I'm trying to choose the best distribution family for generalized linear regression. My outcome is cross-sectional, over-dispersed proportion data (# of behaviors/20-22 possible behaviors). I used the functions
plotdist from the package
fitdistrplus to visually rule out the binomial and poisson distributions, so now I'm choosing between the beta-binomial, quasibinomial, and negative binomial distributions.
Note: I don't really understand the beta-binomial distribution, but a lot of searching on this site suggested that it's often most appropriate for overdispersed proportion data.
Key info: I'm inclined to select the negative binomial distribution because
(1) I understand
glm.nb has the lowest AIC, provides similar results to both the beta-binomial and quasibinomial analyses, and my outcome closely aligns visually with the theoretical negbin distribution (see graphs below).
fitdistrpluspackage does not support the betabinomial distribution, so I don't know how to visually compare my data with its theoretical distribution. Is it possible to visually compare the binomial and beta-binomial distributions? How would I do that in R?
- What are the pros and cons of selecting the negative binomial in this case? I read in Wagner (2015) that the negative binomial is supposed to approximate the beta-binomial distribution. What does that mean for my analysis?
Wagner, B., Riggs, B., & Mikulich-Gilbertson, S. 2015. The importance of distribution-choice in modeling substance use data: a comparison of negative binomial, beta binomial, and zero-inflated distributions. American Journal of Drug and Alcohol Abuse, 41(6), 489–497.