I am trying to model count data in R that is apparently underdispersed (Dispersion Parameter ~ .40). This is probably why a
family = poisson or a negative binomial (
glm.nb) model are not significant. When I look at the descriptives of my data, I don't have the typical skew of count data and the residuals in my two experimental conditions are homogeneous, too.
So my questions are:
Do I even have to use special regression analyses for my count data, if my count data doesn't really behave like count data? I face non-normality sometimes (usually due to the kurtosis), but I used the percentile bootstrap method for comparing trimmed means (Wilcox, 2012) to account for non-normality. Can methods for count data be substituted by any robust method suggested by Wilcox and realized in the WRS package?
If I have to use regression analyses for count data, how do I account for the under-dispersion? The Poisson and the negative binomial distribution assume a higher dispersion, so that shouldn't be appropriate, right? I was thinking about applying the quasi-Poisson distribution, but that's usually recommended for over-dispersion. I read about beta-binomial models which seem to be able to account for over- as well as underdispersion are availabe in the
VGAMpackage of R. The authors however seem to recommend a tilded Poisson distribution, but I can't find it in the package.
Can anyone recommend a procedure for underdispersed data and maybe provide some example R code for it?