I have a GLMM with Poisson distribution and random spatial block. My experimental design is 2x2 factorial, with 4 blocks, resulting in 16 total data points. Here is the specification of the model in R using the lme4 package.
lmer(rich ~ morph*caged + (1|block), family=poisson, data=bexData)
When I call summary on this object, I am returned
AIC BIC logLik deviance 18.58 22.44 -4.288 8.576 Random effects: Groups Name Variance Std.Dev. block (Intercept) 0 0 Number of obs: 16, groups: block, 4
I have left out the fixed effect parameter tests and correlations for brevity.
Here are my primary questions:
Can you use this output to calculate overdispersion?
- I have read that overdispersion can be calculated as the residual deviance divided by the residual degrees of freedom. Is that 8.576 / (16 - 4)? (Zuur et al., Mixed Effects Models)
If this calculation is correct, the estimator phi = 0.715. This indicates that there is not overdispersion in my data.
- Does this indicate that there is underdispersion?
- Is this a problem?
- Can anybody offer advice as to thresholds for over/underdispersion at which corrections to the models should be made? Zuur has said in one book that 5 is a common cutoff. Do people agree with that?
- How can such corrections be made?
I've also noticed here that the variance for the random effect is 0.
- Does this mean that there are precisely no error correlations between data points within my blocking factor?
- If this is so, why would a generalised linear model of the form shown at bottom have an AIC substantially higher, around 55?
- is AIC a reasonable method for choosing GLMM over GLM (as suggested by Zuur)?
glm(rich ~ morph*caged, data=bexData, family=poisson)