Correspondence analysis with linear constraints of cross- classification tables using orthogonal polynomials

Within the context of the non-iterative procedures for performing correspondence analysis with linear constraints, a strategy is proposed to impose linear constraints in analyzing a contingency tables with one or two ordered sets of categories. At the heart of the approach is the partition of the Pearson chi-squared statistic which involves terms that summarize the asso- ciation between the nominal/ordinal variables using bivariate moments based on orthogonal polynomials. Linear constraints are then included directly on suitable matrices which reflect the most important components overcoming the problem to impose linear constraints based on subjective decisions. A possible use of this constrained two-way approach for sliced three ordered sets of categories is also suggested.