Regression Models for Count Data in R

By Achim Zeileis, Christian Kleiber, S. Jackman. 2008

2,545 citations recorded by the source corpus.

The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of zero-inflated and hurdle regression models in the functions zeroinfl() and hurdle() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both model classes are able to incorporate over-dispersion and excess zeros - two problems that typically occur in count data sets in economics and the social and political sciences - better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d8d139a250b7d30ac917dda842096b65819f1a8e

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Citations in the corpus

Modeling zero-inflated count data with glmmTMB (2017, methodology): “In R, there are five main packages available for modeling zero-inflated data: pscl, INLA, MCMCglmm, glmmADMB, and brms (Table 1; Zeileis et al., 2008; Rue et al., 2009; Hadfield, 2010; Skaug et al., 2012; Bürkner, in press).”
The consequences of checking for zero‐inflation and overdispersion in the analysis of count data (2019, methodology): “ation between Y and X, we dene the following hypothesis test: H 0 : X = 0 vs. H 1 : X 6= 0. A simple likelihood ratio test (LRT), or Wald test will provide a p-value to evaluate this hypothesis; see Zeileis et al. (2008). The LRT and Wald test are asymptotically equivalent. For the likelihood ratio ”
Half-Normal Plots and Overdispersed Models in R: The hnp Package (2017, methodology): “New functions were written for zero-inﬂated binomial and zero-inﬂated beta-binomial models ﬁtted with glmmADMB (Skaug et al. 2014) and for zero-inﬂated and hurdle Poisson and negative binomial models ﬁtted with pscl (Zeileis et al. 2008).”
Bamboo overabundance alters forest structure and dynamics in the Atlantic Forest hotspot (2012, methodology): “, 2008), pscl (Zeileis et al., 2008; Jackman, 2010), and bbmle (Bolker, 2009).”
Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data (2015, methodology): “Linear predictors for the count and zero-inflation part can be specified in the package pscl (Zeileis, Kleiber, and Jackman 2008), while the scale parameter of the negative binomial distribution is always assumed constant.”
Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R (2020, methodology): “A basic negative binomial hurdle model is fitted with the hurdle function from the pscl package (Zeileis et al. 2008) using the Aghion et al.”
Visualizing Count Data Regressions Using Rootograms (2016, methodology): “…distributions fitted via fitdistr() (to objects of class ‘numeric’, Venables and Ripley 2002), zero-inflated models (objects of class ‘zeroinfl’, Zeileis, Kleiber, and Jackman 2008), zero-truncated models (objects of class ‘zerotrunc’, as fitted by the zerotrunc() function in countreg),…”
Extended Poisson–Tweedie: Properties and regression models for count data (2016, methodology): “, 1998) and solved by including hurdle or ZI components (Zeileis et al., 2008).”
Drivers of taxonomic bias in conservation research: a global analysis of terrestrial mammals (2020, methodology): “We explored the relationship between the different explanatory variables and research 210 productivity at the species level using a hurdle model analysis for zero-inflated count data 211 (Zeileis et al., 2008).”