Trend surface and residual analysis

Abstract

Trend surfaces are continuous graphical and analytical representations by which the spatial distribution of a social variable can be evaluated. Analytical expressions, concepts and computational techniques of developing trend surfaces, residuals and criteria for evaluating them are presented. Contour mapping is employed as an integral part of the presentation and methodology of the analysis. Of computer graphic displays, contouring is the only one that lends itself to the type of further mathematical modeling such as by trend surfaces. Trend surfaces and residuals are complementary constructs. In contrast to usage of the residual in sociology as the error term in the general linear model, residuals are treated as probable loci of anomalous but significant variation of the mapped variable. Qualitative and quantitative aspects of, and theoretical and practical limitations to selection of best-fitting surfaces and residuals are discussed. Distortion of mapping can be encountered by clustering of data points and boundary effects. Applications of trend surfaces and residuals to social variables appearing in the economic georgraphy literature are reported.Contour mappings of unfiltered data, a trend surface model and complementary residuals demonstrate aspects and principles of the techniques applied to population data for Nassau and Suffolk Counties, New York, 1960-1970. Besides arrays of relative highs, lows, regional and local gradients, dominant features, such as a plateau of 100 percent change in population which covers most of the western portion of Suffolk County and the barrier effect of the Suffolk County line on population settlement over the period, emerge from the mapped models. Application of trend surfaces and residuals to social, ecological data is suggested as one model of computer data reduction and analysis of large volumes of regional and census data.