exactRLRT {RLRsim} | R Documentation |
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.
exactRLRT(m, mA = NULL, m0 = NULL, seed = NA, nsim = 10000, log.grid.hi = 8, log.grid.lo = -10, gridlength = 200)
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 , lmer 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 . |
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).
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 |
Fabian Scheipl
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.
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
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: ## Not run: exactRLRT(m.slope, mA, m0) detach(package:lme4) #avoid conflicts 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)