The Order-Restricted RC Model for Ordered Contingency Tables: Estimation and Testing for Fit

Abstract

The RC model has been proposed as a model for ordered contingency tables. It involves parametric scores that are assigned to the rows and columns of the table so that these scores reflect the ordinality of the row and column categories. Efficient estimation of these parameters subject to order constraints remained an open problem mainly due to severe difficulties in computing these estimates and difficulties in deriving an appropriate asymptotic goodness-of-fit test. A nonstandard yet very simple algorithm is derived which produces the desired order-restricted maximum likelihood estimates with probability converging to 1. Testing the order-restricted RC model for fit is also discussed.