Modeling incorrect responses to multiple-choice items with multilinear formula score theory

Multilinear formula score theory (Levine, 1984,1985, 1989a, 1989b) provides powerful methods foraddressing important psychological measurement problems.In this paper, a brief review of multilinear formulascoring (MFS) is given, with specific emphasis onestimating option characteristic curves (OCCS). MFSwas used to estimate OCCS for the Arithmetic Reasoningsubtest of the Armed Services Vocational AptitudeBattery. A close match was obtained between empiricalproportions of option selection for examinees in 25ability intervals and the modeled probabilities of optionselection. In a second analysis, accurately estimatedOCCS were obtained for simulated data. To evaluatethe utility of modeling incorrect responses to theArithmetic Reasoning test, the amounts of statisticalinformation about ability were computed for dichotomousand polychotomous scorings of the items. Consistentwith earlier studies, moderate gains in informationwere obtained for low to slightly above averageabilities. Index terms: item response theory, marginalmaximum likelihood estimation, maximum likelihoodestimation, multilinear formula scoring, optioncharacteristic curves, polychotomous measurement,test information function.