A graded response model for measuring person reliability

This paper extends Lumsden's fluctuation model to the graded response case and, from the resulting basic scaling model, develops a one-dimensional item response theory graded response model (GRM). Under some additional assumptions, it follows that the item category response functions (ICRFs) can be closely approximated by the ICRFs of the standard GRM with equal item discrimination. For fixed item locations, the item responses depend on two individual differences parameters: the person central location and the person reliability. Procedures for estimating the person parameters and for addressing the goodness of fit of the proposed model as compared to the standard GRM are discussed. The accuracy of the person estimates is assessed by means of simulation studies. Finally, all the developments are illustrated using three empirical examples in personality measurement.