Procedures for Estimating Both Ability and Item Parameters.
The typical educational or psychological test usually contains many items and is administered to a group of examinees. When such a test is analyzed, it is of interest to be able to estimate the parameters of the test items and the ability parameters of the examinees. A major factor in the practical application of IRT has been the development of maximum likelihood estimation procedures for these two sets of parameters and the implementation of these procedures in the form of computer programs. The development of these procedures was a rather slow process. Lord (1953), in a very prophetic article, presented the basic framework of the simultaneous estimation of the item and ability parameters via maximum likelihood using a normal ogive model for the item characteristic curves. However, the modern digital computer was not yet available and the computational aspects were not practical. Birnbaum (1968, pp. 420-422) presented a simplified paradigm for jointly estimating the item and ability parameters that has become the basis for many computer implementations of these maximum likelihood estimation procedures. The first actual implementation of this paradigm was due to Lord (1968), who described a computer program which evolved into the widely used LOGIST program (Wingersky, Barton, & Lord, 1982). It was also implemented by Wright and Panachapakesan (1969) in a computer program for the Rasch model that became the BICAL program (Wright & Mead, 1978). Because of the computational demands of these estimation procedures, IRT is not practical without such computer programs. Yet, to wisely select and use such programs one must have an understanding of the basic estimation procedures they implement. Consequently, the present chapter has two goals: first, to present the statistical logic of the Birnbaum paradigm and, second, to explore the domain of parameter estimation under this paradigm from a technical point of view. There has been a great deal of work on various facets of such parameter estimation, and much of it is of interest because it deals with issues of importance to the application of the theory.