New advances in Nonparametric Item Response Theory (NIRT)
State of the art talk by Andries van der Ark, Department of Methodology and Statistics, Tilburg University, the Netherlands
Chair: Klaas Sijtsma, Wednesday 22nd July, 17.15 - 18.00, Palmeston Lecture Theatre, Fisher Building.
NIRT models consist of weak assumptions implying ordinal measurement. Typical assumptions are unidimensionality of the latent trait, local independence, and monotonicity of the item response function. Ordinal measurement implied by NIRT models includes stochastic ordering of respondents on the latent trait using their test scores and stochastic ordering of items on the latent trait using their mean item scores. Before ordering respondents and items, it is important to investigate whether the assumptions of the NIRT model hold. Mokken scale analysis, a scaling procedure for both dichotomous and polytomous items, provides tools to investigate whether the assumptions of NIRT models hold in test-data. It consists of an automated item selection procedure to partition a set of items into scales and several methods to test observable consequences of NIRT model assumptions. Recently, both the selection of items and the testing of observable consequences have been improved.
After a brief introduction to NIRT models and ordinal measurement, I will discuss these new tools for NIRT, including statistical testing of scalability coefficients using marginal models, an improved method for item selection using a genetic algorithm, and methods for investigating an invariant item ordering.