I have long-term collection data, and I'd like to test, whether the number of animals collected is influenced by weather effects. My model looks like below:
glmer(SumOfCatch ~ I(pc.act.1^2) +I(pc.act.2^2) + I(pc.may.1^2) + I(pc.may.2^2) + SampSize + as.factor(samp.prog) + (1|year/month), control=glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=1e9,npt=5)), family="poisson", data=a2)
Explanation of the used variables:
- SumOfCatch: number of animals collected
- pc.act.1, pc.act.2: axes of a principal component representing weather conditions during sampling
- pc.may.1, pc.may.2: axes of a PC representing weather conditions in May
- SampSize: number of pitfall traps, or collecting transects of standard lengths
- samp.prog: method of sampling
- year: year of sampling (from 1993 to 2002)
- month: month of sampling (from Aug to Nov)
The fitted model's residuals show considerable inhomogeneity (heteroscedasticity?) when plotted against fitted values (see Fig.1):
My main question is: is this a problem making the reliability of my model questionable? If so, what can I do to resolve it?
So far I have tried the followings:
- control for overdispersion by defining observation-level random effects, i.e. using a unique ID for each observation, and applying this ID variable as random effect; although my data do show considerable overdispersion, this did not help as the residuals became even more ugly (see Fig. 2)
- I fitted models without random effects, with quasi-Poisson glm and glm.nb; also yielded similar residual vs. fitted plots to the original model
As far as I know, there might be ways for the estimation of heteroscedasticity-consistent standard errors, but I have failed to find any such method for Poisson (or any other kind of) GLMMs in R.
In response to @FlorianHartig: the number of observations in my dataset is N=554, I think this is a fair obs. number for such a model, but of course, the more the merrier. I post two figures, first of which is the DHARMa scaled residual plot (suggested by Florian) of the main model.
The second figure is from a second model, in which the only difference is that it contains the observation-level random effect (the first does not).
Figure of the relationship between a weather-variable (as predictor, i.e. x-axis) and sampling success (response):
Figures showing predictor values vs. residuals: