COMPUTING CONDITIONAL MAXIMUM-LIKELIHOOD-ESTIMATES FOR GENERALIZED RASCH MODELS USING SIMPLE LOGLINEAR MODELS WITH DIAGONALS PARAMETERS

Generalized Rasch models for multiple-response items proposed by Andersen (1973) are related to quasi-symmetric loglinear models. The loglinear models are obtained by treating subject parameters in the Rasch models as random effects. Fitting the loglinear models yields estimates of item parameters in the generalized Rasch models that are also conditional maximum likelihood estimates when the subject effects are treated as fixed. For models that apply naturally when there are ordinal response categories, the related loglinear models are simple quasi-symmetric models having diagonals parameters. Our results generalize Tjur's (1982) observation about the connection between binary-response Rasch models and loglinear models.