Estimating mixture fit index for cognitive diagnosis models

Abstract

Rudas et al. (1994) proposed the use of a mixture fit index as goodness-of-fit measure in contingency tables. It assumes that observations can be classified into two groups, namely: those that conform to a parametric model and those that do not. The mixture fit index gives the proportion of misfitting observations. This study applies the mixture fit index to detect aberrant response patterns in the cognitive diagnosis model (CDM) framework. Using nonlinear programming and bisection method, the proposed algorithm iteratively estimates the mixture fit index and posterior probabilities are then used to calculate the likelihood that response patterns belong in the aberrant group. Preliminary results show that the proposed procedure can identify aberrant response patterns for short tests.