Detection of Person Misfit in Computerized Adaptive Tests with Polytomous Items

Abstract

Item scores that do not fit an assumed item response theory model may cause the latent trait value to be inaccurately estimated. For a computerized adaptive test (CAT) using dichotomous items, several person-fit statistics for detecting mis.tting item score patterns have been proposed. Both for paper-and-pencil (P&P) tests and CATs, detection ofperson mis.t with polytomous items is hardly explored. In this study, the nominal and empirical null distributions ofthe standardized log-likelihood statistic for polytomous items are compared both for P&P tests and CATs. Results showed that the empirical distribution of this statistic differed from the assumed standard normal distribution for both P&P tests and CATs. Second, a new person-fit statistic based on the cumulative sum (CUSUM) procedure from statistical process control was proposed. By means ofsimulated data, critical values were determined that can be used to classify a pattern as fitting or misfitting. The effectiveness of the CUSUM to detect simulees with item preknowledge was investigated. Detection rates using the CUSUM were high for realistic numbers ofdisclosed items.