Double Ordinal Correspondence Analysis with External Information

Within the context of the non-iterative procedures for performing correspondence analysis with linear constraints, a strategy is proposed in order to impose linear constraints in analyzing a contingency tables which are of ordinal nature. Linear constraints are imposed using the polynomial approach to correspondence analysis. The classical approach to correspondence analysis decomposes the Pearson chi- squared statistic into singular values by partitioning the matrix of Pearson contingencies using singular value decomposition. The polynomial approach to correspondence analysis decomposes the same statistic into bivariate moments, such as linear by linear, linear by quadratic, etc., by partitioning the matrix of Pearson contingencies using orthogonal polynomials rather than singular value decomposition. With this approach one can obtain location, dispersion and higher order components for the row and column categories by identifying statistically significant sources of variation. 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.