This is the fourth 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 discusses binomial regression models as applied to ungrouped data. An understanding of this chapter requires familiarity with the content of the previous three chapters of the manual as well as a thorough knowledge of statistical analysis. Binomial regression models are applied to individual cases (records) in which the dependent variable has only two responses expressed as "0" and "1." They are part of a family of regression models called "limited dependent variables" where the range of possible values is restricted. Binomial regression models are useful when there is a discrete choice between two alternatives; however, the problem with a binomial variable is that the underlying probabilities are not measured, but only inferred from a discrete binomial choice. Thus, the models proposed estimate the underlying probability using only the two alternative values for the dependent variable. The two models examined in this chapter are the logistic (usually called "logit") model and the probit model, which are the two most common forms for estimating the underlying probabilities. The logit is more convenient to use, given that the exponential coefficients can be expressed in terms of the odds ratio. The next chapter shows how a Markov Chain Monte Carlo (MCMC) version of the logit can be adapted in the estimation of spatial autocorrelation in the dependent variable. Extensive figures, tables, and mathematical models are provided. 18 references