Variable-Length Computerized Adaptive Testing Using the Higher Order DINA Model

Abstract

Cognitive diagnosis models provide profile information about a set of latent binary attributes, whereas item response models yield a summary report on a latent continuous trait. To utilize the advantages of both models, higher order cognitive diagnosis models were developed in which information about both latent binary attributes and latent continuous traits is available. To facilitate the utility of cognitive diagnosis models, corresponding computerized adaptive testing (CAT) algorithms were developed. Most of them adopt the fixed-length rule to terminate CAT and are limited to ordinary cognitive diagnosis models. In this study, the higher order deterministic-input, noisy-and-gate (DINA) model was used as an example, and three criteria based on the minimum-precision termination rule were implemented: one for the latent class, one for the latent trait, and the other for both. The simulation results demonstrated that all of the termination criteria were successful when items were selected according to the Kullback-Leibler information and the posterior-weighted Kullback-Leibler information, and the minimum-precision rule outperformed the fixed-length rule with a similar test length in recovering the latent attributes and the latent trait.