the content of the output of indirect_effect() or cond_indirect().

Usage

## S3 method for class 'indirect'
print(
  x,
  digits = 3,
  pvalue = NULL,
  pvalue_digits = 3,
  se = NULL,
  level = 0.95,
  se_ci = TRUE,
  wrap_computation = TRUE,
  ...
)

Arguments

x

The output of indirect_effect() or cond_indirect().

digits

Number of digits to display. Default is 3.

pvalue

pvalue_digits

Number of decimal places to display for the p-value. Default is 3.

se

Logical. If TRUE and confidence interval has been formed, the standard error of the estimates are also printed. It is simply the standard deviation of the bootstrap estimates or Monte Carlo simulated values, depending on the method used to form the confidence intervals. Default to FALSE if confidence interval has been formed. Default to TRUE if no confidence interval has been computed and the original standard errors are to be used. See Details on when the original standard errors will be used by default. Default is NULL and its value determined as stated above.

level

The level of confidence for the confidence interval computed from the original standard errors. Used only for paths without mediators and both x- and y-variables are not standardized.

se_ci

Logical. If TRUE and confidence interval has not been computed, the function will try to compute them from stored standard error if the original standard error is to be used. Ignored if confidence interval has already been computed. Default to TRUE.

wrap_computation

Logical. If TRUE, the default, long computational symbols and values will be wrapped to fit to the screen width.

...

Other arguments. Not used.

Details

The print method of the indirect-class object.

We recommend using confidence interval directly. Therefore, p-value is not printed by default. Nevertheless, users who need it can request it by setting pvalue to TRUE.

Using Original Standard Errors

If these conditions are met, the stored standard error, if available, will be used to test an effect and form it confidence interval:

Confidence interval has not been formed (e.g., by bootstrapping or Monte Carlo).
The path has no mediators.
The model has only one group.
Both the x-variable and the y-variable are not standardized.

If the model is fitted by structural equation modeling using lavaan, then the variance-covariance computed by lavaan will be used, and the p-value and confidence interval are computed from the z statistic.

Caution

If the model is fitted by structural equation modeling and has moderators, the standard errors, p-values, and confidence interval computed from the variance-covariance matrices for conditional effects can only be trusted if all covariances involving the product terms are free. If any some of them are fixed, for example, fixed to zero, it is possible that the model is not invariant to linear transformation of the variables.

Value

x is returned invisibly. Called for its side effect.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x   + b1 * w1 + d1 * x:w1
m2 ~ a2 * m1  + b2 * w2 + d2 * m1:w2
m3 ~ a3 * m2  + b3 * w3 + d3 * m2:w3
y  ~ a4 * m3  + b4 * w4 + d4 * m3:w4
"
fit <- sem(mod, dat,
           meanstructure = TRUE, fixed.x = FALSE,
           se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

wvalues <- c(w1 = 5, w2 = 4, w3 = 2, w4 = 3)

indirect_1 <- cond_indirect(x = "x", y = "y",
                            m = c("m1", "m2", "m3"),
                            fit = fit,
                            wvalues = wvalues)
indirect_1

dat <- modmed_x1m3w4y1
mod2 <-
"
m1 ~ a1 * x
m2 ~ a2 * m1
m3 ~ a3 * m2
y  ~ a4 * m3 + x
"
fit2 <- sem(mod2, dat,
            meanstructure = TRUE, fixed.x = FALSE,
            se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

indirect_2 <- indirect_effect(x = "x", y = "y",
                              m = c("m1", "m2", "m3"),
                              fit = fit2)
indirect_2
print(indirect_2, digits = 5)

Print an 'indirect_list' Class Object

Description

Print the content of the output of many_indirect_effects().

Usage

## S3 method for class 'indirect_list'
print(
  x,
  digits = 3,
  annotation = TRUE,
  pvalue = FALSE,
  pvalue_digits = 3,
  se = FALSE,
  for_each_path = FALSE,
  ...
)

Arguments

x

The output of many_indirect_effects().

digits

Number of digits to display. Default is 3.

annotation

Logical. Whether the annotation after the table of effects is to be printed. Default is TRUE.

pvalue

Logical. If TRUE, asymmetric p-values based on bootstrapping will be printed if available.

pvalue_digits

Number of decimal places to display for the p-values. Default is 3.

se

for_each_path

Logical. If TRUE, each of the paths will be printed individually, using the print-method of the output of indirect_effect(). Default is FALSE.

...

Other arguments. If for_each_path is TRUE, they will be passed to the print method of the output of indirect_effect(). Ignored otherwise.

Details

The print method of the indirect_list-class object.

Value

x is returned invisibly. Called for its side effect.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

Examples


library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
           fixed.x = FALSE)
# All indirect paths from x to y
paths <- all_indirect_paths(fit,
                           x = "x",
                           y = "y")
paths
# Indirect effect estimates
out <- many_indirect_effects(paths,
                             fit = fit)
out

Print an 'indirect_proportion'-Class Object

Description

Print the content of an 'indirect_proportion'-class object, the output of indirect_proportion().

Usage

## S3 method for class 'indirect_proportion'
print(x, digits = 3, annotation = TRUE, ...)

Arguments

x

An 'indirect_proportion'-class object.

digits

Number of digits to display. Default is 3.

annotation

Logical. Whether additional information should be printed. Default is TRUE.

...

Optional arguments. Not used.

Details

The print method of the indirect_proportion-class object, which is produced by indirect_proportion(). In addition to the proportion of effect mediated, it also prints additional information such as the path for which the proportion is computed, and all indirect path(s) from the x-variable to the y-variable.

To get the proportion as a scalar, use the coef method of indirect_proportion objects.

Value

x is returned invisibly. Called for its side effect.

Examples


library(lavaan)
dat <- data_med
head(dat)
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, fixed.x = FALSE)
out <- indirect_proportion(x = "x",
                           y = "y",
                           m = "m",
                           fit = fit)
out
print(out, digits = 5)

Print an `lm_list`-Class Object

Description

Print the content of the output of lm2list().

Usage

## S3 method for class 'lm_list'
print(x, ...)

Arguments

x

The output of lm2list().

...

Other arguments. Not used.

Value

x is returned invisibly. Called for its side effect.

Examples


data(data_serial_parallel)
lm_m11 <- lm(m11 ~ x + c1 + c2, data_serial_parallel)
lm_m12 <- lm(m12 ~ m11 + x + c1 + c2, data_serial_parallel)
lm_m2 <- lm(m2 ~ x + c1 + c2, data_serial_parallel)
lm_y <- lm(y ~ m11 + m12 + m2 + x + c1 + c2, data_serial_parallel)
# Join them to form a lm_list-class object
lm_serial_parallel <- lm2list(lm_m11, lm_m12, lm_m2, lm_y)
lm_serial_parallel

Print a `mc_out`-Class Object

Description

Print the content of the output of do_mc() or related functions.

Usage

## S3 method for class 'mc_out'
print(x, ...)

Arguments

x

The output of do_mc(), or any mc_out-class object returned by similar functions.

...

Other arguments. Not used.

Value

x is returned invisibly. Called for its side effect.

Examples


library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"
fit <- sem(mod, dat)
# In real research, R should be 5000 or even 10000
mc_out <- do_mc(fit, R = 100, seed = 1234)

# Print the output of do_boot()
mc_out

Pseudo Johnson-Neyman Probing

Description

Use the pseudo Johnson-Neyman approach (Hayes, 2022) to find the range of values of a moderator in which the conditional effect is not significant.

Usage

pseudo_johnson_neyman(
  object = NULL,
  w_lower = NULL,
  w_upper = NULL,
  optimize_method = c("uniroot", "optimize"),
  extendInt = c("no", "yes", "downX", "upX"),
  tol = .Machine$double.eps^0.25,
  level = 0.95
)

johnson_neyman(
  object = NULL,
  w_lower = NULL,
  w_upper = NULL,
  optimize_method = c("uniroot", "optimize"),
  extendInt = c("no", "yes", "downX", "upX"),
  tol = .Machine$double.eps^0.25,
  level = 0.95
)

## S3 method for class 'pseudo_johnson_neyman'
print(x, digits = 3, ...)

Arguments

object

A cond_indirect_effects-class object, which is the output of cond_indirect_effects().

w_lower

The smallest value of the moderator when doing the search. If set to ⁠NULL,⁠ the default, it will be 10 standard deviations below mean, which should be small enough.

w_upper

The largest value of the moderator when doing the search. If set to ⁠NULL,⁠ the default, it will be 10 standard deviations above mean, which should be large enough.

optimize_method

The optimization method to be used. Either "uniroot" (the default) or "optimize", corresponding to stats::uniroot() and stats::optimize(), respectively.

extendInt

Used by stats::uniroot(). If "no", then search will be conducted strictly within c(w_lower, w_upper). Otherwise, the range is extended based on this argument if the solution is not found. Please refer to stats::uniroot() for details.

tol

The tolerance level used by both stats::uniroot() and stats::optimize().

level

The level of confidence of the confidence level. One minus this level is the level of significance. Default is .95, equivalent to a level of significance of .05.

x

The output of pseudo_johnson_neyman().

digits

Number of digits to display. Default is 3.

...

Other arguments. Not used.

Details

This function uses the pseudo Johnson-Neyman approach proposed by Hayes (2022) to find the values of a moderator at which a conditional effect is "nearly just significant" based on confidence interval. If an effect is moderated, there will be two such points (though one can be very large or small) forming a range. The conditional effect is not significant within this range, and significant outside this range, based on the confidence interval.

This function receives the output of cond_indirect_effects() and search for, within a specific range, the two values of the moderator at which the conditional effect is "nearly just significant", that is, the confidence interval "nearly touches" zero.

Note that numerical method is used to find the points. Therefore, strictly speaking, the effects at the end points are still either significant or not significant, even if the confidence limit is very close to zero.

Though numerical method is used, if the test is conducted using the standard error (see below), the result is equivalent to the (true) Johnson-Neyman (1936) probing. The function johnson_neyman() is just an alias to pseudo_johnson_neyman(), with the name consistent with what it does in this special case.

Supported Methods

This function supports models fitted by lm(), lavaan::sem(), and lavaan.mi::sem.mi(). This function also supports both bootstrapping and Monte Carlo confidence intervals. It also supports conditional direct paths (no mediator) and conditional indirect paths (with one or more mediator), with x and/or y standardized.

Requirements

To be eligible for using this function, one of these conditions must be met:

One form of confidence intervals (e.g, bootstrapping or Monte Carlo) must has been requested (e.g., setting boot_ci = TRUE or mc_ci = TRUE) when calling cond_indirect_effects().
Tests can be done using stored standard errors: A path with no mediator and both the x- and y-variables are not standardized.

For pre-computed confidence intervals, the confidence level of the confidence intervals adopted when calling cond_indirect_effects() will be used by this function.

For tests conducted by standard errors, the argument level is used to control the level of significance.

Possible failures

Even if a path has only one moderator, it is possible that no solution, or more than one solution, is/are found if the relation between this moderator and the conditional effect is not linear.

Solution may also be not found if the conditional effect is significant over a wide range of value of the moderator.

It is advised to use plot_effect_vs_w() to examine the relation between the effect and the moderator first before calling this function.

Speed

Note that, for conditional indirect effects, the search can be slow because the confidence interval needs to be recomputed for each new value of the moderator.

Limitations

This function currently only supports a path with only one moderator,
This function does not yet support multigroup models.

Value

A list of the class pseudo_johnson_neyman (with a print method, print.pseudo_johnson_neyman()). It has these major elements:

cond_effects: An output of cond_indirect_effects() for the two levels of the moderator found.
w_min_valid: Logical. If TRUE, the conditional effect is just significant at the lower level of the moderator found, and so is significant below this point. If FALSE, then the lower level of the moderator found is just the lower bound of the range searched, that is, w_lower.
w_max_valid: Logical. If TRUE, the conditional effect is just significant at the higher level of the moderator found, and so is significant above this point. If FALSE, then the higher level of the moderator found is just the upper bound of the range searched, that is, w_upper.

Methods (by generic)

print(pseudo_johnson_neyman): Print method for output of pseudo_johnson_neyman().

References

Johnson, P. O., & Neyman, J. (1936). Test of certain linear hypotheses and their application to some educational problems. Statistical Research Memoirs, 1, 57–93.

Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (Third edition). The Guilford Press.

Examples


library(lavaan)

dat <- data_med_mod_a
dat$wx <- dat$x * dat$w
mod <-
"
m ~ x + w + wx
y ~ m + x
"
fit <- sem(mod, dat)

# In real research, R should be 2000 or even 5000
# In real research, no need to set parallel and progress to FALSE
# Parallel processing is enabled by default and
# progress is displayed by default.
boot_out <- do_boot(fit,
                    R = 40,
                    seed = 4314,
                    parallel = FALSE,
                    progress = FALSE)
out <- cond_indirect_effects(x = "x", y = "y", m = "m",
                             wlevels = "w",
                             fit = fit,
                             boot_ci = TRUE,
                             boot_out = boot_out)

# Visualize the relation first
plot_effect_vs_w(out)

out_jn <- pseudo_johnson_neyman(out)
out_jn

# Plot the range
plot_effect_vs_w(out_jn$cond_effects)

Mediation Models By Regression

Description

Simple-to-use functions for fitting regression models and testing indirect effects using just one function.

Usage

q_mediation(
  x,
  y,
  m = NULL,
  cov = NULL,
  data = NULL,
  boot_ci = TRUE,
  level = 0.95,
  R = 100,
  seed = NULL,
  boot_type = c("perc", "bc"),
  model = NULL,
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  progress = TRUE
)

q_simple_mediation(
  x,
  y,
  m = NULL,
  cov = NULL,
  data = NULL,
  boot_ci = TRUE,
  level = 0.95,
  R = 100,
  seed = NULL,
  boot_type = c("perc", "bc"),
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  progress = TRUE
)

q_serial_mediation(
  x,
  y,
  m = NULL,
  cov = NULL,
  data = NULL,
  boot_ci = TRUE,
  level = 0.95,
  R = 100,
  seed = NULL,
  boot_type = c("perc", "bc"),
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  progress = TRUE
)

q_parallel_mediation(
  x,
  y,
  m = NULL,
  cov = NULL,
  data = NULL,
  boot_ci = TRUE,
  level = 0.95,
  R = 100,
  seed = NULL,
  boot_type = c("perc", "bc"),
  parallel = TRUE,
  ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
  progress = TRUE
)

## S3 method for class 'q_mediation'
print(
  x,
  digits = 4,
  annotation = TRUE,
  pvalue = TRUE,
  pvalue_digits = 4,
  se = TRUE,
  for_each_path = FALSE,
  se_ci = TRUE,
  wrap_computation = TRUE,
  lm_ci = TRUE,
  lm_beta = TRUE,
  lm_ci_level = 0.95,
  ...
)

Arguments

x

For q_mediation(), q_simple_mediation(), q_serial_mediation(), and q_parallel_mediation(), it is the name of the predictor. For the print method of these functions, x is the output of these functions.

y

The name of the outcome.

m

A character vector of the name(s) of the mediator(s). For a simple mediation model, it must has only one name. For serial and parallel mediation models, it can have one or more names. For a serial mediation models, the direction of the paths go from the first names to the last names. For example, c("m1", "m3", "m4") denoted that the path is m1 -> m3 -> m4.

cov

The names of the covariates, if any. If it is a character vector, then the outcome (y) and all mediators (m) regress on all the covariates. If it is a named list of character vectors, then the covariates in an element predict only the variable with the name of this element. For example, list(m1 = "c1", dv = c("c2", "c3")) indicates that c1 predicts "m1", while c2 and c3 predicts "dv". Default is NULL, no covariates.

data

The data frame. Note that listwise deletion will be used and only cases with no missing data on all variables in the model (e.g., x, m, y and cov) will be retained.

boot_ci

Logical. Whether bootstrap confidence interval will be formed. Default is TRUE.

level

The level of confidence of the confidence interval. Default is .95 (for 95% confidence intervals).

R

The number of bootstrap samples. Default is 100. Should be set to 5000 or at least 10000.

seed

The seed for the random number generator. Default is NULL. Should nearly always be set to an integer to make the results reproducible.

boot_type

The type of the bootstrap confidence intervals. Default is "perc", percentile confidence interval. Set "bc" for bias-corrected confidence interval.

model

The type of model. For q_mediation(), it can be "simple" (simple mediation model), "serial" (serial mediation model), or "parallel" (parallel mediation model). It is recommended to call the corresponding wrappers directly (q_simple_mediation(), q_serial_mediation(), and q_parallel_mediation()) instead of call q_mediation().

parallel

If TRUE, default, parallel processing will be used when doing bootstrapping.

ncores

progress

Logical. Display bootstrapping progress or not. Default is TRUE.

digits

Number of digits to display. Default is 4.

annotation

Logical. Whether the annotation after the table of effects is to be printed. Default is TRUE.

pvalue

Logical. If TRUE, asymmetric p-values based on bootstrapping will be printed if available. Default is TRUE.

pvalue_digits

Number of decimal places to display for the p-values. Default is 4.

se

for_each_path

Logical. If TRUE, each of the paths will be printed individually, using the print-method of the output of indirect_effect(). Default is FALSE.

se_ci

wrap_computation

Logical. If TRUE, the default, long computational symbols and values will be wrapped to fit to the screen width.

lm_ci

If TRUE, when printing the regression results of stats::lm(), confidence interval based on t statistic and standard error will be computed and added to the output. Default is TRUE.

lm_beta

If TRUE, when printing the regression results of stats::lm(), standardized coefficients are computed and included in the printout. Only numeric variables will be computed, and any derived terms, such as product terms, will be formed after standardization. Default is TRUE.

lm_ci_level

The level of confidence of the confidence interval. Ignored if lm_ci is not TRUE.

...

Other arguments. If for_each_path is TRUE, they will be passed to the print method of the output of indirect_effect(). Ignored otherwise.

Details

The family of "q" (quick) functions are for testing mediation effects in common models. These functions do the following in one single call:

Fit the regression models.
Compute and test all the indirect effects.

They are easy-to-use and are suitable for common models which are not too complicated. For now, there are "q" functions for these models:

A simple mediation: One predictor (x), one mediator (m), one outcome (y), and optionally some control variables (covariates) (q_simple_mediation())
A serial mediation model: One predictor (x), one or more mediators (m), one outcome (y), and optionally some control variables (covariates). The mediators positioned sequentially between x and y (q_serial_mediation()):
- x -> m1 -> m2 -> ... -> y
A parallel mediation model: One predictor (x), one or more mediators (m), one outcome (y), and optionally some control variables (covariates). The mediators positioned in parallel between x and y (q_parallel_mediation()):
- x -> m1 -> y
- x -> m2 -> y
- ...

Users only need to specify the x, m, and y variables, and covariates or control variables, if any (by cov), and the functions will automatically identify all indirect effects and total effects.

Note that they are not intended to be flexible. For models that are different from these common models, it is recommended to fit the models manually, either by structural equation modelling (e.g., lavaan::sem()) or by regression analysis using stats::lm() or lmhelprs::many_lm(). See https://sfcheung.github.io/manymome/articles/med_lm.html for an illustration on how to compute and test indirect effects for an arbitrary mediation model.

Workflow

This is the workflow of the "q" functions:

Do listwise deletion based on all the variables used in the models.
Generate the regression models based on the variables specified.
Fit all the models by OLS regression using stats::lm().
Call all_indirect_paths() to identify all indirect paths.
Call many_indirect_effects() to compute all indirect effects and form their confidence intervals.
Call total_indirect_effect() to compute the total indirect effect.
Return all the results for printing.

The output of the "q" functions have a print method for printing all the major results.

Notes

Flexibility

The "q" functions are designed to be easy to use. They are not designed to be flexible. For maximum flexibility, fit the models manually and call functions such as indirect_effect() separately. See https://sfcheung.github.io/manymome/articles/med_lm.html for illustrations.

Monte Carlo Confidence Intervals

We do not recommend using Monte Carlo confidence intervals for models fitted by regression because the covariances between parameter estimates are assumed to be zero, which may not be the case in some models. Therefore, the "q" functions do not support Monte Carlo confidence intervals. If Monte Carlo intervals are desired, please fit the model by structural equation modeling using lavaan::sem().

Value

The function q_mediation() returns a q_mediation class object, with its print method.

The function q_simple_mediation() returns a q_simple_mediation class object, which is a subclass of q_mediation.

The function q_serial_mediation() returns a q_serial_mediation class object, which is a subclass of q_mediation.

The function q_parallel_mediation() returns a q_parallel_mediation class object, which is a subclass of q_mediation.

Methods (by generic)

print(q_mediation): The print method of the outputs of q_mediation(), q_simple_mediation(), q_serial_mediation(), and q_parallel_mediation().

Functions

q_mediation(): The general "q" function for common mediation models. Not to be used directly.
q_simple_mediation(): A wrapper of q_mediation() for simple mediation models (a model with only one mediator).
q_serial_mediation(): A wrapper of q_mediation() for serial mediation models.
q_parallel_mediation(): A wrapper of q_mediation() for parallel mediation models.

Examples


# ===== Simple mediation

# Set R to 5000 or 10000 in real studies
# Remove 'parallel' or set it to TRUE for faster bootstrapping
# Remove 'progress' or set it to TRUE to see a progress bar

out <- q_simple_mediation(x = "x",
                          y = "y",
                          m = "m",
                          cov = c("c2", "c1"),
                          data = data_med,
                          R = 40,
                          seed = 1234,
                          parallel = FALSE,
                          progress = FALSE)
# Suppressed printing of p-values due to the small R
# Remove `pvalue = FALSE` when R is large
print(out,
      pvalue = FALSE)

# # Different control variables for m and y
# out <- q_simple_mediation(x = "x",
#                           y = "y",
#                           m = "m",
#                           cov = list(m = "c1",
#                                      y = c("c1", "c2")),
#                           data = data_med,
#                           R = 100,
#                           seed = 1234,
#                           parallel = FALSE,
#                           progress = FALSE)
# out


# ===== Serial mediation

# Set R to 5000 or 10000 in real studies
# Remove 'parallel' or set it to TRUE for faster bootstrapping
# Remove 'progress' or set it to TRUE to see a progress bar

# out <- q_serial_mediation(x = "x",
#                           y = "y",
#                           m = c("m1", "m2"),
#                           cov = c("c2", "c1"),
#                           data = data_serial,
#                           R = 40,
#                           seed = 1234,
#                           parallel = FALSE,
#                           progress = FALSE)

# # Suppressed printing of p-values due to the small R
# # Remove `pvalue = FALSE` when R is large
# print(out,
#       pvalue = FALSE)

# # Different control variables for m and y
# out <- q_serial_mediation(x = "x",
#                           y = "y",
#                           m = c("m1", "m2"),
#                           cov = list(m1 = "c1",
#                                      m2 = c("c2", "c1"),
#                                      y = "c2"),
#                           data = data_serial,
#                           R = 100,
#                           seed = 1234,
#                           parallel = FALSE,
#                           progress = FALSE)
# out


# ===== Parallel mediation

# Set R to 5000 or 10000 in real studies
# Remove 'parallel' or set it to TRUE for faster bootstrapping
# Remove 'progress' or set it to TRUE to see a progress bar

# out <- q_parallel_mediation(x = "x",
#                             y = "y",
#                             m = c("m1", "m2"),
#                             cov = c("c2", "c1"),
#                             data = data_parallel,
#                             R = 40,
#                             seed = 1234,
#                             parallel = FALSE,
#                             progress = FALSE)
# # Suppressed printing of p-values due to the small R
# # Remove `pvalue = FALSE` when R is large
# print(out,
#       pvalue = FALSE)

# # Different control variables for m and y
# out <- q_parallel_mediation(x = "x",
#                             y = "y",
#                             m = c("m1", "m2"),
#                             cov = list(m1 = "c1",
#                                        m2 = c("c2", "c1"),
#                                        y = "c2"),
#                             data = data_parallel,
#                             R = 100,
#                             seed = 1234,
#                             parallel = FALSE,
#                             progress = FALSE)
# out

Sample Dataset: A Simple Latent Mediation Model

Description

Generated from a simple mediation model among xthree latent factors, fx, fm, and fy, xeach has three indicators.

Usage

simple_mediation_latent

Format

A data frame with 200 rows and 11 variables:

x1: Indicator of fx. Numeric.
x2: Indicator of fx. Numeric.
x3: Indicator of fx. Numeric.
m1: Indicator of fm. Numeric.
m2: Indicator of fm. Numeric.
m3: Indicator of fm. Numeric.
y1: Indicator of fy. Numeric.
y2: Indicator of fy. Numeric.
y3: Indicator of fy. Numeric.

Details

The model:

fx =~ x1 + x2 + x3
fm =~ m1 + m2 + m3
fy =~ y1 + y2 + y3
fm ~ a * fx
fy ~ b * fm + cp * fx
indirect := a * b

Extraction Methods for 'cond_indirect_effects' Outputs

Description

For subsetting a 'cond_indirect_effects'-class object.

Usage

## S3 method for class 'cond_indirect_effects'
x[i, j, drop = if (missing(i)) TRUE else length(j) == 1]

Arguments

x

A 'cond_indirect_effects'-class object.

i

A numeric vector of row number(s), a character vector of row name(s), or a logical vector of row(s) to be selected.

j

A numeric vector of column number(s), a character vector of column name(s), or a logical vector of column(s) to be selected.

drop

Whether dropping a dimension if it only have one row/column.

Details

Customized [ for 'cond_indirect_effects'-class objects, to ensure that these operations work as they would be on a data frame object, while information specific to conditional effects is modified correctly.

Value

A 'cond_indirect_effects'-class object. See cond_indirect_effects() for details on this class.

Examples


library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x  + w1 + x:w1
m2 ~ m1
y  ~ m2 + x + w4 + m2:w4
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Examples for cond_indirect():

# Conditional effects from x to m1 when w1 is equal to each of the levels
out1 <- cond_indirect_effects(x = "x", y = "m1",
                      wlevels = "w1", fit = fit)
out1[2, ]

# Conditional Indirect effect from x1 through m1 to y,
# when w1 is equal to each of the levels
out2 <- cond_indirect_effects(x = "x", y = "y", m = c("m1", "m2"),
                      wlevels = c("w1", "w4"), fit = fit)
out2[c(1, 3), ]

Extraction Methods for a 'wlevels'-class Object

Description

For subsetting a 'wlevels'-class object. Attributes related to the levels will be preserved if appropriate.

Usage

## S3 method for class 'wlevels'
x[i, j, drop = if (missing(i)) TRUE else length(j) == 1]

## S3 replacement method for class 'wlevels'
x[i, j] <- value

## S3 replacement method for class 'wlevels'
x[[i, j]] <- value

Arguments

x

A 'wlevels'-class object.

i

A numeric vector of row number(s), a character vector of row name(s), or a logical vector of row(s) to be selected.

j

A numeric vector of column number(s), a character vector of column name(s), or a logical vector of column(s) to be selected.

drop

Whether dropping a dimension if it only have one row/column.

value

Ignored.

Details

Customized [ for 'wlevels'-class objects, to ensure that these operations work as they would be on a data frame object, while information specific to a wlevels-class object modified correctly.

The assignment methods ⁠[<-⁠ and ⁠[[<-⁠ for wlevels-class objects will raise an error. This class of objects should be created by mod_levels() or related functions.

Subsetting the output of mod_levels() is possible but not recommended. It is more reliable to generate the levels using mod_levels() and related functions. Nevertheless, there are situations in which subsetting is preferred.

Value

A 'wlevels'-class object. See mod_levels() and merge_mod_levels() for details on this class.

Examples


data(data_med_mod_ab)
dat <- data_med_mod_ab
# Form the levels from a list of lm() outputs
lm_m <- lm(m ~ x*w1 + c1 + c2, dat)
lm_y <- lm(y ~ m*w2 + x + w1 + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
w1_levels <- mod_levels(lm_out, w = "w1")
w1_levels
w1_levels[2, ]
w1_levels[c(2, 3), ]

dat <- data_med_mod_serial_cat
lm_m1 <- lm(m1 ~ x*w1 + c1 + c2, dat)
lm_y <- lm(y ~ m1 + x + w1 + c1 + c2, dat)
lm_out <- lm2list(lm_m1, lm_y)
w1gp_levels <- mod_levels(lm_out, w = "w1")
w1gp_levels
w1gp_levels[2, ]
w1gp_levels[3, ]

merged_levels <- merge_mod_levels(w1_levels, w1gp_levels)
merged_levels

merged_levels[4:6, ]
merged_levels[1:3, c(2, 3)]
merged_levels[c(1, 4, 7), 1, drop = FALSE]

Summary of an `lm_list`-Class Object

Description

The summary of content of the output of lm2list().

Usage

## S3 method for class 'lm_list'
summary(object, betaselect = FALSE, ci = FALSE, level = 0.95, ...)

## S3 method for class 'summary_lm_list'
print(x, digits = 3, digits_decimal = NULL, ...)

Arguments

object

The output of lm2list().

betaselect

If TRUE, standardized coefficients are computed and included in the printout. Only numeric variables will be computed, and any derived terms, such as product terms, will be formed after standardization. Default is FALSE.

ci

If TRUE, confidence interval based on t statistic and standard error will be computed and added to the output. Default is FALSE.

level

The level of confidence of the confidence interval. Ignored if ci is not TRUE.

...

Other arguments. Not used.

x

An object of class summary_lm_list.

digits

The number of significant digits in printing numerical results.

digits_decimal

The number of digits after the decimal in printing numerical results. Default is NULL. If set to an integer, numerical results in the coefficient table will be printed according this setting, and digits will be ignored.

Value

summary.lm_list() returns a summary_lm_list-class object, which is a list of the summary() outputs of the lm() outputs stored.

print.summary_lm_list() returns x invisibly. Called for its side effect.

Functions

print(summary_lm_list): Print method for output of summary for lm_list.

Examples


data(data_serial_parallel)
lm_m11 <- lm(m11 ~ x + c1 + c2, data_serial_parallel)
lm_m12 <- lm(m12 ~ m11 + x + c1 + c2, data_serial_parallel)
lm_m2 <- lm(m2 ~ x + c1 + c2, data_serial_parallel)
lm_y <- lm(y ~ m11 + m12 + m2 + x + c1 + c2, data_serial_parallel)
# Join them to form a lm_list-class object
lm_serial_parallel <- lm2list(lm_m11, lm_m12, lm_m2, lm_y)
lm_serial_parallel
summary(lm_serial_parallel)

Model Terms of an 'lm_from_lavaan'-Class Object

Description

It extracts the terms object from an lm_from_lavaan-class object.

Usage

## S3 method for class 'lm_from_lavaan'
terms(x, ...)

Arguments

x

An 'lm_from_lavaan'-class object.

...

Additional arguments. Ignored.

Details

A method for lm_from_lavaan-class that converts a regression model for a variable in a lavaan model to a formula object. This function simply calls stats::terms() on the formula object to extract the predictors of a variable.

Value

A terms-class object. See terms.object for details.

Examples

library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
terms(fit_list$m)
terms(fit_list$y)

Total Indirect Effect Between Two Variables

Description

Compute the total indirect effect between two variables in the paths estimated by many_indirect_effects().

Usage

total_indirect_effect(object, x, y)

Arguments

object

The output of many_indirect_effects(), or a list of indirect-class objects.

x

Character. The name of the x variable. All paths starting from x will be included. Can be omitted if all paths have the same x.

y

Character. The name of the y variable. All paths ending at y will be included. Can be omitted if all paths have the same y.

Details

It extracts the indirect-class objects of relevant paths and then add the indirect effects together using the + operator.

Value

An indirect-class object.

Examples


library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
           fixed.x = FALSE)

# All indirect paths, control variables excluded
paths <- all_indirect_paths(fit,
                            exclude = c("c1", "c2"))
paths

# Indirect effect estimates
out <- many_indirect_effects(paths,
                             fit = fit)
out

# Total indirect effect from x to y
total_indirect_effect(out,
                      x = "x",
                      y = "y")

manymome: Mediation, Moderation and Moderated-Mediation After Model Fitting

Description

Author(s)

See Also

Enumerate All Indirect Effects in a Model

Description

Usage

Arguments

Details

Multigroup Models

Value

Functions

Author(s)

See Also

Examples

Check a Path Exists in a Model

Description

Usage

Arguments

Details

Value

Examples

Print the Output of 'cond_indirect_diff()'

Description

Usage

Arguments

Details

Value

See Also

Estimates of Conditional Indirect Effects or Conditional Effects

Description

Usage

Arguments

Details

Value

See Also

Examples

Delta_Med in a 'delta_med'-Class Object

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Extract the Indirect Effect or Conditional Indirect Effect

Description

Usage

Arguments

Details

Value

See Also

Examples

Extract the Indirect Effects from a 'indirect_list' Object

Description

Usage

Arguments

Details

Value

See Also

Examples

Extract the Proportion of Effect Mediated

Description

Usage

Arguments

Details

Value

See Also

Examples

Coefficients of an 'lm_from_lavaan'-Class Object

Description

Usage

Arguments

Details

Value

See Also

Examples

Conditional, Indirect, and Conditional Indirect Effects

`many_indirect_effects()`