This is the fifth 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 examines spatial regression models using the Markov Chain Monte Carlo (MCMC) method. It requires familiarity with the previous four chapters of the manual and a thorough knowledge of statistical analysis. Spatial regression involves adding a spatial component into a regression model. There are two major ways to express this component, either as an explicit spatial variable or as an internally estimated spatial parameter. There are advantages and disadvantages to each approach, and often they are included together. Examples of this are the area of the zone, the distance to the central city, the distance to a particular facility, or an average value of the dependent variable for nearby zones. An alternative approach is to use a spatial parameter within the model that is estimated within the calculations themselves. The advantage of this internally estimated spatial parameter is its simultaneous estimation with the coefficients and its inclusion of the reciprocal effects of nearby zones on the central zone and vice versa. As with a distance-based external variable, the user must make assumptions about the decay of the spatial autocorrelation effect. The remainder of the chapter profiles a number of spatial regression models that apply to normal, Poisson-distributed, and binomial logit models. The choice of any of these models will depend on the actual distribution of the dependent variable and the underlying assumptions for that model. Implications are drawn for an MCMC Normal-CAR or MCMC Normal-SAR model, the MCMC Poisson-Gamma-CAR/SAR and the MCMC Poisson-Lognormal-CAR/SAR models, as well as the MCMC Binomial Logit-CAR/SAR model. These models are applied to the prediction of burglaries in Houston, TX. Extensive tables and figures and 24 references