Zero-and-one Inflated Regression Models And Statistical Diagnostics

Count data is a very common type of data and widely arise in our lives, such as insurance, psychology, economics and biomedical Science and other fields abound. However, when dealing with some issues about 0 and 1 data, we often encounter a lot of special data sets, which are named as zero-and-one inflated data. The mean and variance of such data sets are large. Therefore, we also call them Over-dispersion count data.For such data, we tend to adopt some of more classical count data model to study them, for example, Poisson regression model, Binomial regression model. But the results are often unsatisfactory. So we will consider zero inflated regression models, such as zero-inflated poisson regression models, zero-inflated binomial regression model and zero-inflated negative binomial regression model to study them. Simulation study results show that fitting of this type of model are not very good. More reasonable models will be considered to analysis more and more 0 and 1 data sets.Thus, This paper proposed zero-and-one inflated Poisson regression model (ZOIP) and zero-and-one inflated binomial regression model (ZOIB) and gave parameter estimates for these models. Based on the data deletion model, this paper considered statistical diagnosis of above-mentioned models. By a simulation study, the paper compared with the results of different models. Finally, this paper gives a elementary outlook.