Computer Adaptive Test Based on Latent Rank Theory

A Proposition of the Algorithm and its Validation

Abstract

The purposes of this paper are 1) to propose an algorithm for a computer adaptive test (CAT) based on latent rank theory (LRT), after reviewing the characteristics of LRT, 2) to determine the number of items required for actual CAT implementation using a simulation study, and 3) to discuss further research topics by validating the proposed algorithm after administering the actual CAT.

This paper uses a simulation study to examine the consistency between the true and estimated latent ranks, the degree of convergence in rank membership profile (RMP, which describes test takers’ latent ability in LRT), and the number of items needed to satisfy CAT termination conditions. As a result, a projection is given of the number of items needed to administer CATs, and flaws in the current item bank are also revealed. In addition, the proposed algorithm was reconsidered and further topics were discussed, such as manipulation of item difficulty and evaluation of RMP convergence.