16 Rasch Models

Publisher Summary This chapter begins with the history of the Rasch models (RM) and also discusses some basic concepts and properties of the RM. According to Georg Rasch, the RM should have the following property: a nontrivial likelihood function should exist, which is a function of the item parameters but is independent of the person parameters, and is thus serviceable for a specifically objective comparison of the items. This requirement is satisfied by the conditional likelihood of the data, given the raw scores of all testees. Based on the definition of the RM, this chapter provides a number of useful formulas, both to illustrate the characteristic properties of the RM and to free the derivation and discussion of estimation equations and tests of fit from too many elementary algebraic manipulations. It also discusses the characterizations and scale properties of the RM. Three essentially different approaches to deriving, and hence justifying the choice of, the RM have been taken: (a) postulating sufficient statistics for the person parameter, (b) assuming identifiability of parameters within a marginal maximum likelihood framework, and (c) postulating specific objectivity (SO) and the feasibility of conditional inference as general methodological principles.

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