On Wed, Aug 9, 2017 at 9:54 AM Phillip Alday <phillip.alday at mpi.nl> wrote:
On 08/09/2017 04:46 PM, Douglas Bates wrote:
Technically it is true that the number of parameters does not depend on the number of random effects, only on the number of unique values in the covariance matrices for the random effects. However, I think that leads to an undercount of the effective number of parameters when, say, performing a likelihood ratio test of models that differ in their random effects specification.
This is related to the more general issue of degrees of freedom in mixed models, right?
Yes. But in terms of estimation (especially as implemented in
lme4/MixedModels.jl), increasing the levels of a random effect will generally provide better estimates, right?
Yes. Or, to put it the other way, it is unrealistic to expect to obtain precise estimates of variance components unless there is(are) a large number of levels in the grouping factor(s) for the random effects.