Mixed Poisson Regression for Overdispersed Count Data

Fits mixed Poisson regression models (Poisson-Inverse Gaussian or Negative-Binomial) on data sets with response variables being count data. The models can have varying precision parameter, where a linear regression structure (through a link function) is assumed to hold on the precision parameter. The Expectation-Maximization algorithm for both these models (Poisson Inverse Gaussian and Negative Binomial) is an important contribution of this package. Another important feature of this package is the set of functions to perform global and local influence analysis. See Barreto-Souza and Simas (2016) for further details.

The mixpoissonreg package

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The mixpoissonreg package deals with regression models with response variables being count data. It is aimed towards overdispersed data. It currently provides implementation of two regression models: Negative Binomial and Poisson Inverse Gaussian regression models. For both of these models there are two estimation procedures implemented: the EM-algorithm and direct maximization of the log-likelihood function. The definition of both these regression models along with the EM-algorithm approach for them can be found at Barreto-Souza and Simas (2016). The direct maximization of the log-likelihood is only recommended when the EM-algorithm takes too long to converge. Several global and local influence measures are implemented and easy to interpret through plot visualization. There are plot implementations using base-R and ggplot2. For further details, and also more tutorials, we refer the reader to the vignettes whose links can be found below or by using vignette(mixpoissonreg).

Installing the mixpoissonreg package

The latest stable development version can be installed from github:

#install.packages("devtools")
devtools::install_github("vpnsctl/mixpoissonreg")

Dependencies

The mixpoissonreg package imports the Rfast package. The Rfast package needs the GSL library to be installed. If you are using linux, you most likely will need to install the GSL library.

On Ubuntu (version 18.04 or newer), run:

sudo apt install libgsl-dev

On RedHat or Fedora, run:

yum install gsl gsl-devel

The mixpoissonreg package also imports the following packages: pbapply, Formula, gamlss, gamlss.dist, rlang, statmod, lmtest, generics, magrittr, tibble, dplyr, ggplot2, ggrepel, gridExtra

Useful Resources

• The mixpoissonreg home page contains the documentation (with examples), vignettes, etc.

• The mixpoissonreg Documentation can be accessed directly through this link

• Currently, the mixpoissonreg package has the following vignettes:

  • Getting started: Introduction to the mixpoissonreg package
  • Analyzing overdispersed count data with the mixpoissonreg package
  • Maximum-likelihood estimation with the mixpoissonreg package
  • Building and customizing base-R diagnostic plots with the mixpoissonreg package
  • Building and customizing ggplot2-based diagnostic plots with the mixpoissonreg package
  • Global and local influence analysis with the mixpoissonreg package
  • Confidence and prediction intervals with the mixpoissonreg package
  • mixpoissonreg in the tidyverse

• Theoretical details can be obtained in Barreto-Souza and Simas (2016) and also in its Supplementary Material

Basic usage

The usage of the mixpoissonreg package is analogous to the usage of standard regression functions and packages in R:

library(mixpoissonreg)
fit <- mixpoissonreg(daysabs ~ prog + math + gender | prog, data = Attendance)
fit
#> 
#> Negative Binomial Regression - Expectation-Maximization Algorithm
#> 
#> Call:
#> mixpoissonreg(formula = daysabs ~ prog + math + gender | prog, 
#>     data = Attendance)
#> 
#> Coefficients modeling the mean (with log link):
#>    (Intercept)   progAcademic progVocational           math     gendermale 
#>    2.752418105   -0.424045918   -1.238680841   -0.006791582   -0.257120287 
#> Coefficients modeling the precision (with log link):
#>    (Intercept)   progAcademic progVocational 
#>       1.109533      -1.083443      -1.517825

summary(fit)
#> 
#> Negative Binomial Regression - Expectation-Maximization Algorithm
#> 
#> Call:  
#> mixpoissonreg(formula = daysabs ~ prog + math + gender | prog, 
#>     data = Attendance)
#> 
#> 
#> Pearson residuals:
#>      RSS      Min       1Q   Median       3Q      Max 
#> 323.6397  -1.0648  -0.7204  -0.3654   0.3064   4.8776 
#> 
#> Coefficients modeling the mean (with  link):
#>                 Estimate Std.error z-value Pr(>|z|)    
#> (Intercept)     2.752418  0.152613  18.035  < 2e-16 ***
#> progAcademic   -0.424046  0.132369  -3.204  0.00136 ** 
#> progVocational -1.238681  0.173155  -7.154 8.45e-13 ***
#> math           -0.006792  0.002274  -2.986  0.00283 ** 
#> gendermale     -0.257120  0.116934  -2.199  0.02789 *  
#> 
#> Coefficients modeling the precision (with  link):
#>                Estimate Std.error z-value Pr(>|z|)    
#> (Intercept)      1.1095    0.2783   3.987 6.68e-05 ***
#> progAcademic    -1.0834    0.3074  -3.524 0.000424 ***
#> progVocational  -1.5178    0.3395  -4.471 7.79e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
#> 
#> Efron's pseudo R-squared:  0.1861217 
#> Number of iterations of the EM algorithm = 1930

There are also several methods implemented:

• Visualization: plot (base-R visualization) ; autoplot (ggplot2 visualization) ; local_influence_plot (base-R visualization) ; local_influence_autoplot (ggplot2 visualization)
• Inference: coeftest ; coefci ; lmtest::lrtest (works with the default method) ; lmtest::waldtest (works with the default method) ; predict
• Residual analysis: residuals
• Global influence analysis: influence ; cooks.distance ; hatvalues
• Local influence analysis: local_influence
• Tidyverse compatibility: augment ; glance ; tidy ; tidy_local_influence ; local_influence_benchmarks