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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.

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