A Hierarchical Framework for Modeling Speed and Accuracy on Test Items

Current modeling of response times on test items has been strongly influenced by the paradigm of experimental reaction-time research in psychology. For instance, some of the models have a parameter structure that was chosen to represent a speed-accuracy tradeoff, while others equate speed directly with response time. Also, several response-time models seem to be unclear as to the level of parametrization they represent. A hierarchical framework for modeling speed and accuracy on test items is presented as an alternative to these models. The framework allows a “plug-and-play approach” with alternative choices of models for the response and response-time distributions as well as the distributions of their parameters. Bayesian treatment of the framework with Markov chain Monte Carlo (MCMC) computation facilitates the approach. Use of the framework is illustrated for the choice of a normal-ogive response model, a lognormal model for the response times, and multivariate normal models for their parameters with Gibbs sampling from the joint posterior distribution. This study received funding from the Law School Admission Council (LSAC). The opinions and conclusions contained in this paper are those of the author and do not necessarily reflect the policy and position of LSAC. The author is indebted to the American Institute of Certified Public Accountants for the data set in the empirical example and to Rinke H. Klein Entink for his computational assistance