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.
Drasgow, Fritz, Levine, Michael V, Williams, Bruce, McLaughlin, Mary E & et al. (1989). Modeling incorrect responses to multiple-choice items with multilinear formula score theory. Applied Psychological Measurement, 13, 285-299. doi:10.1177/014662168901300309
Drasgow, Fritz; Levine, Michael V.; Williams, Bruce; McLaughlin, Mary E.; Candell, Gregory L..
Modeling incorrect responses to multiple-choice items with multilinear formula score theory.
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