Appendix C: Negative Binomial Regression Models and Estimation Methods (CrimeStat IV: A Spatial Statistics Program for the Analysis of Crime Incident Locations, Version 4.0)

• NCJ Number: 242995
• Author(s): Dominique Lord; Byung-Jung Park
• Date Published: June 2013
• Length: 17 pages
• Grant Number(s): 2005-IJ-CX-K037
• Agencies: NIJ-Sponsored
• Publication Type: Technical Assistance; Instructional Material (Programmed)
• Award: The Expansion of the Crimestat Spatial Statistics Program to Incorporate Spatial Regression, Space-Time Clustering, Bayesian Journey to Crime Modeling, Incident Detection Methodology and Sparse Matrix

Annotation

This third of three appendixes of the user manual for CrimeStat IV - a spatial statistics package that can analyze crime incident location data - presents the characteristics of Negative Binomial regression models and discusses their estimating methods.

Abstract

The properties of the Negative Binomial models are discussed in sections on the Poisson-Gamma model, which has properties similar to the Poisson model, in which the dependent variable is modeled as a Poisson variable with a mean where the model error is assumed to follow a Gamma distribution. The related NB1 and NB2 models are also discussed. The Poisson-Gamma model with spatial interaction is discussed in another section of the appendix. The Poisson-Gamma (or Negative Binomial model) can also incorporate data that are collected spatially. In order to capture this kind of data, a spatial autocorrelation term must be added to the model. The section on estimation methods describes two methods that can be used for estimating the coefficients of the regression NB models. The two methods are the maximum likelihood estimates (MLE) and the Monte Carlo Markov Chain (MCMC). 17 references