# exactLRT: Likelihood Ratio Tests for simple linear mixed models In RLRsim: Exact (Restricted) Likelihood Ratio Tests for Mixed and Additive Models

## Description

This function provides an exact likelihood ratio test based on simulated values from the finite sample distribution for simultaneous testing of the presence of the variance component and some restrictions of the fixed effects in a simple linear mixed model with known correlation structure of the random effect and i.i.d. errors.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```exactLRT( m, m0, seed = NA, nsim = 10000, log.grid.hi = 8, log.grid.lo = -10, gridlength = 200, parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL ) ```

## Arguments

 `m` The fitted model under the alternative; of class `lme`, `lmerMod` or `spm` `m0` The fitted model under the null hypothesis; of class `lm` `seed` Specify a seed for `set.seed` `nsim` Number of values to simulate `log.grid.hi` Lower value of the grid on the log scale. See `exactLRT`. `log.grid.lo` Lower value of the grid on the log scale. See `exactLRT`. `gridlength` Length of the grid. See `LRTSim`. `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.

## 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 and error terms that are i.i.d. The hypothesis to be tested must be of the form

H0: beta_1=beta0_1,..,beta_q=beta0_q, Var(b)=0

H0: beta_1=beta0_1,..,beta_q=beta0_q, Var(b)=0

versus

H0: beta_1 \neq beta0_1,..or..,beta_q \neq beta0_q ot Var(b)>0

H0: beta_1 \neq beta0_1,..or..,beta_q \neq beta0_q ot Var(b)>0

We use the exact finite sample distribution of the likelihood ratio test statistic as derived by Crainiceanu & Ruppert (2004).

## Value

A list of class `htest` containing the following components:

• `statistic` the observed likelihood ratio

• `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

• `sample` the samples from the null distribution returned by `LRTSim`

## Author(s)

Fabian Scheipl, updates for lme4.0-compatibility by Ben Bolker

## 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.

`LRTSim` for the underlying simulation algorithm; `RLRTSim` and `exactRLRT` for restricted likelihood based tests
 ``` 1 2 3 4 5 6 7 8 9 10``` ```library(nlme); data(Orthodont); ##test for Sex:Age interaction and Subject-Intercept mA<-lme(distance ~ Sex * I(age - 11), random = ~ 1| Subject, data = Orthodont, method = "ML") m0<-lm(distance ~ Sex + I(age - 11), data = Orthodont) summary(mA) summary(m0) exactLRT(m = mA, m0 = m0) ```