This package offers the ability to compute the parameter estimates for a COM-Poisson or zero-inflated (ZI) COM-Poisson regression and associated standard errors. This package also provides a hypothesis test for determining statistically significant data dispersion, and other model diagnostics.
Kimberly Sellers, Thomas Lotze, Andrew M. Raim
This package offers the ability to compute COM-Poisson parameter
estimates and associated standard errors for a regular regression
model or a zero-inflated regression model (via the glm.cmp
function).
Further, the user can perform a hypothesis test to determine the statistically significant need for using COM-Poisson regression to model the data. The test addresses the matter of statistically significant dispersion.
The main order of functions for COM-Poisson regression is as follows:
Compute Poisson estimates (using glm for Poisson regression
or pscl for ZIP regression).
Use Poisson estimates as starting values to determine COM-Poisson
estimates (using glm.cmp).
Compute associated standard errors (using sdev function).
From here, there are many ways to proceed, so order is irrelevant:
Perform a hypothesis test to assess for statistically significant
dispersion (using equitest or parametric.bootstrap).
Compute leverage (using leverage) and deviance (using deviance).
Predict the outcome for new examples, using predict.
The package also supports fitting of the zero-inflated COM-Poisson model (ZICMP). Most of the tools available for COM-Poisson are also available for ZICMP.
As of version 0.5.0 of this package, a hybrid method is used to compute the normalizing constant \(z(\lambda, \nu)\) for the COM-Poisson density. A closed-form approximation (Shmueli et al, 2005; Gillispie & Green, 2015) to the exact sum is used if the given \(\lambda\) is sufficiently large and \(\nu\) is sufficiently small. Otherwise, an exact summation is used, except that the number of terms is truncated to meet a given accuracy. Previous versions of the package used simple truncation (defaulting to 100 terms), but this was found to be inaccurate in some settings.
See the package vignette for a more comprehensive guide on package use and explanations of the computations.
Steven B. Gillispie & Christopher G. Green (2015) Approximating the Conway-Maxwell-Poisson distribution normalization constant, Statistics, 49:5, 1062-1073.
Kimberly F. Sellers & Galit Shmueli (2010). A Flexible Regression Model for Count Data. Annals of Applied Statistics, 4(2), 943-961.
Kimberly F. Sellers and Andrew M. Raim (2016). A Flexible Zero-Inflated Model to Address Data Dispersion. Computational Statistics and Data Analysis, 99, 68-80.
Galit Shmueli, Thomas P. Minka, Joseph B. Kadane, Sharad Borle, and Peter Boatwright (2005). A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution. Journal of Royal Statistical Society C, 54, 127-142.