A doubly-inflated Poisson regression for correlated count data

Erfan Ghasemi, Alireza Akbarzadeh Baghban, Farid Zayeri, Asma Pourhoseingholi and Seyed Mohammadreza Safavi

Journal of Applied Statistics, 2021, vol. 48, issue 6, 1111-1127

Abstract: Count data have emerged in many applied research areas. In recent years, there has been a considerable interest in models for count data. In modelling such data, it is common to face a large frequency of zeroes. The data are regarded as zero-inflated when the frequency of observed zeroes is larger than what is expected from a theoretical distribution such as Poisson distribution, as a standard model for analysing count data. Data analysis, using the simple Poisson model, may lead to over-dispersion. Several classes of different mixture models were proposed for handling zero-inflated data. But they do not apply to cases when inflated counts happen at some other points, in addition to zero. In these cases, a doubly-inflated Poisson model has been suggested which only be used for cross-sectional data and cannot consider correlations between observations. However, correlated count data have a large application, especially in the health and medical fields. The present study aims to introduce a Doubly-Inflated Poisson models with random effect for correlated doubly-inflated data. Then, the best performance of the proposed method is shown via different simulation scenarios. Finally, the proposed model is applied to a dental study.

Date: 2021
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DOI: 10.1080/02664763.2020.1757049

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