GLMM with Poisson
Zofia Ecaterina Taranu <zofia.taranu at ...> writes:
I have a question for conducting a GLMM with the Poisson distribution. I ran the following command:
Mglmm1<-lmer(Richness ~ 1 + NAP + fExp + (1 | fBeach), family=poisson(link="log"),data=RIKZ) summary(Mglmm1)
I prefer glmer() to make it explicit that this is a GLMM (but it doesn't really matter at present).
However, in the summary output does not provide the null and residual deviances to determine wether overdispersion has occurred. How can I calculate these values given the model output below?
The residual deviance is given in the first summary line (with AIC, BIC, logLik). You could get a null deviance by fitting whatever you consider to be the null model (it might be ~1, or it might ~1 + (1|fBeach): you decide). You can get the Pearson chi-squared goodness-of-fit statistic as sum(residuals(Mglmm1)^2) (lme4 gives Pearson residuals for GLMMs by default.) It's also a bit tricky to decide what the residual df are (how do you count random effects?), but we could say that this model has 4 parameters (intercept, NAP, fExp11, among-fBeach variance) and hence 41 residual df, so deviance/residual df is *approximately* 1.5 -- may be worth trying an observation-level random effect to see what happens (or just inflating the standard errors of the estimates by sqrt(1.5)).
Generalized linear mixed model fit by the Laplace approximation
Formula: Richness ~ 1 + NAP + fExp + (1 | fBeach)
Data: RIKZ
AIC BIC logLik deviance
71.56 78.78 -31.78 63.56
Random effects:
Groups Name Variance Std.Dev.
fBeach (Intercept) 0.060445 0.24586
Number of obs: 45, groups: fBeach, 9
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.04181 0.13302 15.350 < 2e-16 ***
NAP -0.50383 0.07421 -6.789 1.13e-11 ***
fExp11 -0.86703 0.22353 -3.879 0.000105 ***
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