An Optimal, Unbiased Classification Rule for Mastery Testing Based on Longitudinal Data

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Abstract
An optimal, unbiased classification rule is proposed based on a longitudinal model for the measurement of change in ability. The proposed methodology can be used as an additional tool for the year-to-year evaluation of student progress as well as consideration of the master testing problem. In general, it predicts future level of knowledge by using information about level of knowledge at entrance, its rate of growth, and the amount of within-individual variation. An illustration shows how the individual-oriented threshold value above which a student can be considered a master depends on the intra-test score variation and hence differs from student to student. Furthermore, it appears that information about growth of knowledge in the first year substantially improved the prediction of relative position of ability in the future.

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