Order restricted estimation and tests for fit in homogeneous row-column models

The RC model, introduced by Goodman [7] has parametric scores for rows and columns of a two-way contingency table. If the parametric scores assigned to rows and columns of the table reflect the ordinality of the row and column categories then we have an order-restricted RC model. Maximum likelihood estimates of these score parameters subject to the order constraints was given by Ritov and Gilula [13]. For a square contingency table if the same ordered parametric scores are assigned to both rows and columns, then estimating these parameters still remains an open problem. We solve this problem by deriving a non standard yet simple algorithm and have shown that these estimates are indeed the MLE's. Also we propose testing the order-restricted RC model using a parametric bootstrap procedure, which yields reliable p values. Simulation studies are used to evaluate the performance of the restricted estimates and tests of fit. The methods developed are applied on real data sets.