Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros

TLDR

Count data with excess zeros arise in many fields, and while ZIP and ZINB models are common, simultaneous zero‑inflation and correlation from hierarchical designs pose challenges that existing methods may still address. This paper develops a multilevel ZINB regression to address these challenges. The model estimates parameters via an EM algorithm combined with penalized likelihood and REML for variance components, and also considers alternative ZIP strategies. The approach is illustrated on a dataset of decayed, missing, and filled teeth in 12‑year‑old children.

Abstract

Count data with excess zeros often occurs in areas such as public health, epidemiology, psychology, sociology, engineering, and agriculture. Zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression are useful for modeling such data, but because of hierarchical study design or the data collection procedure, zero-inflation and correlation may occur simultaneously. To overcome these challenges ZIP or ZINB may still be used. In this paper, multilevel ZINB regression is used to overcome these problems. The method of parameter estimation is an expectation-maximization algorithm in conjunction with the penalized likelihood and restricted maximum likelihood estimates for variance components. Alternative modeling strategies, namely the ZIP distribution are also considered. An application of the proposed model is shown on decayed, missing, and filled teeth of children aged 12 years old.