exactLRT {RLRsim}R Documentation

Likelihood Ratio Tests for simple linear mixed models

Description

This function provides an exact likelihood ratio test based on simulated values from the finite sample distribution for simultaneous testing of the presence of the variance component and some restrictions of the fixed effects in a simple linear mixed model with known correlation structure of the random effect and i.i.d. errors.

Usage

exactLRT(m, m0, seed = NA, nsim = 10000, log.grid.hi = 8,
    log.grid.lo = -10, gridlength = 200)

Arguments

m The fitted model under the alternative; of class lme, lmer or spm
m0 The fitted model under the null hypothesis; of class lm
seed Specify a seed for set.seed
nsim Number of values to simulate
log.grid.hi Lower value of the grid on the log scale. See exactLRT.
log.grid.lo Lower value of the grid on the log scale. See exactLRT.
gridlength Length of the grid. See LRTSim.

Details

The model under the alternative must be a linear mixed model y=X*beta+Z*b+epsilon with a single random effect b with known correlation structure and error terms that are i.i.d. The hypothesis to be tested must be of the form

H0: beta_1=beta0_1,..,beta_q=beta0_q, Var(b)=0

versus

H0: beta_1 neq beta0_1,..or..,beta_q neq beta0_q ot Var(b)>0

We use the exact finite sample distribution of the likelihood ratio test statistic as derived by Crainiceanu & Ruppert (2004).

Value

A list of class htest containing the following components:

statistic
p p-value for the observed test statistic
method a character string indicating what type of test was performed and how many values were simulated to determine the critical value

Author(s)

Fabian Scheipl

References

Crainiceanu, C. and Ruppert, D. (2004) Likelihood ratio tests in linear mixed models with one variance component, Journal of the Royal Statistical Society: Series B,66,165–185.

See Also

LRTSim for the underlying simulation algorithm; RLRTSim and exactRLRT for restricted likelihood based tests

Examples

library(nlme);
data(Orthodont);

##test for Sex:Age interaction and Subject-Intercept
mA<-lme(distance ~ Sex * I(age - 11), random = ~ 1| Subject,
    data = Orthodont, method = "ML")
m0<-lm(distance ~ Sex + I(age - 11), data = Orthodont)
summary(mA)
summary(m0)
exactLRT(m = mA, m0 = m0)

[Package RLRsim version 2.0-2 Index]