Regularized nonsymmetric correspondence analysis

Nonsymmetric correspondence analysis (NSCA) is designed to analyze two-way contingency tables in which rows and columns assume an asymmetric role, e.g., columns depend on rows, but not vice versa. A ridge type of regularization was incorporated into a variety of NSCA: Ordinary NSCA, and Partial and/or Constrained NSCA. The regularization has proven useful in obtaining estimates of parameters, which are on average closer to the true population values. An optimal value of the regularization parameter is found by a GG-fold cross validation method, and the best dimensionality of the solution space is determined by permutation tests. A bootstrap method is used to evaluate the stability of the solution. A small Monte Carlo study and an illustrative example demonstrate the usefulness of the proposed procedures.