Rinke H. Klein Entink

The log‐transform has been a convenient choice in response time modelling on test items. However, motivated by a dataset of the Medical College Admission Test where the lognormal model violated the normality assumption, the possibilities of the broader class of Box–Cox transformations for response time modelling are investigated. After an introduction and an outline of a broader framework for analysing responses and response times simultaneously, the performance of a Box–Cox normal model for describing response times is investigated using simulation studies and a real data example. A transformation‐invariant implementation of the deviance information criterium (DIC) is developed that allows for comparing model fit between models with different transformation parameters. Showing an enhanced description of the shape of the response time distributions, its application in an educational measurement context is discussed at length.

Response times on test items are easily collected in modern computerized testing. When collecting both (binary) responses and (continuous) response times on test items, it is possible to measure the accuracy and speed of test takers. To study the relationships between these two constructs, the model is extended with a multivariate multilevel regression structure which allows the incorporation of covariates to explain the variance in speed and accuracy between individuals and groups of test takers. A Bayesian approach with Markov chain Monte Carlo (MCMC) computation enables straightforward estimation of all model parameters. Model-specific implementations of a Bayes factor (BF) and deviance information criterium (DIC) for model selection are proposed which are easily calculated as byproducts of the MCMC computation. Both results from simulation studies and real-data examples are given to illustrate several novel analyses possible with this modeling framework.

In current psychological research, the analysis of data from computer-based assessments or experiments is often confined to accuracy scores. Response times, although being an important source of additional information, are either neglected or analyzed separately. In this article, a new model is developed that allows the simultaneous analysis of accuracy scores and response times of cognitive tests with a rule-based design. The model is capable of simultaneously estimating ability and speed on the person side as well as difficulty and time intensity on the task side, thus dissociating information that is often confounded in current analysis procedures. Further, by integrating design matrices on the task side, it becomes possible to assess the effects of design parameters (e.g., cognitive processes) on both task difficulty and time intensity, offering deeper insights into the task structure. A Bayesian approach, using Markov Chain Monte Carlo methods, has been developed to estimate the model. An application of the model in the context of educational assessment is illustrated using a large-scale investigation of figural reasoning ability.