A Bayesian semiparametric item response model with dirichlet process priors

In Item Response Theory (IRT), item characteristic curves (ICCs) are illustrated through logistic models or normal ogive models, and the probability that examinees give the correct answer is usually a monotonically increasing function of their ability parameters. However, since only limited patterns of shapes can be obtained from logistic models or normal ogive models, there is a possibility that the model applied does not fit the data. As a result, the existing method can be rejected because it cannot deal with various item response patterns. To overcome these problems, we propose a new semiparametric IRT model using a Dirichlet process mixture logistic distribution. Our method does not rely on assumptions but only requires that the ICCs be a monotonically nondecreasing function; that is, our method can deal with more types of item response patterns than the existing methods, such as the one-parameter normal ogive models or the two- or three-parameter logistic models. We conducted two simulation studies whose results indicate that the proposed method can express more patterns of shapes for ICCs and can estimate the ability parameters more accurately than the existing parametric and nonparametric methods. The proposed method has also been applied to Facial Expression Recognition data with noteworthy results.