An Iterative Scale Purification Procedure on l_z for the Detection of Aberrant Responses

Many person-fit statistics have been proposed to detect aberrant response behaviors (e.g., cheating, guessing). Among them, l_z is one of the most widely used indices. The computation of l_z assumes the item and person parameters are known. In reality, they often have to be estimated from data. The better the estimation, the better l_z will perform. When aberrant behaviors occur, the person and item parameter estimations are inaccurate, which in turn degrade the performance of l_z. In this study, an iterative procedure was developed to attain more accurate person parameter estimates for improved performance of l_z. A series of simulations were conducted to evaluate the iterative procedure under two conditions of item parameters, known and unknown, and three aberrant response styles of difficulty-sharing cheating, random-sharing cheating, and random guessing. The results demonstrated the superiority of the iterative procedure over the non-iterative one in maintaining control of Type-I error rates and improving the power of detecting aberrant responses. The proposed procedure was applied to a high-stake intelligence test.