Redefining the modifiable areal unit problem within spatial econometrics : the case of the scale problem

The paper focuses on the issue of the modifiable areal unit problem (MAUP), which is frequently discussed within spatial econometrics. This issue concerns the changeability of the characteristics of the analysed phenomena under the impact of the change in the composition of territorial units (see Openshaw, Taylor 1979; Arbia 1989). The article indicates four conditions which need to be fulfilled if the correctness of spatial analyses is to be maintained. Also, the paper introduces the concept of the quasi composition of regions (QCR). It was defined as a set of particular compositions of territorial units for subsequent aggregation scales. Particular compositions of territorial units are selected in a way that allows a correct analysis within the undertaken research problem to be conducted. The chief asset of the paper is the proposal to redefine the concept of the modifiable areal unit problem. Both the scale problem and the aggregation problem were linked to the accepted quasi composition of regions. The redefinition of the concept is vital for the research conducted since analysing phenomena based on compositions of territorial units which are excluded from the quasi composition of regions leads to the formulation of incorrect conclusions. Within the undertaken research problem there exists only one particular composition of territorial units which allows the identification and description of the dependence for analysed phenomena. Within the considered modifiable areal unit problem two potential problems were defined and they can occur while making spatial analyses. The first is the final areal interpretation problem (FAIP) that occurs when the characteristics of phenomena or the dependence are designated for too large region. The other issue is the aggregation scale interpretation problem (ASIP). It occurs when a quasi composition of regions is enlarged by an aggregation scale where the correctness of the results of the undertaken research problem is not preserved. In both cases it is possible to reach a situation where the obtained characteristics will be deprived of the cognitive value.