Application of Mixture Models for Doubly Inflated Count Data

Abstract

In health and social science and other fields where count data analysis is important, zero-inflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k > 0 occurs with high frequency. The zero- and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation–maximization (EM) algorithm to obtain the parameter estimates for grouped zero and k-inflated count data. The asymptotic standard errors are derived using the complete data approach. We compare the zero- and k-inflated Poisson model with its zero-inflated and non-inflated counterparts. The best model is selected based on commonly used criteria. The theoretical results are supplemented with the analysis of two real-life datasets from health sciences.

Multiple Arbitrarily Inflated Negative Binomial Regression Model and its Application

“…We use the negative loglikelihood (−ℓ) and the Akaike information criterion (AIC) to compare the results. The result in Table 2 shows that the MAINB {2-3,10-12,>12} distribution fits the data best and better than what was proposed in previous articles by ZOIP Arora (2018). It is also shown that all MAINB {2-3,10-12,>12} parameters are significant, indicating the existence of inflation at the counts proposed in our study.…”