Journal ArticleDOI
Zero-inflated Poisson regression, with an application to defects in manufacturing
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TLDR
Zero-inflated Poisson (ZIP) regression as discussed by the authors is a model for counting data with excess zeros, which assumes that with probability p the only possible observation is 0, and with probability 1 − p, a Poisson(λ) random variable is observed.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...read more
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glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling
Mollie Elizabeth Brooks,Kasper Kristensen,Koen J. van Benthem,Arni Magnusson,Casper Willestofte Berg,Anders Nielsen,Hans J. Skaug,Martin Mächler,Benjamin M. Bolker +8 more
TL;DR: The glmmTMB package fits many types of GLMMs and extensions, including models with continuously distributed responses, but here the authors focus on count responses and its ability to estimate the Conway-Maxwell-Poisson distribution parameterized by the mean is unique.
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Negative Binomial Regression
TL;DR: In this article, the authors introduce the concept of risk in count response models and assess the performance of count models, including Poisson regression, negative binomial regression, and truncated count models.
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Analyzing developmental trajectories: A semiparametric, group-based approach
TL;DR: Agroup-based method for identifying distinctive groups of individual trajectories within the population and for profiling the characteristics of group members is demonstrated.
Journal ArticleDOI
A SAS procedure based on mixture models for estimating developmental trajectories
TL;DR: In this paper, a new SAS procedure, TRAJ, is proposed to fit semiparametric mixtures of censored normal, Poisson, zero-inflated Poisson and Bernoulli distributions to longitudinal data.
Journal ArticleDOI
Regression Models for Count Data in R
TL;DR: In this article, a new implementation of hurdle and zero-inflated regression models in the functions hurdle() and zeroinfl() from the package pscl is introduced, which reuses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models.
References
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Book
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Peter McCullagh,John A. Nelder +1 more
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