Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression

Models in R


Dimitris Karlis1 and Ioannis Ntzoufras2

Department of Statistics, Athens University of Economics and Business,

76, Patission Str., 10434, Athens, Greece,

e-mails: , .


Journal of Statistical Software, Volume 14, Issue 10, 2005.




In this paper we present R/SPLUS functions for the maximum likelihood estimation of the parameters of  bivariate and diagonal inflated bivariate Poisson regression models. An Expectation - Maximization (EM) algorithm is facilitated. Inflated models allow for modelling both over-dispersion (or under-dispersion) and negative correlation and thus they are appropriate for a wide range of applications. Extensions of the algorithms for several other models are also discussed. Detailed guidance and implementation on simulated and real data sets using R/SPLUS functions is provided.



Keywords:  Bivariate Poisson distribution; EM algorithm;  Zero and Diagonal Inflated Models; SPLUS routines;  ECM algorithm; multivariate count data.



Bivpois R package 0.50-3:


  • Download R source code for bivpois package 0.50-3 for direct use in the current versions of R

Bivpois R package 0.50-3:


  • Download R bivpois package 0.50-3 - 02/7/2007 for  R.2.5.1:
    • zip file of bivpois package
    • tar.gz file of bivpois package
    • Corrected version [2/7/2007]. Original version of the paper [31/8/2005].
    • Pdf version of the manual/help files

Difference from previous version: One minor bug was fixed in order to run also in R version 2.5.1

Bivpois R package 0.50-2:


  • Download R bivpois package 0.50-2 - 31/8/2005 for  R.2.0.1:
    • zip file of bivpois package

Bivpois R package 0.50-1:


  • Download R bivpois package 0.50-1 - 31/5/2005 for  R.2.0.1:
    • zip file of bivpois package
    • tar.gz file of bivpois package
    • Pdf version of the paper
    • Pdf version of the manual/help files

Bivpois R package 0.43: 7/5/2003

  • Download R bivpois package 0.43-1 - 7/5/2005 for  R.2.0.1 [zip file of bivpois package 0.43 for Windows] (only this version runs in version 2.0.1; no changes were made in the syntax of the package functions) [tar.gz for UNIX]

Bivpois R package 0.41: 13/7/2004

  • Download Paper [pdf] (bivpois package 0.41: 13/7/2004)
  • Download R bivpois package 0.41 - 13/7/2004 for R.1.4 to R.1.9  [zip file of bivpois package 0.41] [zip extended file of bivpois package scripts, tables commands for examples 1-4 and fitted models of example 3]

Version 0.2: 16/11/2003

  • Download Paper [pdf] (version 0.2: 16/11/2003)
  • Download R/SPLUS functions (version 0.2: 12/11/2003) [zip file with functions and short helpfiles] [zip file with commands and data used in the paper]


Previous version of the paper (22/10/2003) entitled: EM algorithms for Bivariate Poisson regression and Inflated Bivariate Poisson regression models is not available any more.



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Last revised: 01/12/2015