spaMM (version 4.5.0)

get_RLRsim_args: Extractors of arguments for functions from package RLRsim

Description

get_RLRsim_args extracts a list of arguments suitable for a call to RLRsim::RLRTSim() or RLRsim::LRTSim(). These functions use an efficient simulation procedure to compute restricted or marginal likelihood ratio tests, respectively, comparing a fixed-effect model and a mixed-effect model with one random effect. They are notably used to test for the presence of one random effect, although the models compared by marginal likelihood (LRTSim()) may differ both in their random and in their fixed effects (as shown in the Example). The tests are exact for small samples (up to simulation error) for LMMs with no free parameters in the random effect (beyond the variance being tested), so not for time-series or spatial models with estimated correlation parameters. Heteroscedasticity of the residuals or of the random effect variance are also not taken into account by the simulation procedure (see Value field below for an hint why this is so).

get_RLRTSim_args is the older extractor, originally for RLRsim::RLRTSim() only, now handling also ML fits with a warning (though the possible absence of the nullfit argument will result in an error).

Usage

get_RLRsim_args(fullfit, nullfit, verbose=TRUE, REML=NA, ...)
get_RLRTSim_args(object, verbose=TRUE, ...)

Value

A list of arguments for a call to RLRsim::RLRTSim() or RLRsim::LRTSim(). The main arguments are the design matrix for the fixed effects, and the ZA matrix and L detailed in random-effects (here represented by the Z and sqrt.Sigma elements). The models handled by the testing procedure are the ones that are sufficiently characterized by these two matrices. LRTSim additionally requires q, the difference in number of parameters of fixed effects between the models.

Arguments

object, fullfit

An object of class HLfit, as returned by the fitting functions in spaMM, for the more complete model to be compared.

nullfit

Same for the less complete model; required only for (marginal) LR test, as opposed to restricted LR test.

verbose

NA or boolean; Whether to display some message or not.

REML

For programming purposes, not documented.

...

Additional arguments (currently not used).

Details

If the models compared do not differ in their fixed effects, under the null hypothesis there is a probability mass P for a zero likelihood ratio, and the distribution of p-values can be uniform only on the range (0,1-P). If the fixed effects differ (as handled by RLRsim::LRTSim()), this does not occur.

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.

See Also

The bootstrap procedure in LRT is more general but slower. It appears to provide results quite similar to those of RLRsim when both are applicable.

Examples

if (FALSE) {
## Derived from example in RLRsim::LRTSim
 set.seed(123)
 dat <- data.frame(g = rep(1:10, e = 10), x = (x<-rnorm(100)), 
                   y = 0.1 * x + rnorm(100))
 m <- fitme(y ~ x + (1|g), data=dat)
 m0 <- fitme(y ~ 1, data=dat) 
 (obs.LRT <- 2*(logLik(m)-logLik(m0)))
 args <- get_RLRsim_args(m,m0)
 sim.LRT <- do.call(RLRsim::LRTSim, args )
 (RLRpval <- (sum(sim.LRT >= obs.LRT) + 1) / (length(sim.LRT) + 1))
 ## comparable test using LRT():
 # (bootpval <- LRT(m,m0, boot.repl = 199L)$rawBootLRT$p_value)
}