Goodness of fit test for a zero-inflated Bernoulli regression model

Abstract

The goodness of fit (GOF) test is an intensely crucial and meaningful issue in scientific research because it is widely applied in sciences such as statistics, applied mathematics, economics, finance, engineering, and so on. To the extent of this article, we first revisit the GOF test for the logistic model, and then we propose the GOF test for the zero-inflated Bernoulli (ZIBer) model. We seek to establish Karl Pearson’s chi-square test and unweighted residual sum of square test for this model. Afterward, we demonstrate that both tests have an asymptotic normal distribution with a mean and standard deviation that they derived. Simulation studies and an actual data set are also studied to illustrate the effectiveness of the proposed method.