The person response function as a tool in person-fit research

Item responses that do not fit an item response theory (IRT) model may caus e the latent trait value to be inaccurately estimated. In the past two deca des several statistics have been proposed that can be used to identify nonf itting item score patterns. These statistics all yield scalar values. Here, the use of the person response function (PRF) For identifying nonfitting i tem score patterns was investigated. The PRF is a function and can be used for diagnostic purposes. First. the PRF is defined in a class of IRT models that imply an invariant item ordering. Second, a person-fit method propose d by Trabin & Weiss (1983) is reformulated in a nonparametric IRT context a ssuming invariant item ordering, and statistical theory proposed by Rosenba um (1987a) is adapted to test locally whether a PRF is nonincreasing. Third , a simulation study was conducted to compare the use of the PRF with the p erson-fit statistic ZU3. It is concluded that the PRF can be used as a diag nostic tool in person-fit research.