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Appendix B: Ordinary Least Squares and Poisson Regression Models (CrimeStat IV: A Spatial Statistics Program for the Analysis of Crime Incident Locations, Version 4.0)

NCJ Number
Luc Anselin
Date Published
June 2013
14 pages

This second of three appendixes of the user manual for CrimeStat IV - a spatial statistics package that can analyze crime incident location data - provides a brief description of the statistical background, estimators, and model characteristics for a regression specification, estimated by means of both Ordinary Least Squares (OLS) and Poisson regression.


In discussing OLS regression, the appendix notes that OLS also corresponds to Maximum Likelihood (ML) estimation. The appendix contains the statistical model and all expressions that are required to perform estimation and essential model diagnostics. Both concise matrix notation and more extensive full summation notation are used to provide a direct link to "loop" structures in the software code, except when full summation is too unwieldy. Some references are provided for general methodological descriptions. The examination of the Poisson regression model focuses on the likelihood function, predicted values and residuals, and estimation steps. Also discussed are inference and the likelihood ratio test. 7 references

Date Published: June 1, 2013