Modeling dichotomous item responses with free-knot splines

Item response theory (IRT) models are a class of generalized mixed effect (GME) models used by psychometricians to describe the response behavior of individuals to a set of categorically scored items. The typical assumptions of IRT are Unidimensionality  (U)(U) of the random effect; Conditional (or Local) Independence (CI), the item responses are independent given the random effect; and Monotonicity (M), the probability of a correct response is a non-decreasing function of the random effect. The simple parametric models available in the psychometric literature have proved to be too restrictive in many data sets. Non-parametric regression models are a powerful tool for the estimation of non-linear curves, and have been used in IRT as a flexible way to model the item response function. This paper develops a new method for the non-parametric estimation of item response functions based on reversible-jump Markov Chain Monte Carlo, and demonstrates the practicality of the method by examining two data sets.