Comparação entre alguns modelos de regressão de contagem

Abstract

Count data reflects the number of occurrences of a behavior of interest in a given period of time (for example, a team’s goals number in Brasileirão). A common behavior of this type of data is the presence of many zeros observed, i.e. zero-inflation, which ends up somewhat overturning the estimates obtained by the Poisson and Negative Binomial Regression models, usually used to model these type of data. With this in mind, this work set out to study the variations of these models, following two fronts: The first considering models that contain a possible excess of zeros and a second, which compares models from recent literature to check whether they are good alternatives in terms estimates and performance. In total, seven models were trained, the two mentioned above, plus: Poisson-Tweedie, Bell, Zero-inflated Poisson, Zero-inflated Negative Binomial and Zero-inflated Bell. Thus, different simulation scenarios were studied by computing metrics such as mean, standard deviation, REQM and model selection criteria, such as AIC and BIC. It is worth noting that both the classical and Bayesian study methods were used for comparative classification of estimates. In addition to the simulation studies, two applications to real data are presented. As a result of the different scenarios, we understand that the models that have an exclusive part to accommodate possible excesses of zeros had greater adherence to the data in applications. Regarding the models presented in recent literature, we can state that there is similarity in the adjustments made, which validates previous studies and guarantees that they are good alternatives to the Poisson and Negative Binomial models.