The Rasch Model
Of all the facets of IRT, the Rasch model for dichotomously scored items is probably the most widely recognized by practitioners. This is due in no small part to the efforts of Professor Benjamin D. Wright of the University of Chicago. As a result of the work of Wright and his followers, this Rasch model has received considerable attention in applied settings. Unfortunately, the early literature dealing with this Rasch model was somewhat disjoint from the main body of IRT literature. The original work due to Rasch (1960, 1961, 1966a, 1966b) was within the framework of a strictly probabilistic approach to item analysis and made no reference to any of the IRT literature. The 1960 book by Rasch has been reissued with a foreword and afterword by Wright (Rasch, 1980). Since the original work, a number of extensions and variations of the several Rasch models have appeared, and the article by Masters and Wright (1984) organizes five different Rasch measurement models within a coherent IRT framework. In the present chapter, the Rasch model label will refer only the case of dichotomously scored items. The widely known work due to Wright (Wright, 1968; Wright & Panchapakesan, 1969) dealt with parameter estimation procedures and properties of this model. The book by Wright and Stone (1979) provides an excellent discussion of how to use the Rasch model in test analysis and test construction. Work by Andersen (1972, 1973a, 1973b) has dealt with conditional maximum likelihood estimation procedures. Although there was a certain degree of continuity within the early Rasch model literature, it lacked an integration with the bulk of the work on IRT. To this end, this chapter attempts to present the Rasch model for dichotomously scored items in a coherent fashion. The historically separate development makes this somewhat difficult and, as a result, a certain amount of presentation that parallels earlier chapters will be necessary. The notation of the preceding chapters will be used in an attempt to link the Rasch model somewhat more closely to previous work. Some care must be exercised because the terms represented by a common symbol may have subtle differences in lueaning.