exactLRT {RLRsim}

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,
  parallel = c("no", "multicore", "snow"),
  ncpus = 1L,
  cl = NULL
)

Arguments

m

The fitted model under the alternative; of class lme, lmerMod 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.

parallel

The type of parallel operation to be used (if any). If missing, the default is "no parallelization").

ncpus

integer: number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs. Defaults to 1, i.e., no parallelization.

cl

An optional parallel or snow cluster for use if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the call.

Details

The model under the alternative must be a linear mixed model y=X\beta+Zb+\varepsilon 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

H_0: \beta_{p+1-q}=\beta^0_{p+1-q},\dots,\beta_{p}=\beta^0_{p};\quad

Var(b)=0

versus

H_A:\; \beta_{p+1-q}\neq \beta^0_{p+1-q}\;\mbox{or}\dots

\mbox{or}\;\beta_{p}\neq \beta^0_{p}\;\;\mbox{or}\;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 the observed likelihood ratio

• 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

• sample the samples from the null distribution returned by LRTSim

Author(s)

Fabian Scheipl, updates for lme4.0-compatibility by Ben Bolker

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)