Exploratory Visual Inspection of Category Associations and Correlation Estimation in Multidimensional Subspaces

In this paper, we aimed to estimate associations among categories in a multi-way contingency table. To simplify estimation and interpretation of results, we stacked multiple variables to form a two-way stacked table and analyzed it using the biplot in correspondence analysis (CA) paradigm. The correspondence analysis biplot allowed visual inspection of category associations in a twodimensional plane, and the CA solution numerically estimated the category relationships. We utilized parallel analysis and identified two statistically meaningful dimensions with which a plane was constructed. In the plane, we examined metric space mapping, which was converted into correlations, between school districts and categories of school-relevant variables. The results showed differential correlation patterns among school districts and this correlational information may be useful for stake holders or policy makers to pinpoint possible causes of low school performance and school-relevant behaviors.