Response moderation models for conditional dependence between response time and response accuracy

It is becoming more feasible and common to register response times in the application of psychometric tests. Researchers thus have the opportunity to jointly model response accuracy and response time, which provides users with more relevant information. The most common choice is to use the hierarchical model (van der Linden, 2007, Psychometrika, 72, 287), which assumes conditional independence between response time and accuracy, given a person's speed and ability. However, this assumption may be violated in practice if, for example, persons vary their speed or differ in their response strategies, leading to conditional dependence between response time and accuracy and confounding measurement. We propose six nested hierarchical models for response time and accuracy that allow for conditional dependence, and discuss their relationship to existing models. Unlike existing approaches, the proposed hierarchical models allow for various forms of conditional dependence in the model and allow the effect of continuous residual response time on response accuracy to be item-specific, person-specific, or both. Estimation procedures for the models are proposed, as well as two information criteria that can be used for model selection. Parameter recovery and usefulness of the information criteria are investigated using simulation, indicating that the procedure works well and is likely to select the appropriate model. Two empirical applications are discussed to illustrate the different types of conditional dependence that may occur in practice and how these can be captured using the proposed hierarchical models.