LRTSim {RLRsim} | R Documentation |
These functions simulate values from the (exact) finite sample distribution of the
(restricted) likelihood
ratio statistic for testing the presence of the variance component
(and restrictions of the fixed effects) in a simple linear mixed model with known
correlation structure of the random effect and i.i.d. errors. They are usually called by
exactLRT
or exactRLRT
.
LRTSim(X, Z, q, sqrt.Sigma, seed = NA, nsim = 10000, log.grid.hi = 8, log.grid.lo=-10, gridlength=200) RLRTSim(X, Z, sqrt.Sigma, lambda0 = NA, seed = NA, nsim = 10000, use.approx=0, log.grid.hi=8, log.grid.lo=-10, gridlength=200)
X |
The fixed effects design matrix of the model under the alternative |
Z |
The random effects design matrix of the model under the alternative |
q |
The number of parameters restrictions on the fixed effects (see Details) |
sqrt.Sigma |
The upper triangular cholesky factor of the correlation matrix of the random effect |
lambda0 |
The value of the ratio of the variance of the random effect and the errors under the null |
seed |
Specify a seed for set.seed |
nsim |
Number of values to simulate |
use.approx |
If 0, the exact distribution is simulated. If between 0 and 1, only the largest
eigenvalues whose sum represents at least use.approx *(sum of all eigenvalues) are used. |
log.grid.hi |
Lower value of the grid on the log scale. See Details |
log.grid.lo |
Lower value of the grid on the log scale. See Details |
gridlength |
Length of the grid for the grid search over lambda. See Details |
The model under the alternative must be a linear mixed model
y=X*beta+Z*b+epsilon with
a single random effect b with known correlation
structure Sigma and i.i.d errors.
The simulated distribution of the likelihood ratio statistic
was derived by Crainiceanu & Ruppert (2004).
The simulation algorithm uses a gridsearch over a log-regular grid
of values of lambda=Var(b)/Var(epsilon) to maximize the
likelihood under the alternative for nsim
realizations of y
drawn under the null hypothesis.
log.grid.hi
and log.grid.lo
are the lower and upper
limits of this grid on the log scale.
gridlength
is the number of points on the grid.\
These are just wrapper functions for the underlying C code.
A vector with the simulated values of the (R)LRT 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.
Scheipl, F. (2007) Testing for nonparametric terms and random effects in structured additive regression. Diploma thesis.\ http://www.statistik.lmu.de/~scheipl/downloads/DIPLOM.zip.
library(lme4) g <- rep(1:10, e = 10) x <- rnorm(100) y <- 0.1 * x + rnorm(100) m <- lmer(y ~ x + (1|g), method="ML") m0 <- lm(y ~ 1) (obs.LRT <- 2*(logLik(m)-logLik(m0))) X <- m@X Z <- t(as.matrix(m@Zt)) sim.LRT <- LRTSim(X, Z, 1, diag(10)) (pval <- mean(sim.LRT > obs.LRT))