[R-sig-ME] GLMM with Poisson

[Ben Bolker]

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 ***
> ---