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.
© 2023 by the authors.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Article states: The data that support the findings of this study are openly available in “Data Files” at https://www.cdc.gov/nchs/nhis/1997-2018.htm (accessed on 27 May 2022)
Original Publication Citation
Arora, M., & Chaganty, N. R. (2023). Application of mixture models for doubly inflated count data. Analytics, 2(1), 265-283. https://doi.org/10.3390/analytics2010014
Arora, Monika and Chaganty, N. Rao, "Application of Mixture Models for Doubly Inflated Count Data" (2023). Mathematics & Statistics Faculty Publications. 226.