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Activity Number:
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237
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
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Sponsor:
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Social Statistics Section
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| Abstract - #302174 |
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Title:
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An Adaptive Free-Knot Spline for Polytomous Item Response Models
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Author(s):
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Matthew S. Johnson*+ and Ilaria DiMatteo
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Companies:
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Carnegie Mellon University and United Nations
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Address:
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55 Lexington Ave., New York, NY, 10010,
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Keywords:
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item response theory ; MCMC ; reversible jump ; adaptive splines
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Abstract:
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Item response theory (IRT) models are a class of models used in psychometrics to describe the response behavior of individuals to a set of categorical items. IRT models utilize a random effect to describe the relationship between responses of a single individual by assuming (a) the random effect is unidimensional, and (b) conditional independence of the item responses given the random effect. There are two subclasses of IRT models: monotone and unimodal (unfolding) item response models. Monotone response models assume that the probability that an individual scores higher than t on an item is a monotone function of the random effect. Unimodal item response models assume this function is unimodal. Adaptive free-knot splines are a powerful tool for the estimation of nonlinear functions and have been used in IRT as a flexible way to model the item response function. This paper presents a reversible-jump Markov chain Monte Carlo algorithm to estimate both the number and location of the knots of a spline approximated item response function. The paper demonstrates the practicality of the approach by applying the technique to a data set from behavioral psychology.
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