In the past several decades, there has been an increasing interest in the development of statistics used to identify examinees who respond to test items in a manner that is divergent from the underlying test model. One statistic that has received a great deal of attention is the lz index (Drasgow, Levine, & Williams, 1985). Trabin & Weiss (1983) developed a slightly different approach for identifying model-divergent response patterns, based on the discrepancy between observed and expected person response functions (PRFs). Here, the PRF method was compared theoretically and empirically to 1z. Although the results suggest that the performance of lz was, in most conditions studied, superior to the PRF method, the PRF method was useful in investigating why a response vector was model divergent. The PRF method can be used along with lz to identify different types of model divergent response patterns.
Nering, M. L., & Meijer, R. R. (1998). A comparison of the person response function and the Iz person-fit statistic. Applied psychological measurement, 22(1), 53-69. https://doi.org/10.1177/01466216980221004