I am attempting to identify the effects of mealtime habits on fast food consumption. In this case, the dependent variable is number of times per week a respondent reported eating fast food. As this is count data, I'm using a Poisson or Poisson-related distribution. However there are a few issues with this data. First, tests for overdispersion revealed that my dependent variable is indeed overdispersed:
Overdispersion test data: model8.poisson z = 8.2298, p-value < 2.2e-16 alternative hypothesis: true dispersion is greater than 1 sample estimates: dispersion 1.950116
So, a poisson regression is inappropriate.
I also estimated quasipoisson and zero-inflated models, and tested for model fit versus the poisson models. Both the quasi-poisson and zero-inflated were better fits.
Ord plot shows a positive slope (
1.62) and a negative intercept (
-1.82) which suggests that I should use a log-series model. I have a rudimentary understanding of poisson quasi-poisson distribution models, and negative binomial models. However, I can't find anything on log-series models.
Are there specialized models for these types of data, or should I use one of the other Poisson-related distributions or models (quasipoisson, zero-inflated, negative binomial)?
If there are specialized models, is there an r package for them?
If there are not, which type of model would best fit these data?