Browsing by Author "Mead, Alan D."

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    Distinguishing among parametric item response models for polychotomous ordered data
    (1994) Maydeu-Olivares, Albert; Drasgow, Fritz; Mead, Alan D.
    Several item response models have been proposed for fitting Likert-type data. Thissen & Steinberg (1986) classified most of these models into difference models and divide-by-total models. Although they have different mathematical forms, divide-by-total and difference models with the same number of parameters seem to provide very similar fit to the data. The ideal observer method was used to compare two models with the same number of parameters-Samejima’s (1969) graded response model (a difference model) and Thissen & Steinberg’s (1986) extension of Masters’ (1982) partial credit model (a divide-by-total model-to investigate whether difference models or divide-by-total models should be preferred for fitting Likert-type data. The models were found to be very similar under the conditions investigated, which included scale lengths from 5 to 25 items (five-option items were used) and calibration samples of 250 to 3,000. The results suggest that both models fit approximately equally well in most practical applications. Index terms: graded response model, IRT, Likert scales, partial credit model, polychotomous models, psychometrics.
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    Fitting polytomous item response theory models to multiple-choice tests
    (1995) Drasgow, Fritz; Levine, Michael V.; Tsien, Sherman; Williams, Bruce; Mead, Alan D.
    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.