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 Ander sen (1973) are related to quasi-symmetric loglinear models. The loglin ear models are obtained by treating subject parameters in the Rasch mo dels as random effects. Fitting the loglinear models yields estimates of item parameters in the generalized Rasch models that are also condi tional maximum likelihood estimates when the subject effects are treat ed as fixed. For models that apply naturally when there are ordinal re sponse categories, the related loglinear models are simple quasi-symme tric models having diagonals parameters. Our results generalize Tjur's (1982) observation about the connection between binary-response Rasch models and loglinear models.