COMPoissonReg-package: Estimate parameters for COM-Poisson regression

In COMPoissonReg: Conway-Maxwell Poisson (COM-Poisson) Regression

Estimate parameters for COM-Poisson regression

Description

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.

Details

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:

1. Compute Poisson estimates (using glm for Poisson regression or pscl for ZIP regression).

2. Use Poisson estimates as starting values to determine COM-Poisson estimates (using glm.cmp).

3. 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(λ, ν) 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 λ is sufficiently large and ν 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.

Author(s)

Kimberly Sellers, Thomas Lotze, Andrew M. Raim

References

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.

COMPoissonReg documentation built on Dec. 2, 2022, 5:07 p.m.