Deriving Stopping Rules for Multidimensional Computerized Adaptive Testing
Chun Wang, Hua-Hua Chang, and Keith A. Boughton
In this study, four stopping rules were proposed for MCAT:
D-rule: minimum determinant rule of variance-covariance matrix;
E-rule: minimum eigenvalue of variance-covariance matrix
T-rule: maximum overall variance of variance-covariance matrix
K-rule: maximum KL divergence rule.
The main purpose of this study is to investigate whether these four rule can terminate the test when the ability estimation achieve certain level, even for the extreme ability
It was found that using the D-, E-, or T-rule, examinees with extreme ability tended to have tests that were twice as long as those moderate examinees.
Comments & Questions:
1. The current study used compensatory MIRT. There are some limitations for this model. For example, it was assumed that the items measure only one latent trait. When items measure more than one dimension simultaneously, the model may not applicable. MRCMLM is an alternative to deal with within- and between- multidimensionality. It is desirable to investigate the propose stopping rules under the MRCMLM.
2. The current study did not compare the reliability of ability under four stopping rule, which is very interest to readers. However, whether the reliablity from there four stopping rule is doubtful since the statistics were developed under different framework.