Counting outcomes such as days of physical activity or servings of fruits and vegetables often have distributions that are highly skewed toward the right with a preponderance of zeros, posing analytical challenges. This paper demonstrates how such outcomes may be analyzed with several modifications to Poisson regression. Five regression models 1) Poisson, 2) overdispersed Poisson, 3) negative b...

Mixture distributions provide flexibility in modeling data collected from populations having unexplained heterogeneity. While interpretations of regression parameters from traditional finite mixture models are specific to unobserved subpopulations or latent classes, investigators are often interested in making inferences about the marginal mean of a count variable in the overall population. Rec...

The Poisson regression is a popular approach in modeling count data. However, many situations often the variance of data greater than mean (over-dispersed data) and generalized or mixed models such as gamma (negative binomial), inverse Gaussian, lognormal, Lindley have been proposed alternatives to for describing over-dispersed In some situations, source over-dispersion large percentage zeros d...

Within the family of zero-inflated Poisson distributions, the data has Poisson distribution if any only if the mean equals the variance. In this paper we compare two closely related test statistics constructed based on this idea. Our results show that although these two tests are asymptotically equivalent under the null hypothesis and are equally efficient, one test is always more efficient tha...

It is well known that occurrence counts of words in documents are often modeled poorly by standard distributions like the binomial or Poisson. Observed counts vary more than simple models predict, prompting the use of overdispersed models like Gamma-Poisson or Beta-binomial mixtures as robust alternatives. Another deficiency of standard models is due to the fact that most words never occur in a...

SAS® PROC GLIMMIX fits generalized linear mixed models for nonnormal data with random effects, thus combining features of both PROC GENMOD and PROC MIXED. I will review the ideas behind PROC GLIMMIX and offer examples of Poisson and binary data. PROC NLMIXED also has the capacity to fit these kinds of models. After a brief introduction to that procedure, I will show an example of a zero-inflate...