R: Restricted Likelihood Ratio Tests for additive and linear...

exactRLRT {RLRsim} | R Documentation

## Restricted Likelihood Ratio Tests for additive and linear mixed models

### Description

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.

### Usage

    exactRLRT(
      m,
      mA = NULL,
      m0 = NULL,
      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 or, for testing in models with multiple variance components, the reduced model containing only the random effect to be tested (see Details), an `lme`, `lmerMod` 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`.
`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

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).

No simulation is performed if the observed test statistic is 0. (i.e., if the fit of the model fitted under the alternative is indistinguishable from the model fit under H0), since the p-value is always 1 in this case.

### Value

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

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 `RLRTSim`

### Author(s)

Fabian Scheipl, bug fixes by Andrzej Galecki, updates for lme4-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.

Greven, S., Crainiceanu, C., Kuechenhoff, H., and Peters, A. (2008) Restricted Likelihood Ratio Testing for Zero Variance Components in Linear Mixed Models, Journal of Computational and Graphical Statistics, 17 (4): 870–891.

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.

### See Also

`RLRTSim` for the underlying simulation algorithm; `exactLRT` for likelihood based tests

### Examples

    data(sleepstudy, package = "lme4")
    mA <- lme4::lmer(Reaction ~ I(Days-4.5) + (1|Subject) + (0 + I(Days-4.5)|Subject),
      data = 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)

    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)

[Package RLRsim version 3.1-7 Index]