[R-sig-ME] Question about continuous distributions in GLMM

[Rune Haubo]

On 9 May 2018 at 20:16, Victoria Ortiz <vicrotas at gmail.com> wrote:
>  Hi,
> I'm so sorry for the delay in the response, I was with a lot of work.
>
> With "variance components" I mean the partition of the total variance into
> the different factors that explain it. Our interest is to have a
> quantification of the portion of the variance explained by the different
> factors, both random and fixed. Translated to the biology of our data, this
> means to estimate genetic, genotype x environment variation, and
> environment variation of the total phenotypic variation for a given trait
> in a population. In particular, the objective is to compare this estimators
> between diferent populations analyzed separately.
>
> Additionaly, reading another topics of this mail list, I found that the
> classical model for testing the interaction and obtain the variance
> components would be a model like the following:
>
> m2 <- lmer ( variable ~ fixed factor  1 * fixed factor 2 + (1 | random
> factor) + (1 | fixed factor 1:random factor2) + (1 | fixed factor 2:random
> factor) + (1| fixed factor 1:fixed factor 2:random factor))
>
> So, with this model, in the summary I can see the partition of the total
> variance of the random effects. Is this right?

Yes, this model will decompose the variance of the response into
variance components for the random effects and the residual variance.
>
> Finally, if I want the p-values of the random effects, I should analize the
> full and reduce models sequentially. Also, I found that another way to do
> it is with the 'ranova' function from the lmerTest package, but the results
> are very dissimilar. I don't know in wich analysis should I trust, I think
> that in this case the sequentially one is correct.

Can you quantify how these approaches are different? If you run
lmerTest::ranova(m2) it should provide (REML) likelihood ratio tests
of the random terms by deleting these from the full model one-by-one.
Note that if the model is fitted with REML (default) the tests are
REML-likelihood ratio tests - otherwise ML likelihood ratio tests.

Perhaps you use anova(m2, reduce_m2) or equivalently anova(m2,
reduce_m2, refit=TRUE) which produce ML likelihood ratio tests while
fitting your model with REML and that is the source of the difference?
[For tests of random effect terms I recommend the REML likelihood
ratio tests produced by lmerTest::ranova over the ML LR tests produced
by anova(m2, reduce_m2, refit=TRUE) but other tools, e.g. package
RLRsim may produce even more accurate tests].

Cheers
Rune