[R] choosing between Poisson regression models: no interactions vs. interactions

[Ben Bolker]

James Milks <james.milks <at> wright.edu> writes:

> 
> My problem is deciding which model to use.  I have created several,  
> one without interaction terms (Total.vines~Site+Species+DBH), one  
> with an interaction term between Site and Species  
> (Total.vines~Site*Species+DBH), and one with interactions between all  
> variables (Total.vines~Site*Species*DBH).  Here is my output from R  
> for the first two models (the last model has the same number (and  
> identity) of significant variables as the second model, even though  
> the last model had more interaction terms overall):
> 

  A few comments:

 - the narrow answer to your question is to use the
interaction model: this would be the answer in several
different statistical frameworks.  In information-criteria-land,
the AIC is 10 points lower which constitutes a much better
expected predictive accuracy.  In classical likelihood-ratio-testing
land (try anova(model1,model2,test="Chisq")), you can probably also reject
the null hypothesis that adding the interaction terms doesn't
improve the model (sorry about the convoluted language, but that's
what you get in LRT-land).  Also, the presence of *any* statistically
significant interaction suggests that you probably can't neglect interactions.
The number of significant terms in each model is largely
irrelevant.

  - You should probably consider whether there is overdispersion
in your data (e.g. try fitting a quasipoisson or negative binomial
model, although you can't use AIC or LRT (=anova()) with quasipoisson
models), since there usually is in ecological data.

  - your question suggests you might want to read up a bit
more on generalized linear models  -- Agresti's intro to categorical
data analysis or Crawley's intro to data analysis with S-PLUS
would work.  (If you're familiar with logistic regression, Poisson
regression should follow almost exactly the same rules and conventions.)

  good luck,
    Ben Bolker