An Information Matrix Test for the Collapsing of Categories Under the Partial Credit Model

Daphna Harel and Russell J. Steele
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Daphna Harel: New York University
Russell J. Steele: McGill University

Journal of Educational and Behavioral Statistics, 2018, vol. 43, issue 6, 721-750

Abstract: Collapsing categories is a commonly used data reduction technique; however, to date there do not exist principled methods to determine whether collapsing categories is appropriate in practice. With ordinal responses under the partial credit model, when collapsing categories, the true model for the collapsed data is no longer a partial credit model, and therefore refitting a partial credit model may result in model misspecification. This article details the implementation and performance of an information matrix test (IMT) to assess the implications of collapsing categories for a given data set under the partial credit model and compares its performance to the application of a nominal response model (NRM) and the S − X 2 goodness-of-fit statistic. The IMT and NRM-based test are able to correctly determine the true number of categories for an item, given reasonable power through this goodness-of-fit test. We conclude by applying the test to a well-studied data set from the literature.

Keywords: collapsing categories; information matrix test; partial credit model; item response theory (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:43:y:2018:i:6:p:721-750

DOI: 10.3102/1076998618787478

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