Zero-inflated logit probit model: a novel model for binary data

Abstract

–This article proposes a novel model in the family zero-inflated (ZI) binary models which we named it a ZI Logit Probit (ZILP) model. This model can be employed to analyze the binary data that has an exorbitant number of zero counts. In the scope of this work, we first present the general formula, connected functions, and estimating equation (EE) of the ZILP model. We next rely on some popular regularity conditions to present theory of large-sample for this model. To have many numerical proofs, multiple simulations and a real medical data set were executed in this study. We perform the number of infected blood cells (IBC) data set to test the effectiveness and stability of the maximum likelihood estimation (MLE) method in estimating the parameters for the ZILP model. The results obtained in the analysis of actual medical data are significant and important in practice. The results indicated that smoking status would have no effect on the number of IBCs, however, gender would more or less have an effect on the number of IBCs. Finally, some discussions and conclusions are given in this article.