Methods for detecting item score patterns that are unlikely, given that a parametric item response theory model gives an adequate description of the data or given the responses of other persons in the group, are discussed. The use of person-fit statistics in empirical data analysis is briefly discussed. (SLD)

Reviews developments in nonparametric item-response theory (NIRT), from its historic origins in item-response theory (IRT) and scale analysis to new theoretical results for practical test construction. Discusses theoretical results from NIRT often relevant to IRT. Contains 134 references. (SLD)

A method is proposed for investigating the intersection of item response functions in the nonparametric item-response-theory model of R. J. Mokken (1971). Results from a Monte Carlo study support the proposed use of the transposed data matrix H(sup T) as an extension to Mokken's approach. (SLD)

Person-fit statistics test whether the likelihood of a respondent's complete vector of item scores on a test is low given the hypothesized item response theory model. This binary information may be insufficient for diagnosing the cause of a misfitting item-score vector. The authors propose a comprehensive methodology for person-fit analysis in the…

In this article, an overview of nonparametric item response theory methods for determining the dimensionality of item response data is provided. Four methods were considered: MSP, DETECT, HCA/CCPROX, and DIMTEST. First, the methods were compared theoretically. Second, a simulation study was done to compare the effectiveness of MSP, DETECT, and…

Methods are discussed that can be used to investigate the fit of an item score pattern to a test model. Model-based tests and personality inventories are administered to more than 100 million people a year and, as a result, individual fit is of great concern. Item Response Theory (IRT) modeling and person-fit statistics that are formulated in the…

The person-response function (PRF) relates the probability of an individual's correct answer to the difficulty of items measuring the same latent trait. Local deviations of the observed PRF from the expected PRF indicate person misfit. We discuss two new approaches to investigate person fit. The first approach uses kernel smoothing to estimate…

Presents componential item response theory as a model-oriented approach to studying processes and strategies underlying the incorrect/correct responses to cognitive test tasks. Results from 417 elementary school students show that combining knowledge of solution strategies with Item Response Theory modeling produced a useful unidimensional scale…