Garson G.D. Correspondence Analysis

New York: Statistical Associates Publishing, 2012. — 37 p.Correspondence analysis is useful when the research focus is on mapping values (levels) of categorical variables. It is a method of factoring categorical variables and displaying them in a property space which maps their association in two or more dimensions. Correspondence analysis is a special case of canonical correlation, where one set of entities (category levels rather than variables as in conventional canonical correlation) is related to another set.
Correspondence analysis is often used where a tabular approach is less effective due to large tables with many rows and/or columns, and/or due to categories being nominal, with no particular order. Correspondence analysis been popular in marketing research, used to display customer color preference, size preference, and taste preference in relation to preferences for Brands A, B, and C. for instance.
Correspondence analysis starts with tabular data on categorical variables, usually two-way cross-classifications. However, the technique is generalizable to n-way tables with more than two variables though only two are supported by SPSS. The variables must be discrete: nominal, ordinal, or continuous variables segmented into ranges. The technique defines a measure of distance between any two points, where points are the values (categories) of the discrete variables. Since distance is a type of measure of association (correlation), the distance matrix can be the input to principal components analysis just as correlation matrices may be the input for conventional factor analysis. However, where conventional factor analysis determines which variables cluster together, correspondence analysis determines which category values are close together. This is visualized on the
correspondence map, which plots points (categories) along the computed factor axes.