Formula Scoring, Basic Theory and Applications
ILLINOIS UNIV AT URBANA MODEL BASED MEASUREMENT LAB
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Formula scoring is a systematic study of measurement statistics expressed as sums of products of item scores. The theory is currently being used to compute non-parametric estimates of ability distributions, item response functions, and option response functions. The theory has been used to design algorithms for estimating item response functions from adaptive test data on-line calibration, monitoring and correcting drift in observed score distributions for adaptive tests on-line equating, computing optimal tests for cheating, and combining appropriateness measurement information from several subtests. In this paper a portion of the theory is developed from a few principles. Applications are considered to the problems of deciding whether ability has the same distribution in two demographic groups, to finding latent class models that are equivalent to item response models, and to controlling drift in adaptive testing programs. Keywords Latent trait theory, Item response theory, Formula score, Rasch model, Equating, Foundations, Quasidensities, Densities, Non-parametric density estimation, Ability distributions, Identifiability.
- Statistics and Probability