OLS Regression Modeling (CrimeStat IV: A Spatial Statistics Program for the Analysis of Crime Incident Locations, Version 4.0)

• NCJ Number: 242975
• Author(s): Ned Levine; Dominique Lord
• Date Published: June 2013
• Length: 37 pages
• Grant Number(s): 2005-IJ-CX-K037
• Agencies: NIJ-Sponsored
• Publication Type: Technical Assistance; Instructional Material (Programmed)

Annotation

This is the first 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.

Abstract

This chapter, "OLS Regression Modeling," reviews the basics of regression modeling and prediction and discusses the Ordinary Least Squares (OLS) model in CrimeStat. The chapter first addresses "functional relationships" between a dependent variable and one or more independent variables. This is followed by a section on "Normal Linear Relationships." Topics addressed in this section are Ordinary Least Squares, maximum likelihood estimation, and assumptions of Normal Linear Regression. Examples are provided of modeling burglaries by zones, and a Normal Linear Regression. This section concludes with discussions of estimated error in the model for individual coefficients and violations of assumptions for Normal Linear Regression. The chapter's second major section is entitled "Corrections to Violated Assumptions in Normal Linear Regression." Topics discussed in this section are the elimination of unimportant variables, the elimination of multicollinearity, and transforming the dependent variable. An example is provided of the effect on Houston (Texas) burglaries of transforming the dependent variable. An example is also provided of modeling a skewed variable with OLS. The chapter's third major section addresses diagnostic tests and OLS. Topics covered in this section are the minimum and maximum values for the variables, skewness tests, tests for spatial autocorrelation in the dependent variable, and multicollinearity tests. This chapter also makes a passing reference to another version of the OLS model, i.e., the Markov Chain Monte Carlo (MCMC) version, which is discussed in chapter 17 of the user manual. 15 references