Pitfalls in higher order model extensions of basic spatial regression methodology

Spatial regression methodology has been around for most of the 50 years (1961-2011) that the Southern Regional Science Association has been in existence. Cliff and Ord (1969) devised a parsimonious specification for the structure of spatial dependence among observations that could be used to empirically model spatial interdependence. Later work (Cliff and Ord, 1973, 1981; Ord, 1975) further developed these ideas into basic spatial regression models, which were popularized and augmented by Anselin (1988). We discuss several issues that have arisen in recent work that attempts to extend basic models of spatial interdependence to include more types of spatial and non-spatial interdependencies. Understanding these issues should help future work avoid several pitfalls that plague current and past attempts at extensions along these lines.