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Best practice for co/variance component testing in LMM

3 messages · Maarten Jung, Ben Pelzer

Original
Maarten Jung
# 
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?

Cheers,
Maarten

[1] http://www.jstor.org/stable/27643833
Ben Pelzer
# 
Hi Maarten,

It sounds as if paragraph 6.2.1 in Snijders & Bosker 2nd edition of 
"Multilevel Analysis" gives an answer to your question. Regards,

Ben.
On 18-6-2018 10:09, Maarten Jung wrote:
Maarten Jung
# 
Hi Ben,

unfortunately it doesn't.
S & B only describe (1) the appropriate chi-bar-square distribution
for the test of a single variance component and (2) the appropriate
chi-bar-square distributions for testing a single random slope which
(in their approach) includes testing if the corresponding covariances
are zero. This seems to me as if their tests for (2) build on the idea
that the covariance paramters are not on the boundary but the
variances component of interest (the one of the random slope) is?

However, they do not describe how one should test if multiple
uncorrelated variance components are equal to zero and the LRT they
describe are only asymptotically correct.

It may well be that there are better options/ "exact" tests (similar
to RLRsim) for testing if multiple co/variance components improve the
model fit and that's what I'm looking for.

Cheers,
Maarten
On Mon, Jun 18, 2018 at 7:54 PM, Ben Pelzer <b.pelzer at maw.ru.nl> wrote: