This article aims to provide a theoretical framework for computerized adaptive tests (CAT) and item response theory models for polytomous items. Besides that, it aims to introduce the simulation and live CAT software to the related researchers. Computerized adaptive test algorithm, assumptions of item response theory models, nominal response…

In recent years, the computerised adaptive test (CAT) has gained popularity over conventional exams in evaluating student capabilities with desired accuracy. However, the key limitation of CAT is that it requires a large pool of pre-calibrated questions. In the absence of such a pre-calibrated question bank, offline exams with uncalibrated…

Proposes an algorithm that minimizes the asymptotic variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The criterion results in a closed-form expression that is easy to evaluate. Also shows how the algorithm can be modified if the interest is in a test with a "simple ability structure."…