This is the second of 10 chapters on "Spatial Modeling II" from the user manual for CrimeStat IV, a spatial statistics package that can analyze crime incident location data.
This chapter, "Poisson Regression Modeling," discusses the Poisson family of count data models. This family is part of the generalized linear models (GLMs), in which the Ordinary Least Squares (OLS) normal model is a special case. Poisson regression is a modeling method that overcomes some of the problems of traditional regression in which the errors are assumed to be normally distributed (Cameron & Trivedi, 1998). The Poisson model overcomes some of the problems of the normal model. It has some desirable statistical properties that make it useful for predicting crime incidents. These properties are explained in this chapter. An example of Poisson regression pertains to likelihood statistics, model error estimates, dispersion tests, and individual coefficient statistics. These are illustrated with the Houston (Texas) burglary database. Problems with the Poisson regression model are discussed as over-dispersion and under-dispersion in the residual errors. This is followed with an example of Poisson regression with linear dispersion correction. A table shows the results of running the Poisson model with the linear dispersion corrections in predicting burglaries in Houston. A second type of dispersion correction involves a mixed function model, the Poisson-Gamma (Negative Binomial) regression. A table also illustrates the results of the negative binomial model for Houston burglaries. The usefulness of the negative binomial is also shown when the dependent variable is skewed. The chapter concludes with a discussion of the limitations of the maximum likelihood approach. 24 references and extensive tables and figures
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