Version: 1.0.0
Title: Sparse Regression with Paired Covariates
Description: Implements sparse regression with paired covariates (<doi:10.1007/s11634-019-00375-6>). The paired lasso is designed for settings where each covariate in one set forms a pair with a covariate in the other set (one-to-one correspondence). For the optional correlation shrinkage, install ashr (https://github.com/stephens999/ashr) and CorShrink (https://github.com/kkdey/CorShrink) from GitHub (see README).
Depends: R (≥ 3.0.0)
Imports: glmnet, Matrix, survival
Suggests: knitr, testthat, rmarkdown, remotes, pROC, edgeR, ashr, CorShrink
License: GPL-3
Encoding: UTF-8
VignetteBuilder: knitr
RoxygenNote: 7.3.2
URL: https://github.com/rauschenberger/palasso, https://rauschenberger.github.io/palasso/
BugReports: https://github.com/rauschenberger/palasso/issues
NeedsCompilation: no
Packaged: 2024-09-26 12:43:23 UTC; armin.rauschenberger
Author: Armin Rauschenberger ORCID iD [aut, cre]
Maintainer: Armin Rauschenberger <armin.rauschenberger@uni.lu>
Repository: CRAN
Date/Publication: 2024-09-26 22:40:02 UTC

Paired lasso

Description

The function palasso fits the paired lasso. Use this function if you have paired covariates and want a sparse model.

Usage

palasso(y = y, X = X, max = 10, ...)

Arguments

y

response: vector of length n

X

covariates: list of matrices, each with n rows (samples) and p columns (variables)

max

maximum number of non-zero coefficients: positive numeric, or NULL (no sparsity constraint)

...

further arguments for cv.glmnet or glmnet

Details

Let x denote one entry of the list X. See glmnet for alternative specifications of y and x. Among the further arguments, family must equal "gaussian", "binomial", "poisson", or "cox", and penalty.factor must not be used.

Hidden arguments: Deactivate adaptive lasso by setting adaptive to FALSE, activate standard lasso by setting standard to TRUE, and activate shrinkage by setting shrink to TRUE.

Value

This function returns an object of class palasso. Available methods include predict, coef, weights, fitted, residuals, deviance, logLik, and summary.

References

Armin Rauschenberger, Iiuliana Ciocanea-Teodorescu, Marianne A. Jonker, Renee X. Menezes, and Mark A. van de Wiel (2020). "Sparse classification with paired covariates." Advances in Data Analysis and Classification 14:571-588. doi:10.1007/s11634-019-00375-6. (Click here to access PDF. Contact: armin.rauschenberger@uni.lu.)

Examples

set.seed(1)
n <- 50; p <- 20
y <- rbinom(n=n,size=1,prob=0.5)
X <- lapply(1:2,function(x) matrix(rnorm(n*p),nrow=n,ncol=p))
object <- palasso(y=y,X=X,family="binomial") # adaptive=TRUE,standard=FALSE
names(object)

Arguments

Description

Checks the validity of the provided arguments.

Usage

.args(...)

Arguments

...

Arguments supplied to palasso, other than y, X and max.

Value

Returns the arguments as a list, including default values for missing arguments.

Examples

NA

Combining p-values

Description

This function combines local p-values to a global p-value.

Usage

.combine(x, method = "simes")

Arguments

x

local p-values: numeric vector of length k

method

character "fisher", "tippet", "sidak", or "simes"

Value

These functions return a numeric vector of length p (main effects), or a numeric matrix with p rows and p columns (interaction effects).

References

Westfall, P. H. (2005). "Combining p-values". Encyclopedia of Biostatistics doi:10.1002/0470011815.b2a15181

Examples

# independence
p <- runif(10)
palasso:::.combine(p)

## dependence 
#runif <- function(n,cor=0){
#    Sigma <- matrix(cor,nrow=n,ncol=n)
#     diag(Sigma) <- 1
#     mu <- rep(0,times=n)
#     q <- MASS::mvrnorm(n=1,mu=mu,Sigma=Sigma)
#     stats::pnorm(q=q)
#}
#p <- runif(n=10,cor=0.8)
#combine(p)

Correlation

Description

Calculates the correlation between the response and the covariates. Shrinks the correlation coefficients for each covariate set separately.

Usage

.cor(y, x, args)

Arguments

y

vector of length n

x

matrix with n rows and p columns

args

options for paired lasso: list of arguments (output from .dims and .args)

Value

list of vectors

Examples

NA

Cross-validation

Description

Repeatedly leaves out samples, and predicts their response.

Usage

.cv(y, x, foldid, lambda, args)

Arguments

y

response: vector of length n

x

covariates: matrix with n rows (samples) and k * p columns (variables)

foldid

fold identifiers: vector of length n, with entries from 1 to nfolds

lambda

lambda sequence: vector of decreasing positive values

args

options for paired lasso: list of arguments (output from .dims and .args)

Value

Returns matrix of predicted values (except "cox")

Examples

NA

Dimensionality

Description

This function extracts the dimensions.

Usage

.dims(y, X, args = NULL)

Arguments

y

response: vector of length n

X

covariates: list of matrices, each with n rows (samples) and p columns (variables)

args

options for paired lasso: list of arguments (output from .dims and .args)

Value

The function .dims extracts the dimensionality. It returns the numbers of samples, covariate pairs and covariate sets. It also returns the number of weighting schemes, and the names of these weighting schemes.

Examples

NA

Extraction

Description

Extracts cv.glmnet-like object.

Usage

.extract(fit, lambda, cvm, type.measure)

Arguments

fit

matrix with one row for each sample ("gaussian", "binomial" and "poisson"), or one row for each fold (only "cox"), and one column for each lambda (output from .fit)

lambda

lambda sequence: vector of decreasing positive values

cvm

mean cross-validated loss: vector of same length as lambda (output from .loss)

type.measure

... loss function: character "deviance", "mse", "mae", "class", or "auc"

Examples

NA

Model bag

Description

Fits all models from the chosen bag.

Usage

.fit(y, x, args)

Arguments

y

response: vector of length n

x

covariates: matrix with n rows (samples) and k * p columns (variables)

args

options for paired lasso: list of arguments (output from .dims and .args)

Value

list of glmnet-like objects

Examples

NA

Cross-validation folds

Description

Assigns samples to cross-validation folds, balancing the folds in the case of a binary or survival response.

Usage

.folds(y, nfolds, foldid = NULL)

Arguments

y

response: vector of length n

nfolds

number of folds: positive integer (>= 10 recommended)

foldid

fold identifiers: vector of length n, with entries from 1 to nfolds

Value

Returns the fold identifiers.

Examples

NA

Cross-validation loss

Description

Calculates mean cross-validated loss

Usage

.loss(y, fit, family, type.measure, foldid = NULL)

Arguments

y

response: vector of length n

fit

matrix with one row for each sample ("gaussian", "binomial" and "poisson"), or one row for each fold (only "cox"), and one column for each lambda (output from .fit)

family

model family: character "gaussian", "binomial", "poisson", or "cox"

type.measure

... loss function: character "deviance", "mse", "mae", "class", or "auc"

foldid

fold identifiers: vector of length n, with entries from 1 to nfolds

Value

Returns list of vectors, one for each model.

Examples

NA

Weighting schemes

Description

Calculates the weighting schemes.

Usage

.weight(cor, args)

Arguments

cor

correlation coefficients: list of k vectors of length p (one vector for each covariate set with one entry for each covariate)

args

options for paired lasso: list of arguments (output from .dims and .args)

Value

list of named vectors (one for each weighting scheme)

Examples

NA

Arguments for "palasso"

Description

This page lists the arguments for the (internal) "palasso" function(s).

Arguments

y

response: vector of length n

X

covariates: list of matrices, each with n rows (samples) and p columns (variables)

max

maximum number of non-zero coefficients: positive numeric, or NULL (no sparsity constraint)

...

further arguments for cv.glmnet or glmnet

x

covariates: matrix with n rows (samples) and k * p columns (variables)

args

options for paired lasso: list of arguments (output from .dims and .args)

nfolds

number of folds: positive integer (>= 10 recommended)

foldid

fold identifiers: vector of length n, with entries from 1 to nfolds

cor

correlation coefficients: list of k vectors of length p (one vector for each covariate set with one entry for each covariate)

lambda

lambda sequence: vector of decreasing positive values

family

model family: character "gaussian", "binomial", "poisson", or "cox"

type.measure

... loss function: character "deviance", "mse", "mae", "class", or "auc"

fit

matrix with one row for each sample ("gaussian", "binomial" and "poisson"), or one row for each fold (only "cox"), and one column for each lambda (output from .fit)

cvm

mean cross-validated loss: vector of same length as lambda (output from .loss)

Methods for class "palasso"

Description

This page lists the main methods for class "palasso".

Usage

## S3 method for class 'palasso'
predict(object, newdata, model = "paired", s = "lambda.min", max = NULL, ...)

## S3 method for class 'palasso'
coef(object, model = "paired", s = "lambda.min", max = NULL, ...)

## S3 method for class 'palasso'
weights(object, model = "paired", max = NULL, ...)

## S3 method for class 'palasso'
fitted(object, model = "paired", s = "lambda.min", max = NULL, ...)

## S3 method for class 'palasso'
residuals(object, model = "paired", s = "lambda.min", max = NULL, ...)

## S3 method for class 'palasso'
deviance(object, model = "paired", max = NULL, ...)

## S3 method for class 'palasso'
logLik(object, model = "paired", max = NULL, ...)

## S3 method for class 'palasso'
summary(object, model = "paired", ...)

Arguments

object

palasso object

newdata

covariates: list of matrices, each with n rows (samples) and p columns (variables)

model

character "paired", or an entry of names(object)

s

penalty parameter: character "lambda.min" or "lambda.1se", positive numeric, or NULL (entire sequence)

max

maximum number of non-zero coefficients, positive integer, or NULL

...

further arguments for predict.cv.glmnet, coef.cv.glmnet, or deviance.glmnet

Details

By default, the function predict returns the linear predictor (type="link"). Consider predicting the response (type="response").

See Also

Use palasso to fit the paired lasso.

Analysis functions for manuscript

Description

Functions for the palasso manuscript.

Usage

.prepare(X, filter = 1, cutoff = "zero", scale = TRUE)

.simulate(x, effects)

.predict(
  y,
  X,
  nfolds.ext = 5,
  nfolds.int = 5,
  adaptive = TRUE,
  standard = TRUE,
  elastic = TRUE,
  shrink = TRUE,
  family = "binomial",
  ...
)

.select(y, X, index, nfolds = 5, standard = TRUE, adaptive = TRUE, ...)

Arguments

X

covariates: matrix with n rows and p columns

filter

numeric, multiplying the sample size

cutoff

character "zero", "knee", or "half"

scale

logical

x

covariates: list of length k, including matrices with n rows and p columns

effects

number of causal covariates: vector of length k

y

response: vector of length n

nfolds.ext

number of external folds

...

arguments for palasso

index

indices of causal covariates: list of length k, including vectors

Details

.prepare: pre-processes sequencing data by removing features with a low total abundance, and adjusting for different library sizes; obtains two transformations of the same data by (1) binarising the counts with some cutoff and (2) taking the Anscombe transform; scales all covariates to mean zero and unit variance.

.simulate: simulates the response by exploiting two experimental covariate matrices; allows for different numbers of non-zero coefficients for X and Z.

.predict: estimates the predictive performance of different lasso models (standard X and/or Z, adaptive X and/or Z, paired X and Z); minimises the loss function "deviance", but also returns other loss functions; supports logistic and Cox regression.

.select: estimates the selective performance of different lasso models (standard X and/or Z, adaptive X and/or Z, paired X and Z); limits the number of covariates to 10; returns the number of selected covariates, and the number of correctly selected covariates.

See Also

Use palasso to fit the paired lasso.

Examples

## Not run: set.seed(1)
n <- 30; p <- 40
X <- matrix(rpois(n*p,lambda=3),nrow=n,ncol=p)
x <- palasso:::.prepare(X)
y <- palasso:::.simulate(x,effects=c(1,2))
predict <- palasso:::.predict(y,x)
select <- palasso:::.select(y,x,attributes(y))
## End(Not run)

Plot functions for manuscript

Description

Functions for the palasso manuscript.

Usage

plot_score(X, choice = NULL, ylab = "count")

plot_table(
  X,
  margin = 2,
  labels = TRUE,
  colour = TRUE,
  las = 1,
  cex = 1,
  cutoff = NA
)

plot_circle(b, w, cutoff = NULL, group = NULL)

plot_box(
  X,
  choice = NULL,
  ylab = "",
  ylim = NULL,
  zero = FALSE,
  invert = FALSE
)

plot_pairs(x, y = NULL, ...)

plot_diff(x, y, prob = 0.95, ylab = "", xlab = "", ...)

Arguments

X

matrix with n rows and p columns

choice

numeric between 1 and p

margin

0 (none), 1 (rows), or 2 (columns)

cutoff

numeric between 0 and 1

b

between-group correlation: vector of length p

w

within-group correlation: matrix with p rows and p columns

group

vector of length p

x, y

vectors of equal length

...

additional arguments

prob

confidence interval: numeric between 0 and 1

Details

The function plot_score compares a selected column to each of the other columns. It counts the number of rows where the entry in the selected column is smaller (blue), equal (white), or larger (red).

Value

to do

See Also

Use palasso to fit the paired lasso.

Examples

### score ###
n <- 10; p <- 4
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
palasso:::plot_score(X)

### table ###
n <- 5; p <- 3
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
palasso:::plot_table(X,margin=2)

### circle ###
n <- 50; p <- 25
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
Z <- matrix(rnorm(n*p),nrow=n,ncol=p)
b <- sapply(seq_len(p),function(i) abs(cor(X[,i],Z[,i])))
w <- pmax(abs(cor(X)),abs(cor(Z)),na.rm=TRUE)
palasso:::plot_circle(b,w,cutoff=0)

### box ###
n <- 10; p <- 5
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
palasso:::plot_box(X,choice=5)

### pairs ###
n <- 10
x <- runif(n)
y <- runif(n)
palasso:::plot_pairs(x,y)

### diff ###
n <- 100
x <- runif(n)
y <- runif(n)
palasso:::plot_diff(x,y)