# Which type of regression model for count data should I use for log-series?

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?

## migrated from stackoverflow.comAug 12 '18 at 19:19

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• Please describe your models in more detail. This sounds very odd. – Peter Flom Aug 12 '18 at 21:36

Another natural extension to the Poisson GLM is the negative binomial GLM, which is implemented in R using the glm.nb function in the MASS package. The negative binomial distribution is a two-parameter distribution which generalises the Poisson distribution, with an additional parameter that controls "overdispersion" in the variance. The distribution has a natural association with count data through mixtures of Poisson distributions, or through counts of a binary outcome until its opposite.