Identifying person misfit using the person backward stepwise reliability curve (PBRC)

The goal of the present study was to propose a visualization of aberrant response patterns based on the idea put forth by the Cronbach-Mesbach curve. First, an index of person reliability is developed using the K-R 20 formula followed by a backward stepwise procedure in which one person at a time is deleted from the model. Observations for which reliability is no longer monotonically increasing suggest that they are candidates for aberrant responding. Using data from the quantitative domain of a national aptitude test the proposed visualization technique was demonstrated. The external validity of the procedure was tested by contrasting the person fit reliability estimates with those derived from other indices of aberrant responding such as the Ht. Results indicated that individuals not covarying with other individuals concerning their response patterns and concordance to the measurement of a unified latent trait were identified by both the present procedure and Ht and U3 at a rate of 100%. By plotting those individuals using Person Response Curves (PRCs) results confirmed the lack of monotonicity in the relationship between item difficulty and person skill. Consequently, results confirm the usefulness of the present methodology as an index for identifying responders who manifest themselves with aberrant responses and who are not conducive to the measurement of the latent trait.