Prior information at item level in item response theory models

Recently, Bayesian estimation of item response theory (IRT) models via Markov chain Monte Carlo methods has become very popular. The main reason is that this method is free from the limitations of using Gaussian quadrature in marginal maximum likelihood estimation and it is more easily extendable for the estimation of models with complex structures. Moreover, a Bayesian approach allows the incorporation of dependencies among variables and sources of uncertainty. The role of prior distributions is very important in Bayesian statistics, and informative prior distributions can be used in order to improve the accuracy of parameter estimation under particular conditions, for example when the sample size is small. This last aspect is too often disregarded by researchers, who are used to include in the model flat, uninformative priors, especially for item parameters. Differently, this work shows how the introduction of informative prior distributions, even empirical, is effective in improving the accuracy of model estimation. In particular, we will consider the introduction of prior information on the item parameters, which are treated as random variables within a Bayesian approach. Including informative prior distributions at item level does not state the matter of fairness, as it is argued in case priors are used at ability level. The use of empirical priors is also discussed, with respect to intelligence test data.