Zero-and-one-inflated Poisson regression model

In this paper, a zero-and-one-inflated Poisson (ZOIP) regression model is proposed. The maximum likelihood estimation (MLE) and Bayesian estimation for this model are investigated. Three estimation methods of the ZOIP regression model are obtained based on data augmentation method which is expectation-maximization (EM) algorithm, generalized expectation-maximization (GEM) algorithm and Gibbs sampling respectively. A simulation study is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, an accidental deaths data set is analyzed to illustrate the practicability of the proposed method.