Abstract #301702

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JSM 2002 Abstract #301702
Activity Number: 281
Type: Contributed
Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics*
Abstract - #301702
Title: Non-parametric Item Response Function Estimation with Free-Knot Splines
Author(s): Matthew Johnson*+ and Ilaria Di Matteo
Affiliation(s): Educational Testing Service and United Nations
Address: Rosedale Road ms 02-T, Princeton, New Jersey, 08541, USA
Keywords: Item Response models ; Free-knot splines ; reversible-jump McMC ; Bayesian statistics
Abstract:

The problem of estimating the item response function is a basic problem in psychometrics. In most cases, we posit some simple models for the response function, such as the Rasch model, the two-parameter logistic (2PL), three-parameter logistic (3PL), or their probit counterparts. In many cases, the shape suggested by these models is too restrictive and a more flexible function is desirable. Spatially adaptive regression splines offer us that flexibility. In this presentation, we introduce a procedure that builds off the work of DiMatteo, Genovese, and Kass (2002) and uses reversible-jump Markov chain Monte Carlo techniques to fit item response functions with regression splines with unknown numbers of knots and knot locations. We illustrate the procedure with, and application to, educational testing.

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