Modeling Incorrect Responses to Multiple-Choice Items With Multilinear Formula Score Theory

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Abstract
Multilinear formula score theory (Levine, 1984, 1985, 1989a, 1989b) provides powerful methods for addressing important psychological measurement prob lems. In this paper, a brief review of multilinear for mula scoring (MFS) is given, with specific emphasis on estimating option characteristic curves (occs). MFS was used to estimate occs for the Arithmetic Reason ing subtest of the Armed Services Vocational Aptitude Battery. A close match was obtained between empiri cal proportions of option selection for examinees in 25 ability intervals and the modeled probabilities of op tion selection. In a second analysis, accurately esti mated occs were obtained for simulated data. To eval uate the utility of modeling incorrect responses to the Arithmetic Reasoning test, the amounts of statistical information about ability were computed for dichoto mous and polychotomous scorings of the items. Con sistent with earlier studies, moderate gains in informa tion were obtained for low to slightly above average abilities.

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