[R-sig-ME] Best practice for co/variance component testing in LMM

Maarten Jung M@@rten@Jung @ending from m@ilbox@tu-dre@den@de
Mon Jun 18 10:09:42 CEST 2018

What is the best way to test if multiple co/variance components in a
linear mixed model improve the model fit?
When testing the null hypothesis that variance components are zero the
alternative hypothesis is one-sided, the sampling distribution of the
anova()-LR-statistic is not welI approximated by a chi-square
distribution and the LRT is conservative in this "boundary case". I
know there is RLRsim but I couldn't figure out how to test for
multiple variance components with exactRLRT/exactLRT. Besides that
RLRsim cannot be used to test the null hypothesis that a covariance is
equal to zero.
I came up with the idea to use LRT based on chi-bar-square
distributions, which have known weights following a binomial
distribution [1], for testing the (uncorrelated) variance components.
When testing the covariance the parameter value in the null hypothesis
is no longer on the edge of the parameter space and I think the LRT
via anova() should be, at least asymptotically, correct.
Are there better ways and/or other R packages for this purpose,
especially for merMod objects?


[1] http://www.jstor.org/stable/27643833

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