Person-fit analyses are commonly used to detect aberrant responding in self-report data. Nonparametric person fit statistics do not require fitting a parametric test theory model and have performed well compared to other person-fit statistics. However, detection of aberrant responding has primarily focused on dominance response data, thus the…

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

Presents an overview of a wide range of measurement models currently available to the analyst who needs to make accurate and valid inferences about respondents and stimuli from data. Reviews models with and without predictor variables or observed and latent predictors, as well as parametric and nonparametric models, and models for order-restricted…