The approach of power priors for ability estimation in IRT models

The aim of the paper is to propose the introduction of power prior distributions in the ability estimation of item response theory (IRT) models. In the literature, power priors have been proposed to integrate information coming from historical data with current data within Bayesian parameter estimation for generalized linear models. This approach allows to use a weighted posterior distribution based on the historical study as prior distribution for the parameters in the current study. Applications can be found especially in clinical trials and survival studies. Here, power priors are introduced within a Gibbs sampler scheme in the ability estimation step for a unidimensional IRT model. A Markov chain Monte Carlo algorithm is chosen for the high flexibility and possibility of extension to more complex models. The efficiency of the approach is demonstrated in terms of measurement precision by using data from the Hospital Anxiety and Depression Scale with a small sample.