RLRsim (version 3.0)

exactRLRT: Restricted Likelihood Ratio Tests for additive and linear mixed models

Description

This function provides an (exact) restricted likelihood ratio test based on simulated values from the finite sample distribution for testing whether the variance of a random effect is 0 in a linear mixed model with known correlation structure of the tested random effect and i.i.d. errors.

Usage

exactRLRT(m, mA = NULL, m0 = NULL, 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 or, for testing in models with multiple variance components, the reduced model containing only the random effect to be tested (see Details), an lme, lmerMod or spm object

mA

The full model under the alternative for testing in models with multiple variance components

m0

The model under the null for testing in models with multiple variance components

seed

input for set.seed

nsim

Number of values to simulate

log.grid.hi

Lower value of the grid on the log scale. See exactRLRT.

log.grid.lo

Lower value of the grid on the log scale. See exactRLRT.

gridlength

Length of the grid. See exactLRT.

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.

Value

• A list of class htest containing the following components:

  A list of class htest containing the following components:

  • statisticthe observed likelihood ratio
  • pp-value for the observed test statistic
  • methoda character string indicating what type of test was performed and how many values were simulated to determine the critical value
  • samplethe samples from the null distribution returned byRLRTSim

Details

Testing in models with only a single variance component require only the first argument m. For testing in models with multiple variance components, the fitted model m must contain only the random effect set to zero under the null hypothesis, while mA and m0 are the models under the alternative and the null, respectively. For models with a single variance component, the simulated distribution is exact if the number of parameters (fixed and random) is smaller than the number of observations. Extensive simulation studies (see second reference below) confirm that the application of the test to models with multiple variance components is safe and the simulated distribution is correct as long as the number of parameters (fixed and random) is smaller than the number of observations and the nuisance variance components are not superfluous or very small. We use the finite sample distribution of the restricted likelihood ratio test statistic as derived by Crainiceanu & Ruppert (2004).

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.

Greven, S., Crainiceanu, C., Kuechenhoff, H., and Peters, A. (2008) Restricted Likelihood Ratio Testing for Zero Variance Components in Linear Mixed Models, Journal of Computational and Graphical Statistics, 17 (4): 870--891.

Scheipl, F., Greven, S. and Kuechenhoff, H. (2008) Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models. Computational Statistics & Data Analysis, 52(7):3283--3299.

See Also

RLRTSim for the underlying simulation algorithm; exactLRT for likelihood based tests

Examples

library(lme4)
data(sleepstudy)
mA <- lmer(Reaction ~ I(Days-4.5) + (1|Subject) + (0 + I(Days-4.5)|Subject), sleepstudy)
m0 <- update(mA, . ~ . - (0 + I(Days-4.5)|Subject))
m.slope  <- update(mA, . ~ . - (1|Subject))
#test for subject specific slopes:
exactRLRT(m.slope, mA, m0)

library(mgcv)
data(trees)
#test quadratic trend vs. smooth alternative
m.q<-gamm(I(log(Volume)) ~ Height + s(Girth, m = 3), data = trees, method = "REML")$lme
exactRLRT(m.q)
#test linear trend vs. smooth alternative
m.l<-gamm(I(log(Volume)) ~ Height + s(Girth, m = 2), data = trees, method = "REML")$lme
exactRLRT(m.l)