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

[Victoria Ortiz]

 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?

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.

Thank you for your time!
Victoria.

2018-04-27 17:08 GMT-03:00 Ben Bolker <bbolker at gmail.com>:

>
>
> On 2018-04-26 07:45 PM, Victoria Ortiz wrote:
> > I write to ask a simple question about quantitative continuous variables
> > distributions. We have data for morphological traits in insects but they
> do
> > not fit any distribution in GLMM. The design has two fixed variables and
> a
> > random one. We are interested in the variance components of the random
> > variable and its interactions. We tried normal (lm4), gamma (glmer),
> > lognormal (GLMMPQL), tweedie (GLMMTMB) and compound poison (CPLM). There
> is
> > no good fit for any case. In fact, the better model using AIC is normal.
> The
> > residuals vs. predicted graphic and the Q-Q plot have the following
> > form: *https://github.com/vicrotas/Repositorio-de-Vicka/issues/1
> > <https://github.com/vicrotas/Repositorio-de-Vicka/issues/1>*
> >
>
>
>   I'm not quite sure what to suggest about the distribution.  Since this
> looks left-skewed, you might try a power transformation with g > 1 (e.g.
> x^1.5) to shift it.  (That would be applied to the data rather than the
> residuals, so might not work perfectly ...) For a rough idea, you could
> run a Box-Cox analysis on the residuals.
>
>   Alternatively, if you can figure out a permutation approach that works
> (e.g. permutation within and between groups) that could give you a
> distribution-robust way to get a p-value.
>
> >
> >
> > Given that the fit to normal distribution is not good, we want to know if
> > there is any other distribution we could try. What else we can do in this
> > scenario?
> >
> >
> >
> > On the other hand, to estimate the variance components we used the
> > following in lmer:
> >
> >
> >
> > m1 <- lmer ( variable ~ fixed factor  1 * fixed factor 2 + (fixed factor
> 1
> > * fixed factor 2 || random factor))
> >
> >
> >
> > The specific question is if the double bar ('| |') is a good way to
> > estimate the variance components or if there is another way to do it?
>
>   Can you clarify what you mean by "variance components"? Are you
> explicitly trying to partition variance, or are you just trying to make
> sure that you control for among-group variation?
>
>   If your data will support it, I think it would be better to fit the
> unstructured variance-covariance matrix; if not, you could try one of
> the Bayesian methods (blme, MCMCglmm, brms, rstanarm ...) that would
> allow you to regularize/put a prior on the variance-covariance matrix.
>
>
> >
> >
> >
> > Thanks in advance!
> >
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> >
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> >
>
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