Modeling symmetry models in square contingency tables with ordered categories

This paper provides alternative methods for fitting symmetry and diagonal-parameters symmetry models to square tables having ordered categories. We demonstrate here the implementation of the class of models discussed in Goodman (1979c) using GEN-MOD in SAS. We also provide procedures for testing hypotheses involving model parameters. The methodology provided here can readily be used to fit the class of models discussed in Lawal and Upton (1995). If desired, composite models can be fitted. Two data sets, the 4 × 4 unaided distance vision of 4746 Japanese students Tomizawa (1985) and the 5 × 5 British social mobility data Glass (1954) are employed to demonstrate the fitting of these models. Results obtained are consistent with those from Goodman (1972, 1979c, 1986) and Tomizawa (1985, 1987).