Flexible models for non-equidispersed count data: comparative performance of parametric models to deal with underdispersion

Count data as response variables are commonly modeled using Poisson regression models, which require equidispersion, i.e., equal mean and variance. However, this relationship does not always occur, and the variance may be higher or lower than the mean, phenomena are known as overdispersion and underdispersion, respectively. Non-equidispersion, when disregarded, can lead to a number of misinterpretations and inadequate predictions. Here, we compare the use of the COM-Poisson, double Poisson, Gamma-count, and restricted generalized Poisson models as a more flexible class for count problems associated with over- and underdispersion, since they have an additional parameter that allows more flexible analysis. The proposed method is useful in different applications, but here we provide an example using an underdispersed dataset concerning ecological invasion. For validation of the models, we use half-normal plots. The COM-Poisson, double Poisson, and Gamma-count performed best and properly modeled the underdispersion. The use of correct statistical models is recommended to handle this data property using objective criteria to ensure accurate statistical inferences.