Abstract
In this paper the approach to increasing of measurements efficiency in competence assessment is offered. This approach is based in the mathematical models of the modern measurement theory (Item Response Theory) and the model of multistage measurements for interdisciplinary competence assessment. The IRT models are discussed in context of two problems: algorithms for adaptive testing and comparative analysis of their the possibilities for processing empirical results from the dichotomous and polytomous scored items. By this connection some models and some inequalities are resulted which allow to optimize competence assessment.
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