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Links between binary and multi-category logit item response models and quasi-symmetric loglinear models. (English) Zbl 1044.62117

Summary: H. Caussinus’ [ibid., IV. Sér. 29, 77–183 (1965; Zbl 0168.39904)] loglinear model of quasi symmetry has interesting connections with models for within-subject effects with repeated categorical measurements. For binary responses, T. Tjur [Scand. J. Stat., Theory Appl. 9, 23–30 (1982; Zbl 0484.62115)] showed that estimates of main effect parameters in the quasi-symmetry model are also conditional maximum likelihood estimates of item parameters for a fixed effects treatment of subject terms in the Rasch item response model. He showed that they are also nonparametric estimates of item parameters for a random effects treatment of subject terms in the Rasch model.
The author describes some generalizations of the quasi-symmetry model that have similar connections with generalizations of the Rasch model. These include a link between an ordinal quasi-symmetry model and an adjacent-categories logit model with random effects, and a link between a multivariate quasisymmetry model and a logit random effects model for repeated measurements of a multivariate vector of binary responses.

MSC:

62P15 Applications of statistics to psychology
62H17 Contingency tables
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