Andrich (1978) derived a formal equivalency between
Thurstone’s Case V specialization of the law of
comparative judgment for paired comparisons, with a
logistic function substituted for the normal, and the
Rasch model for direct responses. The equivalency
was corroborated by a specific substantial-psychological
interpretation of the Rasch binary item response
probability. Studying the relationships between the
Thurstone and Rasch models from another perspective
than Andrich’s, namely, from a data-theoretical point
of view, it appears that the equivalency is based on an
implicit assumption with respect to the subject population.
This assumption (1) is rather restrictive, and
therefore its empirical validity seems to be low, and
(2) seems to contradict the substantial reasoning corroborating
the Thurstone-Rasch equivalency. It is argued
that the Thurstone model cannot be considered the
sample-independent pair comparison counterpart of the
Rasch model. An alternative pair comparison equivalent
of the Rasch model is tentatively proposed. Finally,
the theoretical and practical implications of Andrich’s
and of the present study are discussed.
Jansen, Paul G. (1984). Relationships between the Thurstone, Coombs, and Rasch approaches to item scaling. Applied Psychological Measurement, 8, 373-383. doi:10.1177/014662168400800401
Jansen, Paul G. W..
Relationships between the Thurstone, Coombs, and Rasch approaches to item scaling.
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