Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing

1992/02/01 by Diane Lambert · 4,001 citations
Decision Sciences · Mathematics · Medicine · #Advanced Statistical Process Monitoring #Environmental health #Mathematics #Medicine #Optimal Experimental Design Methods #Poisson distribution #Poisson regression #Regression #Regression analysis #Statistical Methods and Bayesian Inference #Statistics #Zero (linguistics) #Zero-inflated model

paper · doi:10.2307/1269547

published in Technometrics 34(1), 1 (Taylor & Francis)

openalex publication_date 1992/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Zero-inflated Poisson (ZIP) regression is a model for count data with excess zeros. It assumes that with probability p the only possible observation is 0, and with probability 1 – p, a Poisson(λ) random variable is observed. For example, when manufacturing equipment is properly aligned, defects may be nearly impossible. But when it is misaligned, defects may occur according to a Poisson(λ) distribution. Both the probability p of the perfect, zero defect state and the mean number of defects λ in the imperfect state may depend on covariates. Sometimes p and λ are unrelated; other times p is a simple function of λ such as p = l/(1 + λ T ) for an unknown constant T . In either case, ZIP regression models are easy to fit. The maximum likelihood estimates (MLE's) are approximately normal in large samples, and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the MLE's. Simulations suggest that the confidence intervals based on likelihood ratio test...

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