ELvar: Empirical Likelihood Inference of a Local Variance Component

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

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

ELmethodVar documentation built on Nov. 17, 2025, 9:06 a.m.