  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.
