ABSTRACT
This chapter introduces approaches to modeling dependent variables that reflect binary choice outcomes generated by spatially dependent processes. Spatial dependence in choice outcomes result in a situation where observed choices at one location are similar to choices made at nearby locations. There are a number of scenarios where we might see this type of outcome in observed choices. For example, in the aftermath of Hurricane Katrina the decision of a business owner in New Orleans to rebuild and reopen a store might depend on the decision of neighboring businesses to reopen. When considering origin-destination flows of commuters traveling to work, the choice between mass transit and automobile mode of travel might exhibit spatial dependence because commuters located at nearby origins would be faced with the same presence or absence of mass transit opportunities. Holloway, Shankara, and Rahman (2002) show that binary choices regarding adoption of an agricultural program by Bangladeshi rice producers exhibited spatial dependence. Applications to land-use decisions regarding conversion from agricultural to non-agricultural uses, where land-use decisions of neighboring property owners exert an influence on the decision outcome have also been popular (Zhou and Kockelman, 2008; Irwin and Bockstael, 2004). Probit variants of the SAR model were considered by McMillen (1992), who proposed an EM algorithm as a way to produce consistent (maximum likelihood) measures of dispersion for estimates β from these models. A major contribution to the non-spatial probit literature was the work of Albert and Chib (1993) who proposed treating the binary dependent variable observations as indicators that relate to underlying unobservable or latent levels of utility. They introduce these latent levels as parameters that can be estimated using a Bayesian MCMC framework. We discuss this type of approach in Section 10.1 which we extend to the case of the spatial probit SAR model (LeSage, 2000). We consider a related Tobit (or censored regression) model variant of the SAR model in Section 10.3.
