IRT Parameter Estimation With Response Times as Collateral Information

Hierarchical modeling of responses and response times on test items facilitates the use of response times as collateral information in the estimation of the response parameters. In addition to the regular information in the response data, two sources of collateral information are identified: (a) the joint information in the responses and the response times summarized in the estimates of the second-level parameters and (b) the information in the posterior distribution of the response parameters given the response times. The latter is shown to be a natural empirical prior distribution for the estimation of the response parameters. Unlike traditional hierarchical item response theory (IRT) modeling, where the gain in estimation accuracy is typically paid for by an increase in bias, use of this posterior predictive distribution improves both the accuracy and the bias of IRT parameter estimates. In an empirical study, the improvements are demonstrated for the estimation of the person and item parameters in a three-parameter response model.