Correspondence Analysis with Linear Constraints of Ordinal Cross-Classifications

Within the non-iterative procedures for performing a correspondence analysis with linear constraints, a strategy is proposed to impose linear constraints in analyzing a contingency table with one or two ordered sets of categories. At the heart of the approach is the partition of the Pearson chi-squared statistics which involves terms that summarize the association between the nominal/ordinal variables using bivariate moments based on orthogonal polynomials. Linear constraints are then included directly in suitable matrices reflecting the most important components, overcoming also the problem of imposing linear constraints based on subjective decisions.