Fixing the c Parameter in the Three-Parameter Logistic Model

Abstract

For several decades, the three-parameter logistic model (3PLM) has been the dominant choice for practitioners in the field of educational measurement for modeling examinees’ response data from multiple-choice (MC) items. Past studies, however, have pointed out that the c-parameter of 3PLM should not be interpreted as a guessing parameter. This study found logical, empirical evidence showing that neither the a-, b-, or c-parameters of 3PLM can accurately reflect the discrimination, difficulty, and guessing properties of an item, respectively. This study reconceptualized the problem-solving and guessing processes with a modification of the 3PLM that eliminates ambiguity in modeling the guessing process. A series of studies using various real and simulated data demonstrated that the suggested model, in which the c-parameters were fixed at a computed probability for successful random guessing (i.e., c = 1 / k with k being the number of options), could provide a more feasible, stable, and accurate item estimation solution without sacrificing the model fit compared with a typical 3PLM. Accessed 13,077 times on https://pareonline.net from January 09, 2012 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right.

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