Analysis of Association between Categorical Maps in Multi-layer Gis

Measuring association between categorical maps in GIS typically involves categorical overlay, representation of overlay results as a contingency table, and statistical analysis of the latter with various integral measures of association, log-linear models, etc. However, the analysis of cross-classified nominal areal data faces serious statistical difficulties. Often, it is more convenient to analyze overlaid categorical maps by looking at simple proportions of areas, their increments and decrements. Obvious simplicity, and lack of any statistical/mathematical foundation prevented wide use of percentages and proportions in publications, but not in everyday research practice. This paper shows that systematized analysis of proportions from overlaid maps is a viable alternative to available statistical methods. Mathematically, this approach leads to a weighted-by-area extension of Determinacy Analysis (a method originally developed in sociology). This technique recognizes topologically distinct cases, allows direct interpretation of spatial relationships, and permits more detailed contextual analysis of deviations from expected geographic association. The paper identifies and gives solutions to basic tasks of analysis of overlaid maps: construction of explanations and their refinement; analysis of contributions; and building and examining of aggregations/taxonomies. Two case studies, urban expansion in the east King County, WA, and vegetation mapping accuracy in the Klamath province, CA, are used to demonstrate the solutions.