Visualizing Count Data Regressions Using Rootograms
2016/04/27 by Christian Kleiber, Achim Zeileis · 29 citations
Mathematics · Computer Science · #Statistical Methods and Bayesian Inference #Data Analysis with R #Census and Population Estimation
paper · doi:10.1080/00031305.2016.1173590
Abstract
The rootogram is a graphical tool associated with the work of J. W. Tukey that was originally used for assessing goodness of fit of univariate distributions. Here we extend the rootogram to regression models and show that this is particularly useful for diagnosing and treating issues such as overdispersion and/or excess zeros in count data models. We also introduce a weighted version of the rootogram that can be applied out of sample or to (weighted) subsets of the data, e.g., in finite mixture models. An empirical illustration revisiting a well-known data set from ethology is included, for which a negative binomial hurdle model is employed. Supplementary materials providing two further illustrations are available online: the first, using data from public health, employs a two-component finite mixture of negative binomial models, the second, using data from finance, involves underdispersion. An proglangR implementation of our tools is available in the proglangR~package pkgcountreg. It also contains the data and replication code. The rootogram is a graphical tool associated with the work of J. W. Tukey that was originally used for assessing goodness of fit of univariate distributions. Here we extend the rootogram to regression models and show that this is particularly useful for diagnosing and treating issues such as overdispersion and/or excess zeros in count data models. We also introduce a weighted version of the rootogram that can be applied out of sample or to (weighted) subsets of the data, e.g., in finite mixture models. An empirical illustration revisiting a well-known data set from ethology is included, for which a negative binomial hurdle model is employed. Supplementary materials providing two further illustrations are available online: the first, using data from public health, employs a two-component finite mixture of negative binomial models, the second, using data from finance, involves underdispersion. An R implementation of our tools is available in the R package countreg . It also contains the data and replication code.
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