The Power of Rasch Person-Fit Statistics in Detecting Unusual Response Patterns

Abstract

Five Rasch person-fit indexes were compared on their ability to detect spuriously high and low nonsystematic response patterns. The moderating effects of test dimensionality, type of misfit, and test length were also investigated. Results indicated that (1) all fit indexes were not significantly correlated with Rasch trait estimates; (2) their sampling distributions deviated significantly from the standard normal distribution; (3) using adjusted cutoff criteria to identify misfit, ECI2z, ECI4z, Iz, and WSR-C performed equally well in the detection of misfit regardless of test dimensionality, type of misfit, and test length (however, only lz is recommended for the spuriously high response patterns for a two-dimensional test); (4) the false positive rate for each index was less than the nominal .05 level; (5) Rasch person-fit indexes are more sensitive to spuriously high response patterns than to spuriously low response patterns on a two-dimensional test, but when the test is unidimensional they demonstrate equal sensitivity to both types of misfit; and (6) the detectability of misfit increases with test length.