Poisson-Tweedie Models for Count Data with Excessive Zeros. Comparison with the Negative Binomial Model

Abstract

The presence of a large number of zero counts is quite common in studies involving count data. This causes overdispersion. Therefore, different types of models have been proposed as alternatives and a very frequent practice is to use the negative binomial model. In 2018, Bonat (2018) considered a new type of model, based on the Poisson-Tweedie dispersion models, which can automatically adapt to different degrees of overdispersion in count data. This article presents a simulation study in order to compare the estimates derived from the Poisson-Tweedie model for a wide range of overdispersed data with estimates derived from the negative binomial model. In both models, the relative percent bias of the estimated coefficients was very small. Nevertheless, the Poisson-Tweedie model showed a better performance with smaller values for the mean squared errors, particularly in scenarios with more dispersion. Hence, it would be possible to suggest the data analyst in which situations it would be enough to work with the popular negative binomial model or when it would be best to use the Poisson-Tweedie family. Additionally, the comparison between the fit of the negative binomial model and that of the Poisson-Tweedie family is illustrated by analysing the number of pediatric consultations of a group of children who receive health care in a public health center in Rosario, Argentina. Although the results obtained in both models were similar, the estimates in the Poisson-Tweedie model were more accurate.