Samejima’s Graded Response Model

The logistic versions of Samejima’s (1969) graded response model and Muraki’s (1992) gen-eralized partial-credit model are parameterized differently by MULTILOG (Thissen, 1991) and PARSCALE (Muraki & Bock, 1996). Procedures for obtaining comparable item parameter estimates from MULTILOG and PARSCALE are described and example command files are provided. Index terms: generalized partial-credit model, graded response model, item parameter estimation, item re-sponse theory (parameter estimation), MULTILOG, PARSCALE, polytomous models. MULTILOG (Thissen, 1991) and PARSCALE (Muraki & Bock, 1996) item parameter estimates for the logistic versions of Samejima’s (1969) graded response model (GRM) and Muraki’s (1992) generalized partial-credit model (GPCM) do not initially seem comparable. The reason is that the two computer programs parameterize the models differently. However, comparable item parameter estimates might need to be obtained in certain situations, e.g., when changes in the requirements of an operational testing program require a change from one computer program to the other. This paper provides procedures for obtaining comparable parameter estimates for the two models from the two programs. To simplify comparison of the programs, the notation has been modified here for the MULTILOG and PARSCALE versions of Samejima’s (1969) GRM and Muraki’s (1992