In this article we propose a multiple-inflation Poisson regression to model count response data containing excessive frequencies at more than one non-negative integer values. To handle multiple excessive count responses, we generalize the zero-inflated Poisson regression by replacing its binary regression with the multinomial regression, while Su et al. [Statist. Sinica 23 (2013) 1071–1090] proposed a multiple-inflation Poisson model for consecutive count responses with excessive frequencies. We give several properties of our proposed model, and do statistical inference under the fully Bayesian framework. We perform simulation studies and also analyze the data related to the number of infections collected in five major hospitals in Turkey, using our methodology.
"Bayesian analysis of multiple-inflation Poisson models and its application to infection data." Braz. J. Probab. Stat. 32 (2) 239 - 261, May 2018. https://doi.org/10.1214/16-BJPS340