Version: 0.1
Date: 2025-11-12
Title: Empirical Likelihood Inference of Variance Components in Linear Mixed-Effects Models
Author: Jingru Zhang [aut, cre]
Maintainer: Jingru Zhang <jrzhang001@gmail.com>
Depends: R (≥ 3.5.0)
Description: Provides empirical likelihood-based methods for the inference of variance components in linear mixed-effects models.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL: https://github.com/jingru-zhang/ELmethod
NeedsCompilation: no
Packaged: 2025-11-12 05:59:57 UTC; jingruzhang
Repository: CRAN
Date/Publication: 2025-11-17 09:00:15 UTC

Empirical Likelihood Inference of Variance Components in Linear Mixed-Effects Models

Description

This package provides empirical likelihood-based methods for the inference of variance components in linear mixed-effects models.

Author(s)

Jingru Zhang, Haochang Shou, Hongzhe Li

Maintainer: Jingru Zhang (jrzhang001@gmail.com)

References

Zhang J., Guo W., Carpenter J.S., Leroux A., Merikangas K.R., Martin N.G., Hickie I.B., Shou H., and Li H. (2022). Empirical likelihood tests for variance components in linear mixed-effects models.

See Also

ELvar GELvar

Empirical Likelihood Inference of a Local Variance Component

Description

This function provides an empirical likelihood method for the inference of a local variance component in linear mixed-effects models.

Usage

    ELvar(X,Y,Philist,theta0=0,beta=NA,other=FALSE)

Arguments

X

design matrix for all observations, in which each row represents a p-dimentional covariates.

Y

response vector.

Philist

list of design matrices of variance components. Its i-th element is an ni by ni*d matrix that combines design matrices of variance components by columns for the i-th subject.

theta0

value of the first variance component under the null. Its default value is 0.

beta

fixed effects. Its default value is NA (unknown fixed effects).

other

logical; if TRUE, the function gives auxiliary terms. Its default value is FALSE.

Value

stat

value of the test statistic.

pvalue

approximated p-value based on asymptotic theory.

Zi, Di, Mi, nv1sq

auxiliary terms if other=TRUE.

References

Zhang J., Guo W., Carpenter J.S., Leroux A., Merikangas K.R., Martin N.G., Hickie I.B., Shou H., and Li H. (2022). Empirical likelihood tests for variance components in linear mixed-effects models.

See Also

GELvar

Examples


# Datasets "exampleNE0" and "exampleNE1" contain normal distributed longitudinal data.
# Datasets "exampleTE0" and "exampleTE1" contain t distributed longitudinal data.
# The fist variance components in the datasets "exampleNE0" and "exampleTE0" are zero.
# The fist variance components in the datasets "exampleNE1" and "exampleTE1" are 
# nonzero at the 24, 25, 26, 27 time points.

# X is an N by p matrix with N being the number of all observations and p being 
# the dimension of covariates.
# Y.all is an N by T matrix with T being the number of time points.
# Philist is an n list of design matrices of variance components with n being the 
# number of subjects. Its $i$th element Philist[[i]] is an $n_i$ by $n_id$ matrix 
# that combines design matrices of variance components by columns for the $i$th
# subject, where $n_i$ is the number of repeated measures for the $i$th subject
# and $d$ is the number of variance components.
# beta.all is a p by T matrix. Each column is the fixed effects at time t.
# thetastar is a d by T matrix. Each column is the variance components at time t.

    data(exampleNE0)
    t = 1 # consider the local problem at time t
    re = ELvar(X,Y.all[,t],Philist,theta0=0) # with unknown fixed effects
    re = ELvar(X,Y.all[,t],Philist,theta0=0,beta=beta.all[,t]) # with known fixed effects

Empirical Likelihood Inference of Variance Components over an Interval

Description

This function provides an empirical likelihood method for the inference of variance components over an interval in linear mixed-effects models.

Usage

    GELvar(X,Y.all,Philist,theta0=0,beta.all=NA,permnum=1e3)

Arguments

X

design matrix for all observations, in which each row represents a p-dimentional covariates.

Y.all

response matrix, in which each column is the response vector at time t.

Philist

list of design matrices of variance components. Its i-th element is an ni by d*ni matrix that combines design matrices of variance components by columns for the i-th subject, where ni is the number of repeated measures for the i-th subject and d is the number of variance components.

theta0

value of the first variance component under the null. Its default value is 0.

beta.all

fixed effects. Each column is the fixed effects at time t. Its default value is NA (unknown fixed effects).

permnum

number of perturbation. Its default value is 1000.

Value

stat.global

value of the test statistic over an interval.

pvalue.global

approximated p-value over an interval based on the perturbation.

References

Zhang J., Guo W., Carpenter J.S., Leroux A., Merikangas K.R., Martin N.G., Hickie I.B., Shou H., and Li H. (2022). Empirical likelihood tests for variance components in linear mixed-effects models.

See Also

ELvar

Examples


# Datasets "exampleNE0" and "exampleNE1" contain normal distributed longitudinal data.
# Datasets "exampleTE0" and "exampleTE1" contain t distributed longitudinal data.
# The fist variance components in the datasets "exampleNE0" and "exampleTE0" are zero.
# The fist variance components in the datasets "exampleNE1" and "exampleTE1" are 
# nonzero at the 24, 25, 26, 27 time points.

# X is an N by p matrix with N being the number of all observations and p being 
# the dimension of covariates.
# Y.all is an N by T matrix with T being the number of time points.
# Philist is an n list of design matrices of variance components with n being the 
# number of subjects. Its $i$th element Philist[[i]] is an $n_i$ by $n_id$ matrix 
# that combines design matrices of variance components by columns for the $i$th 
# subject, where $n_i$ is the number of repeated measures for the $i$th subject 
# and $d$ is the number of variance components.
# beta.all is a p by T matrix. Each column is the fixed effects at time t.
# thetastar is a d by T matrix. Each column is the variance components at time t.

    data(exampleNE0)
    re = GELvar(X,Y.all,Philist,theta0=0)

Design Matrices of Variance Components

Description

This is a list of design matrices of variance components. Its i-th element is an ni by d*ni matrix that combines design matrices of variance components by columns for the i-th subject, where ni is the number of repeated measures for the i-th subject and d is the number of variance components.

Design matrix for all observations

Description

This is an N by p matrix with N being the number of all observations and p being the dimension of covariates. Each row represents a p-dimentional covariates.

Response matrix

Description

This is an N by T matrix with N being the number of all observations and T being the number of time points. Each column is the response vector at time t.

A Matrix Representing Fixed Effects

Description

This is a p by T matrix. Each column is the fixed effects at time t.

Empirical Likelihood Inference of Variance Components at multiple time points

Description

This function provides an empirical likelihood method for the inference of variance components at multiple time points in linear mixed-effects models.

Usage

    multiELvar(X,Y.all,Philist,theta0=0,beta.all=NA,other=FALSE)

Arguments

X

design matrix for all observations, in which each row represents a p-dimentional covariates.

Y.all

response matrix, in which each column is the response vector at time t.

Philist

list of design matrices of variance components. Its i-th element is an ni by d*ni matrix that combines design matrices of variance components by columns for the i-th subject, where ni is the number of repeated measures for the i-th subject and d is the number of variance components.

theta0

value of the first variance component under the null. Its default value is 0.

beta.all

fixed effects. Each column is the fixed effects at time t. Its default value is NA (unknown fixed effects).

other

logical; if TRUE, the function gives auxiliary terms. Its default value is FALSE.

Value

stat.all

vector of test statistics at multiple time points.

pvalue.all

vector of approximated p-value at multiple time points based on asymptotic theory.

Z.all, D.all, M.all, nv1sq.all

auxiliary terms if other=TRUE.

References

Zhang J., Guo W., Carpenter J.S., Leroux A., Merikangas K.R., Martin N.G., Hickie I.B., Shou H., and Li H. (2022). Empirical likelihood tests for variance components in linear mixed-effects models.

See Also

GELvar

Examples


# Datasets "exampleNE0" and "exampleNE1" contain normal distributed longitudinal data.
# Datasets "exampleTE0" and "exampleTE1" contain t distributed longitudinal data.
# The fist variance components in the datasets "exampleNE0" and "exampleTE0" are zero.
# The fist variance components in the datasets "exampleNE1" and "exampleTE1" are 
# nonzero at the 24, 25, 26, 27 time points.

# X is an N by p matrix with N being the number of all observations and p being 
# the dimension of covariates.
# Y.all is an N by T matrix with T being the number of time points.
# Philist is an n list of design matrices of variance components with n being the 
# number of subjects. Its $i$th element Philist[[i]] is an $n_i$ by $n_id$ matrix 
# that combines design matrices of variance components by columns for the $i$th 
# subject, where $n_i$ is the number of repeated measures for the $i$th subject 
# and $d$ is the number of variance components.
# beta.all is a p by T matrix. Each column is the fixed effects at time t.
# thetastar is a d by T matrix. Each column is the variance components at time t.

    data(exampleNE0)
    re = multiELvar(X,Y.all,Philist,theta0=0)

A Matrix Representing True Variance Components

Description

This is a d by T matrix, where d is the number of variance components and T is the number of time points. Each column is the true variance components at time t.