Implementing point-symmetry models for square contingency tables having ordered categories in SAS
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In this paper, the class of point-symmetry models in a square contingency table discussed in (Tomizawa, 1985; 1986a; 1986b) are implemented in SAS by employing the non-standard log-linear model approach discussed in (von Eye and Spiel, 1996), and (Lawal, 2001). This approach is simpler than earlier implementation of these models as it unifies the approaches in various papers by Tomizawa. The implementation of these models require the generation of factor and regression variables whose entries derivation are explained in the text. The models are fitted using SAS PROC GENMOD.
We applied our approach to fit these class of models to the 4×4 unaided distance vision data of 4,746 Tokyo University students published in (Tomizawa, 1985; 1986a; 1986b). The results obtained from this approach when applied to these data agree with those published in earlier papers. As an extension, we further apply our method to fit these class of models to the 5×5 Danish social mobility data provid in (Bishop, Fienberg and Holland, 1975). The quasi-point-symmetry models seems to fit these data best based on the Akaike information selection criterion. The method is also applied to another well analyzed 4×4 table of mothers’ education to fathers’ education for eminent black Americans (Agresti, 1989).
KeywordsFactor variable Inclined point symmetry Point-symmetry Reverse proportional point-symmetry square tables
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