A goodness of fit test for zero-inflated Poisson regression models

Zero-inflated Poisson (ZIP) regression models are a special class of statistical models that can be used in place of traditional count data models such as Poisson regression, in the presence of excess zeros within the count data. However, when it comes to evaluating the appropriateness of a fitted ZIP regression model, there is no suitable Goodness of Fit (GOF) test available, which could be due to the added complexity present within the model. Therefore, this paper presents a model based GOF test for ZIP regression models. The proposed model based GOF test was developed in accordance with one of the grouping strategies specified under the well-known Hosmer-Lemeshow test. Extensive simulation studies were conducted to assess the performance of the test with regard to type I error rate and power for 5 different sample sizes, including relatively small as well as large sample sizes. The results indicated that the GOF test is effective in terms of type I error rate, while it maintained above 98% power for all the sample sizes. Furthermore, the applicability of the GOF test to real-world scenarios was further established by applying the GOF test to a real-world zero-inflated dataset with overdispersion.