A Strategy for Developing a Common Metric in Item Response Theory When Parameter Posterior Distributions Are Known

Abstract

Growing interest in fully Bayesian item response models begs the question: To what extent can model parameter posterior draws enhance existing practices? One practice that has traditionally relied on model parameter point estimates but may be improved by using posterior draws is the development of a common metric for two independently calibrated test forms. Before parameter estimates from independently calibrated forms can be compared, at least one form's estimates must be adjusted such that both forms share a common metric. Because this adjustment is estimated, there is a propagation of error effect when it is applied. This effect is typically ignored, which leads to overconfidence in the adjusted estimates; yet, when model parameter posterior draws are available, it may be accounted for with a simple sampling strategy. In this paper, it is shown using simulated data that the proposed sampling strategy results in adjusted posteriors with superior coverage properties than those obtained using traditional point-estimate-based methods.