The Multiple-Choice Model

Abstract

This article deals with some of the problems that have hindered the application of Samejima's and Thissen and Steinberg's multiple-choice models: (a) parameter estimation difficulties owing to the large number of parameters involved, (b) parameter identifiability problems in the Thissen and Steinberg model, and (c) their treatment of omitted responses. The authors propose a new multiple-choice model (Restricted Samejima Multiple-Choice Model) that is more explicit about the assumed omitting mechanisms and takes advantage of this knowledge to improve the estimation of parameters. The three above-mentioned models and the Nominal Response Model were fitted to a 3,224-subject sample that took a Written English Test. Fit plots, X 2 statistics, and information-based fit indexes were obtained to assess the goodness of fit. Results show that the new model proposed fits as well as the other two multiple-choice models and better than the Nominal model. A parameter recovery simulation study was also carried out to confirm that its estimation features are indeed improved. Parameters are better recovered in the new model than in the other two multiple-choice models.