A multivariate zero-inflated binomial model for the analysis of correlated proportional data

Dianliang Deng; Yiguang Sun; Guo-Liang Tian

doi:10.1080/02664763.2021.1918649

A multivariate zero-inflated binomial model for the analysis of correlated proportional data

J Appl Stat. 2021 Apr 24;49(11):2740-2766. doi: 10.1080/02664763.2021.1918649. eCollection 2022.

Authors

Dianliang Deng¹, Yiguang Sun¹, Guo-Liang Tian²

Affiliations

¹ Department of Mathematics and Statistics, University of Regina, Regina, Canada.
² Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen City, Guangdong, People's Republic of China.

Abstract

In this paper, a new multivariate zero-inflated binomial (MZIB) distribution is proposed to analyse the correlated proportional data with excessive zeros. The distributional properties of purposed model are studied. The Fisher scoring algorithm and EM algorithm are given for the computation of estimates of parameters in the proposed MZIB model with/without covariates. The score tests and the likelihood ratio tests are derived for assessing both the zero-inflation and the equality of multiple binomial probabilities in correlated proportional data. A limited simulation study is performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates and to compare the nominal levels and powers of both score tests and likelihood ratio tests. The whitefly data is used to illustrate the proposed methodologies.

Keywords: Correlated proportional data; EM algorithm; likelihood ratio test; multivariate zero-inflated binomial; score test; stochastic representation.

Grants and funding

The research of first author is partially supported by Natural Sciences and Engineering Research Council of Canada(NSERC). Guo-Liang Tian's research was fully supported by National Natural Science Foundation of China (Grant No. 11771199).