Ferramentas de diagnóstico para dados de contagem inflacionados de zeros

Abstract

Count data with excess zeros are common in several applied fields, such as health sciences, social sciences, and agronomy, posing challenges to traditional modeling approaches initially based on the Poisson distribution, which assumes equidispersion. In this study, models within the framework of Generalized Linear Models (GLMs) were investigated and applied to handle such data sets, namely the Poisson model, the Negative Binomial model, and the zero-inflated models ZIP (Zero-Inflated Poisson) and ZINB (Zero-Inflated Negative Binomial). The main objective was to compare the performance of these models using a real data set from a marital therapy study, in which the response variable is the number of steps toward divorce (MSI), characterized by excess zeros and overdispersion. In addition to model fitting, diagnostic tools were developed and applied, including Pearson and deviance residuals, quantile residuals, HNP plots, Quantile–Quantile plots with simulated envelopes, worm plots, and Cook’s distance, in order to assess model adequacy and identify potential influential observations. The results indicated that the ZIP and ZINB models provided a better fit to the data, presenting lower AIC and BIC values and residuals with more satisfactory behavior. The Vuong test did not indicate a statistically significant difference between the ZIP and ZINB models, suggesting that the ZIP model, due to its greater parsimony, may be preferable for the analyzed data set.