20,743
Views
664
CrossRef citations to date
0
Altmetric
STATISTICAL DEVELOPMENTS AND APPLICATIONS

The Analysis of Count Data: A Gentle Introduction to Poisson Regression and Its Alternatives

, &
Pages 121-136 | Received 02 Jan 2008, Published online: 10 Feb 2009

References

  • Aiken , L. S. and West , S. G. 1991 . Multiple Regression: Testing and interpreting interactions , Newbury Park, CA : Sage .
  • Akaike , H. 1973 . “ Information theory and an extension of the maximum likelihood principle ” . In Second international symposium on information theory , Edited by: Petrov , B. N. and Csaki , F. 267 – 281 . Budapest, Hungary : Akademiai Kiado .
  • Allison , P. D. 1999 . Logistic regression using SAS: Theory and application , Cary, NC : SAS Institute Inc .
  • Armeli , S. , Mohr , C. , Todd , M. , Maltby , N. , Tennen , H. Carney , M. A. 2005 . Daily evaluation of anticipated outcomes from alcohol use among college students . Journal of Social and Clinical Psychology , 24 : 767 – 792 .
  • Cameron , A. C. and Trivedi , P. K. 1998 . Regression analysis of count data , New York : Cambridge University Press .
  • Cameron , A. C. and Windmeijer , F. A. G. 1997 . An R-squared measure of goodness of fit for some common nonlinear regression models . Journal of Econometrics , 77 : 329 – 342 .
  • Chernoff , H. 1954 . On the distribution of the likelihood ratio . Annals of Mathematical Statistics. , 25 : 573 – 578 .
  • Chin , H. C. and Quddus , M. A. 2003 . Modeling count data with excess zeroes: An empirical application to traffic accidents . Sociological Methods and Research , 32 : 90 – 116 .
  • Cohen , J. , Cohen , P. , West , S. G. and Aiken , L. S. 2003 . Applied multiple regression/correlation analysis for the behavioral sciences, , 3rd ed. , Mahwah, NJ : Lawrence Erlbaum Associates .
  • Cook , R. D. and Weisberg , S. 1983 . Diagnostics for heteroscedasticity in regression . Biometrika. , 70 : 1 – 10 .
  • Costa , P. T. Jr. and McCrae , R. R. 1992 . NEO–PI–R professional manual. , Odessa, FL : Psychological Assessment Resources, Inc .
  • Cox , D. R. and Snell , E. J. 1989 . Analysis of binary data, , 2nd ed. , London : Chapman & Hall .
  • DeHart , T. , Tennen , H. , Armeli , S. , Todd , M. and Affleck , G. 2008 . Drinking to regulate romantic relationship interactions: The moderating role of self-esteem . Journal of Experimental Social Psychology. , 44 : 537 – 538 .
  • Dobson , A. J. 2002 . An introduction to generalized linear models, , 2nd ed. , New York : Chapman & Hall/CRC .
  • Enders , C. K. 2005 . “ Maximum likelihood estimation ” . In Encyclopedia of statistics in behavioral science , Edited by: Everitt , B. S. and Howell , D. C. 1164 – 1170 . Chichester, England : Wiley .
  • Fahrmier , L. and Tutz , G. 2001 . Multivariate statistical modeling based on generalized linear models, , 2nd ed. , New York : Springer-Verlag .
  • Fox , J. 2008 . Applied regression analysis and generalized linear models, , 2nd ed. , Thousand Oaks, CA : Sage .
  • Freund , J. E. and Walpole , R. E. 1980 . Mathematical statistics, , 3rd ed. , Englewood Cliffs, NJ : Prentice-Hall .
  • Gardner , W. , Mulvey , E. P. and Shaw , E. C. 1995 . Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models . Psychological Bulletin , 118 : 392 – 404 .
  • Greene , W. H. 1994 . Accounting for excess zeros and sample selection in Poisson and negative binomial regression models , New York : Stern School of Business, New York University, Department of Economics . [Working paper No. 94–10]
  • Hall , D. B. and Zhengang , Z. 2004 . Marginal models for zero inflated clustered data . Statistical Modeling , 4 : 161 – 180 .
  • Hilbe , J. M. 2007 . Negative binomial regression , New York : Cambridge .
  • Land , K. C. , McCall , P. L. and Nagin , D. S. 1996 . A comparison of Poisson, negative binomial, and semiparametric mixed Poisson regression models: With empirical applications to criminal careers data . Sociological Methods and Research , 24 : 387 – 442 .
  • Long , J. S. 1997 . Regression models for categorical and limited dependent variables , Thousand Oaks, CA : Sage .
  • MacCallum , R. C. 2003 . Working with imperfect models . Multivariate Behavioral Research , 38 : 113 – 139 .
  • McCullagh , P. and Nelder , J. A. 1989 . Generalized linear models, , 2nd ed. , London : Chapman & Hall .
  • Nagelkerke , N. J. D. 1991 . A note on a general definition of the coefficient of determination . Biometrika , 78 : 691 – 692 .
  • National Institute of Mental Health . 1997 . Computerized diagnostic interview schedule for children, IV (NIMH C-DISC IV) , New York : Author, Columbia University .
  • Nelder , J. A. and Wedderburn , R. W. M. 1972 . Generalized linear models . Journal of the Royal Statistical Society Series A (General) , 135 : 370 – 384 .
  • Pierce , D. A. and Schafer , D. W. 1986 . Residuals in generalized linear models . Journal of the American Statistical Association , 81 : 977 – 986 .
  • Raftery , A. 1995 . Bayesian model selection in social research . Sociological Methodology , 25 : 111 – 196 .
  • Shanahan , C. , Lincoln , A. , Horton , N. , Saitz , R. , Winter , M. and Samet , J. 2005 . Relationship of depressive symptoms and mental health functioning to repeat detoxification . Journal of Substance Abuse Treatment , 29 : 117 – 123 .
  • Siddiqui , O. , Mott , J. , Anderson , T. and Flay , B. 1999 . The application of Poisson random-effects regression models to the analyses of adolescents' current level of smoking . Preventive Medicine , 29 : 92 – 101 .
  • Wainer , H. 2000 . The centercept: An estimable and meaningful regression parameter . Psychological Science , 11 : 434 – 436 .
  • Walters , G. D. 2007 . Predicting institutional adjustment with the Lifestyle Criminality Screening Form and the Antisocial Features and Aggression Scales of the PAI . Journal of Personality Assessment , 88 : 99 – 105 .
  • West , S. G. , Aiken , L. S. and Krull , J. L. 1996 . Experimental personality designs: Analyzing categorical by continuous variable interactions . Journal of Personality , 64 : 1 – 48 .
  • Williams , D. A. 1987 . Generalized linear model diagnostics using the deviance and single case deletions . Applied Statistics , 36 : 181 – 191 .
  • Worrall , J. L. 2002 . If you build it, they will come: Consequences of improved citizen complaint review procedures . Crime & Delinquency , 48 : 355 – 379 .
  • Zeger , S. L. , Liang , K.-L. and Albert , P. S. 1988 . Models for longitudinal data: A generalized estimating equation approach . Biometrics , 44 : 1049 – 1066 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.