Trend Surface and the Spatio-Temporal Analysis of Residential Land-Use Intensity and Household Housing Expenditure

Abstract

Trend surface analysis is a twodimensional, least squares regression technique that is particularly useful in analyzing spatially continuous phenomena as statistical surfaces (Cliff et al. 1975, pp. 49-50). Because it is a power series, polynomial regression model subject to the usual significance tests, it has obvious hypothesis-testing properties and yet, despite an abundance of spatial-economic theory, trend surface is only beginning to be applied in this manner. Its parsimonious use is in part a function of the limited sophistication of extant theories (Norcliffe 1969, pp. 340-341); given the current state of knowledge, it is extremely difficult, if not impossible, to hypothesize explicitly a polynomial surface higher in order than the quadratic. For this reason, many researchers simply write off the technique as being principally inductive in utility (Cliff et al. 1975, p. 56). In spite of this problem, trend surface has been applied, in analytical contexts of varying sophistication, to a variety of economic-related data at the intraurban scale, including population densities (Schroeder and Sjoquist 1976; Bambrock and Greene 1977), housing densities (Cliff et al. 1975, pp. 65-68), land values (McDonald and Bowman 1979), and housing prices (Jackson 1979). Although there is a prodigious literature involving both dynamic and spatial approaches, trend surface has not yet been used in the analysis of residential land-use intensity and household housing expenditure. Moreover, while it has been applied in static, intercity comparisons, it has not been used for cross-sectional, time comparisons as Cliff and his colleagues suggest (1975, p. 68), most likely because of the difficulty in obtaining geographically reconciled data sets. The work that follows bridges this gap and provides some policy considerations as well.