Correspondence Analysis


Correspondence analysis (CA) is a data analytic method appropriate for data matrices consisting of categorical variables. These can be cross-tabulations of two or more categorical variables or can be entity-by-entity (e.g., person-by-variable) data sets of more general interest to social and behavioral scientists, as long as the variables are categorical and homogenous. Although CA is at its core a dimension reduction technique, the method is tightly coupled to a geometric interpretation and a visual mode of presentation: the biplot, where the row and column elements are projected into a low-dimensional space. In this sense, CA is also a data visualization method. This entry proceeds in the following steps. First, it presents more details behind what exactly CA is and how it has been characterized in different kinds of literature. Second, it describes the basic concepts behind CA: profiles, masses, χ2 distances, inertias, and computational details. Third, it discusses an important generalization of CA, known as MCA. Fourth, it details some other extensions of CA, including how the method can be used to analyze one- and two-mode network data and text data. It concludes with an overview of currently available software implementing CA and related methods.

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