# GLM Poisson Regression with Overdispersion

I use R for a poisson regression (GLM) to test for a difference in the number of years of schooling based on race (6 categories) and religion (3 categories), see structure of dataset and output below. Since the original poisson model suffers from rather significant overdispersion I conducted the same analysis but with a quasipoisson distribution.

Structure of dataset:

GLM Quasipoisson regression:

ANOVA - Test predictors relative to the full model:

1. The output of the quasipoisson regressions shows one statistically significant interaction. I read the following "use F tests with an empirical scale parameter instead of chi-squared (The R Book, Crawley M. J. 2013. p. 570)" as yet another suggested technique to deal with overdispersion. Hence, I conduct an ANOVA with an F-test for the model which then shows that the interaction term is not statistically significant. What is the correct way to interpret this result? Should I, based on the ANOVA state that the interaction is not statistically significant and then instead go on trying a model without the interaction term?

• @JanC Not quite. According to Crawley, the significance test in the Pr(>|t|) is exactly the chi-square test that he advocates against. The "reduced" model requires a re-estimate of the dispersion parameter to give you the $F$ test. I think you can fit that full model as ~Race * Religion and the reduced model as ~Race*Religion - RaceMulato:ReligionEvangelic. Then the two models can be supplied to the aov command. May 27 at 15:46