Conceptual Basis

The concept that is developed in this method draws on the local and regional effects identified by Green and Flowerdew (1996). They saw that the structure of data in areal units was highly complex. However, many of the processes within areal unit data may be difficult not only to recognise, but also to quantify and have not, therefore, been quantified beyond the descriptive. Nevertheless, they have been recognised, and it is these effects that the methods presented in the following sections seek to clarify further.

3.5.1.1. Local and Regional Effects

One view of the MAUP is as a problem that relates to the differences between the spatial processes generating data and the units within which they are reported. Green and Flowerdew (1996) present an argument that considers that it is possible to understand the MAUP with respect to interactions between data that occur at the local level and at the regional level. This is presented in relation to cross-correlation. Considering the relationship between two variables, denoted byXandY, it is possible that the relationship is not simplyYi toXi, but alsoYito Xj, whereXjis the Xvariable for a neighbouring zone. Green and Flowerdew (1996) define this as cross- correlation, which occurs when the response variable is affected by the explanatory

variable(s) not just at the same place but also at surrounding locations. This could be seen in an example using house prices, where the price of one house was a function of not its own condition, but also of the upkeep of the houses in the immediate area. It is apparent that this is related to the concept of spatial autocorrelation. They define this to be part of the range of processes that can influence the results of statistical analysis on areal data. Green and Flowerdew (2001) explore this notion further and express it as where “Y is a function of X and there is a cross-correlation effect, then statistical measure, in this case a regression, of Y at the most local level should include as explanatory variables both a local effect, i.e. the value of X at that local level, and a regional effect, i.e. the values of X in the surrounding area” (p.91, emphasis in original). However, in neither Green and Flowerdew (1996) nor Flowerdew et al (2001) are the local and regional effects explicitly defined beyond this abstract concept, and they do not define the extent of a surrounding area. If this concept is to be used, then this is clearly a question that needs to be addressed.

3.5.1.2 Areal units and spatial processes

This method is based on the assumption that the variance of a particular variable may be understood in terms of processes operating at several different spatial scales. There may be individual-level and aggregate-level effects, as is assumed in multi-level modelling. The aggregate-level effects may occur at two scales, as in the discussion by Green and Flowerdew (1996) on local and regional effects, or at more than two scales. However, there are no theoretical reasons to suppose that these effects happen to coincide with the scales at which data are released, such as EDs and wards in the British census. Indeed, it is highly likely that they will not coincide with the areal unit definitions. Therefore, the most likely case for Census data is that data consist of at least one hierarchical structure but are being analysed within a different, imposed, hierarchical structure (the EDs or Ward boundaries). This is further complicated by the fact that the effects occur at one scale in part of the study area and can occur at a different scale elsewhere in the same study area.

For certain variables, it may be possible to conceptually identify the spatial processes causing local and regional effects. A good example is housing rented from the local authority; in many places (Glasgow is a good example), such housing is found in large estates. Even where much of the local authority housing has been sold off under

Britain’s right-to-buy legislation, there may be local spatial patterns in the distribution of which houses have and have not been sold, perhaps influenced by construction type, council housing allocation policy or social stigmatisation. Other spatial processes may include the impacts of local housing markets or job markets on the economic status of residents, patterns of ethnic concentration, suburbanisation, gentrification and urban decline. The geographies of these processes will all be reflected in geographical space and their coincidence or otherwise with areal unit boundaries will affect the magnitude of the MAUP.

The methodology explored here cannot be used to investigate the impact of the sizes and shapes of the basic spatial units (EDs in the case of census data). Instead, it is possible to investigate the relative effects of zones of larger sizes. For example, the success of the system of ward boundaries in reflecting the extent of spatial processes operating to affect variable values in the study area can be assessed, by judging the similarity of the spatial structures to the Census boundaries.

It should be noted that this analysis deals with only one variable at a time. Further work would be necessary to extend it to analyse the correlation and regression coefficients that usually dominate discussion of MAUP effects. It is also the case that zones appropriate for one variable may not be appropriate for another, and also that the spatial processes operative in one study area may show up at a different scale in another.

3.5.1.3 Identifying individual and areal effects for spatial processes

It is possible to identify elements of correlations and covariances that are influenced by areal processes, which can be considered in terms of the local and regional effects, that were discussed above.Usefully, it is also possible to isolate these elements and

statistical measures that reflect only the processes occurring at the given level of analysis, do not involve processes occurring at other areal levels and the individual level. This follows the line of argument within MAUP research that does not seek to provide an overall solution to the problem. Rather it seeks to provide better statistical measures, which enable the isolation of MAUP effects, and therefore a better understanding of the processes behind the MAUP. A methodology for this is given in Tranmer and Steel (2001), and is the culmination of a set of research ideas discussed

by Steel and Holt (1994), Steel et al (1996) and Tranmer (1999). The concepts they discuss were presented in section 3.

These effects can vary over the study area and it is unlikely that they will be reflected by a predetermined geography of the areal unit divisions. Hence, it is not expected that they will be completely captured using the standard geography of publication. In the case of the Census, for instance, this means using the ED or Ward boundaries. Therefore, it may be that the effects will not only be identifiable at the levels of the ED and Ward, but they may also exist at an undetermined level between these two scales. Moreover, we consider that it is possible that scale effects are stronger in one part of the entire study area than another. These issues are discussed further below