Fitting polytomous item response theory models to multiple-choice tests

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Fitting polytomous item response theory models to multiple-choice tests

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Drasgow, Fritz

Levine, Michael V.

Tsien, Sherman

Williams, Bruce

Mead, Alan D.

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1995

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This study examined how well current software implementations of four polytomous item response theory models fit several multiple-choice tests. The models were Bock’s (1972) nominal model, Samejima’s (1979) multiple-choice Model C, Thissen & Steinberg’s (1984) multiple-choice model, and Levine’s (1993) maximum-likelihood formula scoring model. The parameters of the first three of these models were estimated with Thissen’s (1986) MULTILOG computer program; Williams & Levine’s (1993) FORSCORE program was used for Levine’s model. Tests from the Armed Services Vocational Aptitude Battery, the Scholastic Aptitude Test, and the American College Test Assessment were analyzed. The models were fit in estimation samples of approximately 3,000; cross-validation samples of approximately 3,000 were used to evaluate goodness of fit. Both fit plots and X² statistics were used to determine the adequacy of fit. Bock’s model provided surprisingly good fit; adding parameters to the nominal model did not yield improvements in fit. FORSCORE provided generally good fit for Levine’s nonparametric model across all tests. Index terms: Bock’s nominal model, FORSCORE, maximum likelihood formula scoring, MULTILOG, polytomous IRT.

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Applied Psychological Measurement, Volume 19, 1995

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Drasgow, Fritz, Levine, Michael V, Tsien, Sherman, Williams, Bruce & et al. (1995). Fitting polytomous item response theory models to multiple-choice tests. Applied Psychological Measurement, 19, 143-165. doi:10.1177/014662169501900203

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Drasgow, Fritz; Levine, Michael V.; Tsien, Sherman; Williams, Bruce; Mead, Alan D.. (1995). Fitting polytomous item response theory models to multiple-choice tests. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/117478.

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