A Monte Carlo Study of the Effect of Item Characteristic Curve Estimation on the Accuracy of Three Person-Fit Statistics

Abstract

To date, there have been no studies comparing parametric and nonparametric Item Characteristic Curve (ICC) estimation methods on the effectiveness of Person-Fit Statistics (PFS). The primary aim of this study was to determine if the use of ICCs estimated by nonparametric methods would increase the accuracy of item response theory—based PFS for small sample sizes. Using three recognized PFS (lz, ECI2 z, and ECI4z), four estimation methods were compared: two parametric methods (the two-parameter logistic model and three-parameter logistic model) and two nonparametric methods (Nadaraya-Watson's regression and the local logistic regression). Finally, matrices of 100- and 1,000-answer vectors were generated for this Monte Carlo study. For both large and small sample sizes, the accuracy of the PFS was greater when used with the parametric models.