ELmethodVar (version 0.1)

multiELvar: 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)

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.

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.

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)