Scales, levels and processes: Studying spatial patterns of British census variables

Abstract

This paper is based on the assumption that there may be scale effects at all levels of areal data and that they vary both within areal units and between areal units. Spatial distributions are based on processes taking place in geographical space. A mapped pattern may reflect several distinct processes, each of which may affect a different area and operate at a different scale. The challenge for the spatial analyst is to identify these processes and evaluate their importance from the spatial pattern observed. Here the well known modifiable areal unit problem is not really a problem but a resource. Data at different scales can help us identify processes operating at different scales. We build on models and methods described by [Tranmer, M., & Steel, D. G. (2001). Using local census data to investigate scale effects. In N. J. Tate, & P. M. Atkinson (Eds.), Modelling scale in geographical information science (pp. 105–122). Chichester: John Wiley and Sons], which facilitate the identification of processes occurring within areal units. The method is extended using concepts from multi-level modelling and spatial autocorrelation, through the application of local statistics applied to what may be termed area effect estimates. It is illustrated with respect to two very different census variables and three different study areas.

Introduction

The modifiable areal unit problem (MAUP) is a phenomenon whereby different results are obtained in analysis of the same data grouped into different sets of areal units. It vexes the geographical and spatial analyst almost as much today as it did when first identified by Gehlke and Biehl (1934) or when subsequently popularised by Openshaw and Taylor, 1979, Openshaw and Taylor, 1981. The MAUP has been subdivided into two separate but linked issues. One is the zonation issue, which concerns the effects of the arbitrary nature of the boundary division placed upon the data. The other issue is the scale issue, which can be defined as occurring where the statistical results of an analysis may change as the level of analysis changes. These effects occur because spatial processes generating the observed data may exist at scales and for particular areal units that may be reflected more or less accurately by the boundaries in use. Among other authors, Fotheringham and Wong (1991) have demonstrated these effects for US census data, and Tranmer and Steel (2001) have done so for UK data. See Openshaw (1984) for further discussion of these concepts.

Two analytical techniques are applied in this paper to investigate the processes generating spatial patterns. The first technique is the Multi-level model, or MLM (Jones, 1991). The MLM is based on the recognition that a response variable can be affected by processes occurring at both the individual level and the group level. Thus, the MLM can be used to assess the existence, and estimate the magnitude, of processes that operate at the individual person level, and also one or more grouped level. In the classic applications of MLM in education, the groups may correspond to classes or schools; in the current context, the groups may refer to geographical areas over which spatial processes operate.

The second of these techniques is spatial autocorrelation. This has been identified as highly relevant to the analysis of spatial data, such as data that is available for areal units (see for instance Cliff & Ord, 1973). Spatial autocorrelation has been discussed as a factor in the debate concerning the modifiable areal unit problem (see Openshaw & Taylor, 1979). At its simplest, spatial autocorrelation can be thought of as the correlation of a variable at one place with the same variable at neighbouring places. It exemplifies Tobler’s first law of geography that “everything is related to everything else, but near things are more related than distant things” (Tobler, 1970, p. 236). Goodchild (1986) gives a more detailed treatment.

Spatial autocorrelation can inform analysts about the patterning of areal data. It is logical that spatial autocorrelation and multi-level modelling should be analysed together. Jones (1991, p. 8) states, “the degree of auto-correlation in MLM can loosely be conceived as the ratio of ‘variation at the higher level’ to the ‘total variation at all levels’. A value of zero for a spatial autocorrelation coefficient signifies no auto-correlation, indicating that there is no variation at the higher level”. The work presented here builds on this basis, aiming to find evidence for the spatial processes generating the data under analysis, using a combination of adapted multi-level modelling and spatial autocorrelation techniques. The paper also provides conclusions about the patterns displayed by certain British census variables.