Posterior predictive checks for conditional independence between response time and accuracy

Conditional independence (CI) between response time and response accuracy is a fundamental assumption of many joint models for time and accuracy used in educational measurement. In this study, posterior predictive checks (PPCs) are proposed for testing this assumption. These PPCs are based on three discrepancy measures reflecting different observable consequences of different types of violations of CI. Simulation studies are performed to evaluate the specificity of the procedure, its robustness, and its sensitivity to detect different types of conditional dependence and to compare it to existing methods. The new procedure outperforms the existing methods in most of the simulation conditions. The use of the PPCs is illustrated using arithmetics test data.