Person fit in order-restricted latent class models

Person-fit analysis revolves around fitting an item response theory (IRT) model to respondents’ vectors of item scores on a test and drawing statistical inferences about fit or misfit of these vectors. Four person-fit measures were studied in order-restricted latent class models (OR-LCMs). To decide whether the OR-LCM fits an item score vector, a Bayesian framework was adopted and posterior predictive checks were used. First, simulated Type I error rates and detection rates were investigated for the four person-fit measures under varying test and item characteristics. Second, the suitability of the OR-LCM methodology in a nonparametric IRT context was investigated. The result was Type I error rates close to the nominal Type I error rates and detection rates close to the detection rates found in OR-LCMs. This means that the OR-LCM methodology is a suitable alternative for assessing person fit in nonparametric IRT models.