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Browsing by Author "Williams, Bruce"

Now showing 1 - 3 of 3
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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.
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    Measuring the difference between two models
    (1992) Levine, Michael V.; Drasgow, Drasgow, Fritz Fritz; Williams, Bruce; McCusker, Christopher; Thomasson, Gary L.
    Two psychometric models with very different parametric formulas and item response functions can make virtually the same predictions in all applications. By applying some basic results from the theory of hypothesis testing and from signal detection theory, the power of the most powerful test for distinguishing the models can be computed. Measuring model misspecification by computing the power of the most powerful test is proposed. If the power of the most powerful test is low, then the two models will make nearly the same prediction in every application. If the power is high, there will be applications in which the models will make different predictions. This measure, that is, the power of the most powerful test, places various types of model misspecification- item parameter estimation error, multidimensionality, local independence failure, learning and/or fatigue during testing-on a common scale. The theory supporting the method is presented and illustrated with a systematic study of misspecification due to item response function estimation error. In these studies, two joint maximum likelihood estimation methods (LOGIST 2B and LOGIST 5) and two marginal maximum likelihood estimation methods (BILOG and ForScore) were contrasted by measuring the difference between a simulation model and a model obtained by applying an estimation method to simulation data. Marginal estimation was found generally to be superior to joint estimation. The parametric marginal method (BILOG) was superior to the nonparametric method only for three-parameter logistic models. The nonparametric marginal method (ForScore) excelled for more general models. Of the two joint maximum likelihood methods studied, LOGIST s appeared to be more accurate than LOGIST 2B. Index terms: BILOG; forced-choice experiment; ForScore; ideal observer method; item response theory, estimation, models; LOGIST; multilinear formula score theory.
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    Modeling incorrect responses to multiple-choice items with multilinear formula score theory
    (1989) Drasgow, Fritz; Levine, Michael V.; Williams, Bruce; McLaughlin, Mary E.; Candell, Gregory L.
    Multilinear formula score theory (Levine, 1984, 1985, 1989a, 1989b) provides powerful methods for addressing important psychological measurement problems. In this paper, a brief review of multilinear formula scoring (MFS) is given, with specific emphasis on estimating option characteristic curves (OCCS). MFS was used to estimate OCCS for the Arithmetic Reasoning subtest of the Armed Services Vocational Aptitude Battery. A close match was obtained between empirical proportions of option selection for examinees in 25 ability intervals and the modeled probabilities of option selection. In a second analysis, accurately estimated OCCS were obtained for simulated data. To evaluate the utility of modeling incorrect responses to the Arithmetic Reasoning test, the amounts of statistical information about ability were computed for dichotomous and polychotomous scorings of the items. Consistent with earlier studies, moderate gains in information were obtained for low to slightly above average abilities. Index terms: item response theory, marginal maximum likelihood estimation, maximum likelihood estimation, multilinear formula scoring, option characteristic curves, polychotomous measurement, test information function.