Bayesian hierarchical response time modelling-A tutorial

Response time modelling is developing rapidly in the field of psychometrics, and its use is growing in psychology. In most applications, component models for response times are modelled jointly with component models for responses, thereby stabilizing estimation of item response theory model parameters and enabling research on a variety of novel substantive research questions. Bayesian estimation techniques facilitate estimation of response time models. Implementations of these models in standard statistical software, however, are still sparse. In this accessible tutorial, we discuss one of the most common response time models-the lognormal response time model-embedded in the hierarchical framework by van der Linden (2007). We provide detailed guidance on how to specify and estimate this model in a Bayesian hierarchical context. One of the strengths of the presented model is its flexibility, which makes it possible to adapt and extend the model according to researchers' needs and hypotheses on response behaviour. We illustrate this based on three recent model extensions: (a) application to non-cognitive data incorporating the distance-difficulty hypothesis, (b) modelling conditional dependencies between response times and responses, and (c) identifying differences in response behaviour via mixture modelling. This tutorial aims to provide a better understanding of the use and utility of response time models, showcases how these models can easily be adapted and extended, and contributes to a growing need for these models to answer novel substantive research questions in both non-cognitive and cognitive contexts.