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

Ben Bolker bbolker at gmail.com
Fri Apr 27 22:08:00 CEST 2018

```
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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