A Bayesian Beta-Mixture Model for Nonparametric IRT (BBM-IRT)

Journal of Modern Applied Statistical Methods, Forthcoming

16 Pages Posted: 23 Jan 2018

See all articles by Ethan Arenson

Ethan Arenson

University of Illinois at Chicago

George Karabatsos

University of Illinois at Chicago

Date Written: September 5, 2017

Abstract

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model for dichotomous items, which constructs monotone item characteristic (step) curves by a finite mixture of beta distributions, which can support the entire space of monotone curves to any desired degree of accuracy. A simple adaptive random-walk Metropolis-Hastings algorithm is proposed to estimate the posterior distribution of the model parameters. The Bayesian IRT model is illustrated through the analysis of item response data from a 2015 TIMSS test of math performance.

Keywords: Item Response Theory, Bayesian nonparametric, Markov chain Monte Carlo

Suggested Citation

Arenson, Ethan and Karabatsos, George, A Bayesian Beta-Mixture Model for Nonparametric IRT (BBM-IRT) (September 5, 2017). Journal of Modern Applied Statistical Methods, Forthcoming. Available at SSRN: https://ssrn.com/abstract=3102461

Ethan Arenson

University of Illinois at Chicago ( email )

1200 W Harrison St
Chicago, IL 60607
United States

George Karabatsos (Contact Author)

University of Illinois at Chicago ( email )

1040 W Harrison St
Chicago, IL 60607
United States

HOME PAGE: http://georgek.people.uic.edu/

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