Multiple Correspondence Analysis

Correspondence analysis is a method for interpreting tabular data visually in the form of spatial maps in which the rows and columns of the table are depicted as points. The basic form of the method visualizes cross-tabulations found typically in the social sciences, for example, education groups cross-tabulated

with political party voted for or a table of counts of the number of consumers that associate each of a set of brands with a set of attributes. Multiple correspondence analysis generalizes this method to many variables, typically questions in a survey, showing how the response categories interrelate.

As a first example, we use data from Tawnya Covert's article “Consumption and Citizenship during World War II: Product Advertisements in Women's Magazines,” a study in the Journal of Consumer Culture on consumption during the period of the Second World War after Pearl Harbor, as observed through a sample of advertisements aimed at American women. From their wording, the advertisements could be categorized into three types of advertising appeal: unrestricted consumption ads, rationing ads, deferred payment ads, and an additional fourth category gathering other appeals. Table 1 reproduces two tables from this article, stacked one on top of the other: cross-tabulations of product type by appeal and of year by appeal. Since there are no missing data, the column totals of the two tables are identical. The author interprets these data by calculating percentages [Page 1010]in each row; for example, of the 540 advertisements for food, 439 (81.3%) correspond to unrestricted consumption, 11 (2.0%) to deferred spending, 82 (15.2%) to rationed supplies, and 8 (1.5%) to others. This type of table is perfect for the application of correspondence analysis, a method for visualizing count data.

Figure 1 Correspondence Analysis Map of the Cross-Tabulations in Table 1

Note: The map is determined by the first table, and the rows (years) of the second table are added as supplementary points.

Source: Based on data from Covert 2003, 327, 330.

Figure 1 is the correspondence analysis (CA) of the first table (product type by appeal), with the second table (years by appeal) also visualized as so-called supplementary, or passive, points. The basic properties of the method are explained through the interpretation of this map, followed by a description of the extension to multivariate categorical data, called multiple correspondence analysis (MCA).