ITEM RESPONSE THEORY WITH ESTIMATION OF THE LATENT POPULATION DISTRIBUTION USING SPLINE-BASED DENSITIES

CAROL M. WOODS
WASHINGTON UNIVERSITY IN ST. LOUIS
DAVID THISSEN
UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL


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.Asimulation study shows that the newprocedure 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.
Key words: item response theory, marginal maximum likelihood, latent variable, population distribution,
density estimation, splines.