Zero‐inflatedmodeling part I: Traditionalzero‐inflatedcount regression models, their applications, and computational tools

Abstract

Count regression models maintain a steadfast presence in modern applied statistics as highlighted by their usage in diverse areas like biometry, ecology, and insurance. However, a common practical problem with observed count data is the presence of excess zeros relative to the assumed count distribution. The seminal work of Lambert (1992) was one of the first articles to thoroughly treat the problem of zero-inflated count data in the presence of covariates. Since then, a vast literature has emerged regarding zero-inflated count regression models. In this first of two review articles, we survey some of the classic and contemporary literature on parametric zero-inflated count regression models, with emphasis on the utility of different univariate discrete distributions. We highlight some of the primary computational tools available for estimating and assessing the adequacy of these models. We concurrently emphasize the diverse data problems to which these models have been applied.

Individualised risk prediction model for exacerbations in patients with severe asthma: protocol for a multicentre real-world risk modelling study

“…We will use the final set of predictors to develop a zero-inflated negative binomial regression model to predict individualised rate of severe exacerbation in the next 12 months in patients with severe asthma 41. The zero-inflated component captures the potential excess number of patients who will have no severe exacerbations in the following 12 months 41. This model allows flexible prediction of severe exacerbation count, from which the risk of ≥1 severe exacerbation (the primary prediction endpoint) can be calculated.…”

“…41 The zeroinflated component captures the potential excess number of patients who will have no severe exacerbations in the following 12 months. 41 This model allows flexible prediction of severe exacerbation count, from which the risk of ≥1 severe exacerbation (the primary prediction endpoint) can be calculated. In the meantime, the prediction model is flexible enough to also produce predicted rates (secondary prediction endpoint).…”

A Review on Differential Abundance Analysis Methods for Mass Spectrometry-Based Metabolomic Data

“…Two types of zero-inflated data are frequently seen in practice; one is zero-inflated count data and the other is zero-inflated nonnegative continuous data. A recent review summarized zero-inflated count models and their applications [39]. Reviews on zero-inflated nonnegative continuous data are also available [40,41].…”

Enhancing detection of labor violations in the agricultural sector: A multilevel generalized linear regression model of H-2A violation counts

“…We assumed that structural zeros occur with probability F. Therefore, the probability mass function (pmf) for a ZINB can be formulated as follows [97]:…”