Equality Constraints in Multiple Correspondence Analysis

The application of equality constraints on the categories of a variable is a simple but useful extension of multiple correspondence analysis. Equality can be used to incorporate prior knowledge about the relations between categories. Categories may belong to the same variable, to different variables, or both. The simplest form of equality specifies that all variables receive identical data transforms. This is useful, for example, if the same variable is measured on many points of time. This article outlines a procedure to deal with unequal category numbers and with subsets of variables. Though the technical results are not difficult to derive, they are not very well-known. Some applications illustrate the method.