An Examination of Different Methods of Setting Cutoff Values in Person Fit Research

This simulation study evaluates four different methods of setting cutoff values for person fit assessment, including (a) using fixed cutoff values either from theoretical distributions of person fit statistics, or arbitrarily chosen by the researchers in the literature; (b) using the specific percentile rank of empirical sampling distribution of person fit statistics from simulated fitting responses; (c) using bootstrap method to estimate cutoff values of empirical sampling distribution of person fit statistics from simulated fitting responses; and (d) using the p-value methods to identify misfitting responses conditional on ability levels. The Snijders' (2001), as an index with known theoretical distribution, van der Flier's U3 (1982) and Sijtsma's HT coefficient (1986), as indices with unknown theoretical distribution, were chosen. According to the simulation results, different methods of setting cutoff values tend to produce different levels of Type I error and detection rates, indicating it is critical to select an appropriate method for setting cutoff values in person fit research.