A Study on Tests for Zero-Inflated Poisson Regression

In analyzing counts data we sometimes encounter excessive zeros than that can be expected under Poisson distributional assumption. For this kind of data we are to model by an alternative counts distribution such as the zero-inflated Poisson distribution. There have been many tests for zero-inflated distribution against the Poisson distribution; the score test, the likelihood ratio test, and the Vuong test. Each of these tests has some limitation in applying under the nonstandard conditions of boundary constraints and non-nested relationships between models. Some researches suggested the weighted sum of independent chi-squared random variables as an asymptotic distribution of the likelihood ratio test but it is not fully studied in the case of non-nested models, in which the Vuong test can generally be used to compare two competing models. We are purposed to recommend an appropriate testing procedure that performs well in both of level controls and higher powers when we are to compare the ordinary Poisson versus zero-inflated Poisson models. We conduct an empirical study to compare the tests for zero-inflated Poisson regression in respect of powers and level controls based on the different asymptotic distributions.