Counting models for overdispersed data: A review with application to tuberculosis data - Místico Azevedo, Alcinei; Jesus Silva, Ítallo; Carlota Nery, Marcela; Paz Rocha, Honovan; Alves Santana, Rogério (Brazilian Journal of Biometrics, 2023)
The present work reviews distributions for counting data: Poisson; Negative Binomial; COM-Poisson and Generalized Poisson, and their regression models. Aspects such as parameter estimation and model choice criteria are presented. And as an application example, we use the regression models of these distributions to explain the relationship between tuberculosis notifications with the HDI Human Development Index of the 102 cities in the state of Alagoas. The existing relationship between notifications of tuberculosis with HDI is significant and overdispersion at the level α = 5% of probability, and the COM-Poisson distribution regression model was the best fit data, according to the Akaike AIC and Bayesian BIC information criteria.