Nonparametric Person-Fit Analysis of Polytomous Item Scores

Abstract

Person-fit methods are used to uncover atypical test performance as reflected in the pattern of scores on individual items in a test. Unlike parametric person-fit statistics, nonparametric person-fit statistics do not require fitting a parametric test theory model. This study investigates the effectiveness of generalizations of nonparametric person-fit statistics to polytomous item response data. A simulation study using varying test and item characteristics shows that a simple count of the Guttman errors is effective in detecting serious person misfit. The simulation study further shows that in most conditions a simple nonparametric person-fit statistic is as effective as a commonly used parametric person-fit statistic in detecting deviant item score vectors. An empirical example illustrates the use of the nonparametric person-fit statistics in real data.