GELvar: 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)

Value

stat.global: value of the test statistic over an interval.
pvalue.global: approximated p-value over an interval based on the perturbation.

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.

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