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. A simple and more flexible Bayesian nonparametric IRT model for dichotomous items is introduced, 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. An 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.




In the original published version of this article, equations (A1) through (A6) were incorrectly labelled (A9) through (A14). This has been corrected.

Supplementary Files.zip (19 kB)
Supplementary Material: MATLAB code for IRT and TIMSS data