Wald Confidence Intervals for the Parameter in a Bernoulli Component of Zero-Inflated Poisson and Zero-Altered Poisson Models with Different Link Functions

Abstract

This paper aims to study the Wald confidence intervals for the parameters in a Bernoulli component of the zero-inflated Poisson (ZIP) and zero-altered Poisson (ZAP) models. The effects of the model choices between ZIP and ZAP with three different link functions: logit, probit, and complementary log-log, are investigated. Akaike’s information criterion (AIC) is normally used for comparing models with different links in the literature. However, use of AIC is not advisable for the model comparison of non-nested models. To study the performance of the confidence intervals with different links, the coverage probability (CP) should be used because the AIC criterion can be misleading. The effects of the parameters in ZIP and ZAP distributions were also studied. The CPs are estimated from Monte-Carlo simulations, where the data are generated from both ZIP and ZAP distributions. The results show that when the employed model corresponds to the distribution of data, the link function and parameters of the distributions do not have much impact on the CPs. Conversely, if the wrong model is used, the components of the Bernoulli and the mean of count data are essential to determine the CPs of the intervals. Overall, the ZIP models tend to outperform the ZAP models, and the Wald confidence intervals with different links have approximately the same performance, regardless of any model used for fitting the data. If the mean of positive counts is large, both the ZAP and ZIP models tend to produce the same CPs or have the same performance.