ELvar: 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)

Value

stat: value of the test statistic.
pvalue: approximated p-value based on asymptotic theory.
Zi,Di,Mi,nv1sq: auxiliary terms if other=TRUE.

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.

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.

Examples

Run this code


# 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