title: Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities.
abstract: The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.
authors.affiliation: Washington University in St. Louis, St. Louis. cwoods@artsci.wustl.edu.|Department of Psychology, Washington University, Campus Box 1125, St. Louis, MO, 63130-4899, USA. cwoods@artsci.wustl.edu.
authors.forename: Carol M
authors.initials: CM
authors.lastname: Woods
authors.affiliation: University of North Carolina at Chapel Hill, USA.
authors.forename: David
authors.initials: D
authors.lastname: Thissen
keywords: density estimation; item response theory; latent variable; marginal maximum likelihood; population distribution; splines