A Sequential IRT Model for Multiple-Choice Items and a Multidimensional Extension.

For certain multiple-choice tests, it might be theorized that respondents evaluate response options in a stepwise fashion. Statistical models that assume such a process may compete against models that imply a process in which all response options are simultaneously compared, such as Bock's nominal response model. In this article, a sequential response model for multiple-choice items (SRM-MC) is considered. The model is applied to a sentence correction test in which the recognition of error and correction of error can be viewed as separate steps in solving an item. The proposed model permits the introduction of different proficiencies across steps. A fully Bayesian approach to estimating the model is presented, and an empirical comparison is performed against competing models. Empirical results support the proposed model and suggest distinct proficiencies related to recognition and correction.