Abstract
There were two main features of this paper: (1) the likelihood-based person-fit index, lx and the residual-based caution index, Tatsuoka’s ζ have similar mathematical structure except the difference of weight. The weight of lx index is a logit of an item response function (IRF), while the weight of ζ is residual IRF and true score; (2) a degree of coincidence between any two aberrant subjects is defined as a similarity for multidimensional scaling (MDS): Sjk
= (
[PjrPkr + (1 − Pjr)(1 − Pkr)])1/2, where g is the number of item groups, Pjr is the proportion of subject j who answer correctly in the item group r. The larger value of the Sjk, the more similarity will be between the subject j and k.
A dataset of Chinese vocabulary test was investigated using the lx index and MDS. The 3.5% of the aberrant subjects were detected, and classified into 5 types. The result of MDS indicated that it is a useful and effective method for classification of aberrant item response patterns. Suggestions for future research are provided.
