The Problem With the Step Metaphor for Polytomous Models for Ordinal Assessments

AbstractLikert-type items and polytomous models are preferred over yes–no items and dichotomous models for the measurement of attitudes, because a broader range of response categories provides superior item and test information functions. Yet, for ability assessment with multiple-choice tests, the dichotomous three-parameter logistic model (3PLM) is often chosen. Because multiple-choice responses are polytomous before they are categorized as correct or incorrect, a polytomous characterization might render more efficient tests. Early studies suggested that the nominal response model (NRM) is advantageous in this respect. We investigate the reasons for those results and the outcomes of a polytomous characterization based on the multiple-choice model (MCM). An empirical data set is used to compare polytomous (NRM and MCM) and dichotomous (3PLM) characterizations of a test. The results revealed superior item and test information functions from polytomous models. Yet, close inspection suggests that these outcomes are artifactual and two simulation studies confirmed this point. These studies revealed a structural inadequacy of the NRM for multiple-choice items and that the MCM characterization outperforms the 3PLM characterization only when distractor endorsement frequencies vary non-monotonically with ability, although this feature is rarely observed in empirical data sets.

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