W. Gardner et al., REGRESSION-ANALYSES OF COUNTS AND RATES - POISSON, OVERDISPERSED POISSON, AND NEGATIVE BINOMIAL MODELS, Psychological bulletin, 118(3), 1995, pp. 392-404
The regression models appropriate for counted data have seen little us
e in psychology. This article describes problems that occur when ordin
ary linear regression is used to analyze count data and presents 3 alt
ernative regression models. The simplest, the Poisson regression model
, is likely to be misleading unless restrictive assumptions are met be
cause individual counts are usually more variable (''overdispersed'')
than is implied by the model. This model can be modified in 2 ways to
accomodate this problem. In the overdispersed model, a factor can be e
stimated that corrects the regression model's inferential statistics.
In the second alternative, the negative binomial regression model, a r
andom term reflecting unexplained between-subject differences is inclu
ded in the regression model. The authors compare the advantages of the
se approaches.