Trait level estimation for nonfitting response vectors

Item responses that do not fit an item response theory model may cause the latent trait value, 0, to be inaccurately estimated. Although in many studies the proportion of nonmodel-fitting response vectors (NRvs) identified (i.e., the detection rate) has been investigated, less is known about the severity of the inaccuracy of the estimated 0 (0) in relation to the rate at which response patterns are classified as not fitting a model using person-fit statistics. In the present study, three scoring methods-maximum likelihood estimation (MLE), expected a posterior (EAP) estimation, and biweight estimation (BIw)-were used to estimate 0 when NRVS were present. The detection rate of the lz person-fit statistic (Drasgow, Levine, & Williams, 1985) was also investigated. It was found that NRVS influenced the value of 8, and this depended heavily on the type of misfit and the 8 level. It was also found that the BIW scoring method reduced the bias in 0 and improved the detection rate compared to MLE and EAP for examinees located at the extreme ends of the 8 continuum. Results of this study extended the results obtained by Reise (1995) and showed that the low detection rates found in his study were due to the particular kind of procedure used to generate NRVS.