Description Usage Arguments Details Value Author(s) References See Also Examples
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 
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 
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 
nsim 
Number of values to simulate 
log.grid.hi 
Lower value of the grid on the log scale. See

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

gridlength 
Length of the grid. See 
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. 
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).
No simulation is performed if the observed test statistic is 0. (i.e., if the fit of the model fitted under the alternative is indistinguishable from the model fit under H0), since the pvalue is always 1 in this case.
A list of class htest
containing the following components:
A list of class htest
containing the following components:
statistic
the observed likelihood ratio
p
pvalue 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
RLRTSim
Fabian Scheipl, bug fixes by Andrzej Galecki, updates for lme4compatibility by Ben Bolker
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.
RLRTSim
for the underlying simulation algorithm;
exactLRT
for likelihood based tests
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  data(sleepstudy, package = "lme4")
mA < lme4::lmer(Reaction ~ I(Days4.5) + (1Subject) + (0 + I(Days4.5)Subject),
data = sleepstudy)
m0 < update(mA, . ~ .  (0 + I(Days4.5)Subject))
m.slope < update(mA, . ~ .  (1Subject))
#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)

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