Common Errors in Statistics (and How to Avoid Them), 4th Edition

COUNTS

Poisson regression is appropriate when the dependent variable is a count, as is the case with the arrival of individuals in an emergency room. It is also applicable to the spatial distributions of tornadoes and of clusters of galaxies.² To be applicable, the events underlying the outcomes must be independent in the sense that the occurrence of one event will not make the occurrence of a second event in a nonoverlapping interval of time or space any more or less likely. This model takes the loglinear form .

The outcome follows the Poisson distribution, not the normal, and the link function relating the outcome to the linear combination of coefficients and predictors is the logarithm.

Small errors in measurement can result in a substantial bias of the coefficients in the matrix , Häggström [2006].

A strong assumption of the Poisson regression model is that the mean and variance are equal (equidispersion). When the variance of a sample exceeds the mean, the data are said to be overdispersed. Fitting the Poisson model to overdispersed data can lead to misinterpretation of coefficients due to poor estimates of standard errors.

Naturally occurring count data are often overdispersed due to correlated errors in time or space, or other forms of nonindependence of the observations. One ...