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

Y

16

National Science Foundation (NSF)

NSFSES1156372

Bayesian Statistics; Item Response Theory; Nonparametric Statistics; Models; Accuracy; Data Analysis; Achievement Tests; Elementary Secondary Education; International Assessment; Mathematics Achievement; Foreign Countries; Mathematics Tests; Science Achievement; Science Tests; Test Items; Computation

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. [At time of submission to ERIC this article was in press with "Journal of Modern Applied Statistical Methods" v17 n2 2018.]

As Provided

28

2017

ED579801