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, print.p = TRUE, return.sample = FALSE, ...)
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 . |
print.p |
print table with observed variance ratio, observed test statistic -2log RLR and p-value? |
return.sample |
return simulated sample? |
... |
Further parameters to be passed to RLRTSim . |
Tests in models with only a single variance component require only the first argument m
.
For testing in models with multiple variance components, m
contains only the random effect
whose variance is to be tested, 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.
For models with multiple components, theoretical results are still outstanding. Fairly extensive
simulation studies suggest that the application of the test 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.
The exact finite sample distribution of the restricted likelihood ratio test statistic
that is simulated from was derived by Crainiceanu & Ruppert (2004).
If return.sample = FALSE
, the p-value.
Else a list with components
p |
p-value for the observed test statistic |
sample |
the simulated sample of test statistics under the null |
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.
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: 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)