Spatial autocorrelation in spatial interaction: Complexity-to-simplicity in journey-to-work flows

Abstract

Carey (1858) and Ravenstein (1885) first proposed, through analogy, the gravity model of Newtonian physics as a description for economic and social spatial interaction, with Sen and Smith (1995) furnishing a comprehensive treatment of this model more than a century later. In the late 1960s, Wilson spelled out an entropy maximizing derivation of the gravity model, including the use of row and column totals as additional information for modeling purposes (that is, the doublyconstrained version), followed by a utility maximization derivation of it by Niedercorn and Bechdolt (1969). Flowerdew and Atkin (1982) and Flowerdew and Lovett (1988) articulated linkages between the Poisson probability model and spatial interaction. Within this same time interval, Anas (1983) established a linkage between the doubly-constrained gravity model and a logit model of joint origin-destination choice, which indirectly relates to a Poisson specification that includes a separate indicator variable for each origin and each destination (that is, 2n 0-1 binary variables, each having a single 1 and n-1 0s). Curry (1972; also see Curry et al. 1975, 1976) followed by Griffith and Jones (1980), first raised the issue of spatial autocorrelation effects embedded in spatial interaction. These investigations were followed by a formulation of the network autocorrelation concept (see Black 1992; Black and Thomas 1998; Tiefelsdorf and Braun 1999). More recently, LeSage and Pace (2008), Griffith (2008), and Fischer and Griffith (2008) have returned to the issue of spatial autocorrelation effects embedded in spatial interaction, specifying spatial autoregressive and spatial filter versions of the unconstrained gravity model, but in terms of attribute geographic distributions. Chun (2007) moves beyond this conceptualization to that of more explicitly spatially autocorrelated flows.