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Educational and Psychological Measurement
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Methods for Assessing Item, Step, and Threshold Invariance in Polytomous Items Following the Partial Credit Model

Randall D. Penfield

University of Miami, penfield{at}miami.edu

Nicholas D. Myers

University of Miami

Edward W. Wolfe

Virginia Polytechnic Institute and State University

Measurement invariance in the partial credit model (PCM) can be conceptualized in several different but compatible ways. In this article the authors distinguish between three forms of measurement invariance in the PCM: step invariance, item invariance, and threshold invariance. Approaches for modeling these three forms of invariance are proposed, and the mathematical relationship between the three forms is established. Parametric and contingency table approaches for assessing the three forms of invariance are presented, and the application of the parametric and contingency table approaches to a real data set is described. The invariance effect estimates observed for the parametric and contingency table approaches are consistent with the theoretical equivalence of the two approaches.

Key Words: invariance • differential item functioning • differential step functioning • partial credit model

This version was published on October 1, 2008

Educational and Psychological Measurement, Vol. 68, No. 5, 717-733 (2008)
DOI: 10.1177/0013164407312602
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