[RsigME] Binomial GLMM vs GLM question
Ben Bolker
bolker at ufl.edu
Fri May 16 15:18:16 CEST 2008
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Ken Beath wrote:
> Dear Dr. Bates and other LMER experts,
> I am admittedly entry level in my R and mixedmodel knowledge, but
> I'm hoping that someone can help me and also forgive my lack of
> insight. Over 3 years, I monitored survival of 350 egg masses at two
> ponds. I thus have one continuous variable (rainfall) and two discrete
> variables (year and pond). My response variable, mortality, is coded as
> a two column matrix featuring eggs survived and eggs dead. I'm primarily
> interested in the effect of rain on survival, but also if rain has
> different impacts at the different ponds and how much survival varied
> over the three years. Originally, I though I could tackle this with a
> binomial GLM, but do I need a binomial GLMM instead, as rainfall and
> year would be random and pond fixed? The problem with this is trying to
> make biological sense out of the results. I've spent the last week
> reading all the past posts about why pvalues can't be calculated and
> all that, which I'm fine with. But what can I say about the effects of
> rainfall or year on egg survival from the variance estimates? Also,
> doesn't LMER require that random factors be normally distributed,
> because my rainfall measurements are far from it. Is that a problem?
> Thank you in advance for any advice you can give.
> Justin Touchon
>

 I think your misunderstanding the idea of a random effect. This is
 something that is unobserved, causing correlation within a group. In your
 data this might be year or pond but definitely not rainfall which is
 simply a covariate. You have more than one measurement on a pond and more
 than one for each year, so it is likely that there will be correlation
 between them and one way of dealing with this is a random effect. The
 alternative is to use a fixed effects model. In your case, there are only
 2 and 3 groups, so a fixed effects model is the best approach, so a GLM is
 appropriate. If there were say 20 ponds, a random effects model would be
 much more suitable.

 Ken
~ Agreed.
~ One other point to watch out for (not directly related to GLMMs)
is that you should check the scale parameter estimate: I don't know if
the model you have below is sensible or not, but if you do end up
with an estimated scale parameter of 4.6, you must take overdispersion
into account (e.g., with a quasibinomial or betabinomial model).
~ Ben Bolker
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