Aggregated factor correlations

Description

The factor correlations aggregated over k-folds

Usage

agg_cors(models, flag = 0.9, type = "factor")

Arguments

Value

data.frame of mean factor correlations for each factor model and vector with count of folds with a flagged correlation

Examples

data(example.kfa)
agg_cors(example.kfa)

Aggregated factor loadings

Description

The factor loadings aggregated over k-folds

Usage

agg_loadings(models, flag = 0.3, digits = 2)

Arguments

Value

data.frame of mean factor loadings for each factor model and vector with count of folds with a flagged loading

Examples

data(example.kfa)
agg_loadings(example.kfa)

Summary table of model fit

Description

Summary table of model fit aggregated over k-folds

Usage

agg_model_fit(kfits, index = "all", digits = 2)

Arguments

Value

data.frame of aggregated model fit statistics

Examples

data(example.kfa)
fits <- k_model_fit(example.kfa, by.fold = TRUE)
agg_model_fit(fits)

Aggregated scale reliabilities

Description

The factor reliabilities aggregated over k-folds

Usage

agg_rels(models, flag = 0.6, digits = 2)

Arguments

Value

data.frame of mean factor (scale) reliabilities for each factor model and vector with count of folds with a flagged reliability

Examples

data(example.kfa)
agg_rels(example.kfa)

Write confirmatory factor analysis syntax

Description

Uses the factor loadings matrix, presumably from an exploratory factor analysis, to generate lavaan compatible confirmatory factory analysis syntax.

Usage

efa_cfa_syntax(
  loadings,
  simple = TRUE,
  min.loading = NA,
  single.item = c("keep", "drop", "none"),
  identified = TRUE,
  constrain0 = FALSE
)

Arguments

References

Millsap, R. E. (2001). When trivial constraints are not trivial: The choice of uniqueness constraints in confirmatory factor analysis. *Structural Equation Modeling, 8*(1), 1-17. doi:10.1207/S15328007SEM0801_1

Examples

loadings <- matrix(c(rep(.2, 3), rep(.6, 3), rep(.8, 3), rep(.3, 3)), ncol = 2)
# simple structure
efa_cfa_syntax(loadings)
# allow cross-loadings and check if model is identified
efa_cfa_syntax(loadings, simple = FALSE, min.loading = .25)
# allow cross-loadings and ignore identification check
efa_cfa_syntax(loadings, simple = FALSE, min.loading = .25, identified = FALSE)

kfa results from simulated data example

Description

Simulated responses for 900 observations on 20 variables loading onto a 3 factor structure (see example in kfa documentation for model). The simulated data was run through kfa with the call kfa(sim.data, k = 2, m = 3) which tested 1-, 2-, and 3-factor structures over 2 folds.

Usage

data(example.kfa)

Format

An object of class "kfa", which is a four-element list:

• cfas lavaan CFA objects for each k fold

• cfa.syntax syntax used to produce CFA objects

• model.names vector of names for CFA objects

• efa.structures all factor structures identified in the EFA

Examples

data(example.kfa)
agg_cors(example.kfa)

Find k for k-fold cross-validation

Description

This function is specifically for determining k in the context of factor analysis using change in RMSEA as the criterion for identifying the optimal factor model.

Usage

find_k(
  variables,
  n,
  p,
  m = NULL,
  max.k = 10,
  min.n = 200,
  rmsea0 = 0.05,
  rmseaA = 0.08,
  ...
)

Arguments

Value

named vector with the number of folds (k), sample size suggested by the power analysis (power.n), and the actual sample size used for determining k (actual.n).

References

Curran, P. J., Bollen, K. A., Chen, F., Paxton, P., & Kirby, J. B. (2003). Finite sampling properties of the point estimates and confidence intervals of the RMSEA. Sociological Methods & Research, 32(2), 208-252. doi:10.1177/0049124103256130

MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130–149. doi:10.1037/1082-989X.1.2.130

Examples

find_k(n = 900, p = 20, m = 3)

# adjust precision
find_k(n = 900, p = 20, m = 3, rmsea0 = .03, rmseaA = .10)

Standardized factor loadings matrix

Description

Extract standardized factor loadings from lavaan object

Usage

get_std_loadings(object, type = "std.all", df = FALSE)

Arguments

Value

A matrix or data.frame of factor loadings

Examples

data(HolzingerSwineford1939, package = "lavaan")
HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

fit <- lavaan::cfa(HS.model, data = HolzingerSwineford1939)
get_std_loadings(fit)

Available Fit Indices

Description

Shows the fit indices available from kfa object to report in kfa_report

Usage

index_available(models)

Arguments

Value

character vector of index names

Examples

data(example.kfa)
index_available(example.kfa)

Extract model fit

Description

Model fit indices extracted from k-folds

Usage

k_model_fit(models, index = "default", by.fold = TRUE)

Arguments

Value

list of data.frames with average model fit for each factor model

Examples

data(example.kfa)

# customize fit indices to report
k_model_fit(example.kfa, index = c("chisq", "cfi", "rmsea", "srmr"))

# organize results by factor model rather than by fold
k_model_fit(example.kfa, by.fold = FALSE)

Conducts k-fold cross validation for factor analysis

Description

The function splits the data into k folds where each fold contains training data and test data. For each fold, exploratory factor analyses (EFAs) are run on the training data. The structure for each model is transformed into lavaan-compatible confirmatory factor analysis (CFA) syntax. The CFAs are then run on the test data.

Usage

kfa(
  data,
  variables = names(data),
  k = NULL,
  m = floor(length(variables)/4),
  seed = 101,
  cores = NULL,
  custom.cfas = NULL,
  power.args = list(rmsea0 = 0.05, rmseaA = 0.08),
  rotation = "oblimin",
  simple = TRUE,
  min.loading = NA,
  single.item = "none",
  ordered = FALSE,
  estimator = NULL,
  missing = "listwise",
  ...
)

Arguments

Details

In order for custom.cfas to be tested along with the EFA identified structures, each model supplied in custom.cfas must include all variables in lavaan-compatible syntax.

Deciding an appropriate m can be difficult, but is consequential for the possible factor structures to examine, the power analysis to determine k, and overall computation time. The n_factors function in the parameters package can assist with this decision.

When converting EFA results to CFA syntax (via efa_cfa_syntax), the simple structure is defined as each variable loading onto a single factor. This is determined using the largest factor loading for each variable. When simple = FALSE, variables are allowed to cross-load on multiple factors. In this case, all pathways with loadings above the min.loading are retained. However, allowing cross-loading variables can result in model under-identification. The efa_cfa_syntax) function conducts an identification check (i.e., identified = TRUE) and under-identified models are not run in the CFA portion of the analysis.

Value

An object of class "kfa", which is a four-element list:

• cfas lavaan CFA objects for each k fold

• cfa.syntax syntax used to produce CFA objects

• model.names vector of names for CFA objects

• efa.structures all factor structures identified in the EFA

Examples

# simulate data based on a 3-factor model with standardized loadings
sim.mod <- "f1 =~ .7*x1 + .8*x2 + .3*x3 + .7*x4 + .6*x5 + .8*x6 + .4*x7
                f2 =~ .8*x8 + .7*x9 + .6*x10 + .5*x11 + .5*x12 + .7*x13 + .6*x14
                f3 =~ .6*x15 + .5*x16 + .9*x17 + .4*x18 + .7*x19 + .5*x20
                f1 ~~ .2*f2
                f2 ~~ .2*f3
                f1 ~~ .2*f3
                x9 ~~ .2*x10"
set.seed(1161)
sim.data <- simstandard::sim_standardized(sim.mod, n = 900,
                                          latent = FALSE,
                                          errors = FALSE)[c(2:9,1,10:20)]

# include a custom 2-factor model
custom2f <- paste0("f1 =~ ", paste(colnames(sim.data)[1:10], collapse = " + "),
                   "\nf2 =~ ",paste(colnames(sim.data)[11:20], collapse = " + "))


mods <- kfa(data = sim.data,
            k = NULL, # prompts power analysis to determine number of folds
            cores = 2,
            custom.cfas = custom2f)
            

Creates summary report from a k-fold factor analysis

Description

Generates a report summarizing the factor analytic results over k-folds.

Usage

kfa_report(
  models,
  file.name,
  report.title = file.name,
  path = NULL,
  report.format = "html_document",
  word.template = NULL,
  index = "default",
  plots = FALSE,
  load.flag = 0.3,
  cor.flag = 0.9,
  rel.flag = 0.6,
  digits = 2
)

Arguments

Value

A summary report of factor structures and model fit within and between folds.

Examples

# simulate data based on a 3-factor model with standardized loadings
sim.mod <- "f1 =~ .7*x1 + .8*x2 + .3*x3 + .7*x4 + .6*x5 + .8*x6 + .4*x7
                f2 =~ .8*x8 + .7*x9 + .6*x10 + .5*x11 + .5*x12 + .7*x13 + .6*x14
                f3 =~ .6*x15 + .5*x16 + .9*x17 + .4*x18 + .7*x19 + .5*x20
                f1 ~~ .2*f2
                f2 ~~ .2*f3
                f1 ~~ .2*f3
                x9 ~~ .2*x10"
set.seed(1161)
sim.data <- simstandard::sim_standardized(sim.mod, n = 900,
                                          latent = FALSE,
                                          errors = FALSE)[c(2:9,1,10:20)]

# include a custom 2-factor model
custom2f <- paste0("f1 =~ ", paste(colnames(sim.data)[1:10], collapse = " + "),
                   "\nf2 =~ ",paste(colnames(sim.data)[11:20], collapse = " + "))


mods <- kfa(data = sim.data,
            k = NULL, # prompts power analysis to determine number of folds
            cores = 2,
            custom.cfas = custom2f)
            

## Not run: 
kfa_report(mods, file.name = "example_sim_kfa_report",
           report.format = "html_document",
           report.title = "K-fold Factor Analysis - Example Sim")
           
## End(Not run)

Unique factor structures

Description

Extract unique factor structures across the k-folds

Usage

model_structure(models)

Arguments

Value

data.frame with the number of folds the unique factor structure was tested for each factor model.

Examples

data(example.kfa)
model_structure(example.kfa)

Conducts exploratory factor analysis

Description

This function is intended for use on independent samples rather than integrated with k-fold cross-validation.

Usage

run_efa(
  data,
  variables = names(data),
  m = floor(ncol(data)/4),
  rotation = "oblimin",
  simple = TRUE,
  min.loading = NA,
  single.item = c("keep", "drop", "none"),
  identified = TRUE,
  constrain0 = FALSE,
  ordered = FALSE,
  estimator = NULL,
  missing = "listwise",
  ...
)

Arguments

Details

When converting EFA results to CFA syntax (via efa_cfa_syntax), the simple structure is defined as each variable loading onto a single factor. This is determined using the largest factor loading for each variable. When simple = FALSE, variables are allowed to cross-load on multiple factors. In this case, all pathways with loadings above the min.loading are retained. However, allowing cross-loading variables can result in model under-identification. An identification check is run by default, but can be turned off by setting identified = FALSE.

Value

A three-element list:

• efas lavaan object for each m model

• loadings (rotated) factor loading matrix for each m model

• cfa.syntax CFA syntax generated from loadings

References

Millsap, R. E. (2001). When trivial constraints are not trivial: The choice of uniqueness constraints in confirmatory factor analysis. Structural Equation Modeling, 8(1), 1-17. doi:10.1207/S15328007SEM0801_1

Examples

# simulate data based on a 3-factor model with standardized loadings
sim.mod <- "f1 =~ .7*x1 + .8*x2 + .3*x3 + .7*x4 + .6*x5 + .8*x6 + .4*x7
                f2 =~ .8*x8 + .7*x9 + .6*x10 + .5*x11 + .5*x12 + .7*x13 + .6*x14
                f3 =~ .6*x15 + .5*x16 + .9*x17 + .4*x18 + .7*x19 + .5*x20
                f1 ~~ .2*f2
                f2 ~~ .2*f3
                f1 ~~ .2*f3
                x9 ~~ .2*x10"
set.seed(1161)
sim.data <- simstandard::sim_standardized(sim.mod, n = 900,
                                          latent = FALSE,
                                          errors = FALSE)[c(2:9,1,10:20)]
# Run 1-, 2-, and 3-factor models
efas <- run_efa(sim.data, m = 3)

Write exploratory factor analysis syntax

Description

Converts variable names to lavaan-compatible exploratory factor analysis syntax

Usage

write_efa(nf, vnames)

Arguments

Value

character. Use cat() to best examine the returned syntax.

Examples

vnames <- paste("x", 1:10)
syntax <- write_efa(nf = 2, vnames = vnames)
cat(syntax)