Modelling Conditional Dependence Between Response Time and Accuracy in Cognitive Diagnostic Models

With the novel data collection tools and diverse item types, computer-based assessments allow to easily obtain more information about an examinee’s response process such as response time (RT) data. This information has been utilized to increase the measurement precision about the latent ability in the response accuracy models. Van der Linden’s (2007) hierarchical speed-accuracy model has been widely used as a joint modelling framework to harness the information from RT and the response accuracy, simultaneously. The strict assumption of conditional independence between response and RT given latent ability and speed is commonly imposed in the joint modelling framework. Recently multiple studies (e.g., Bolsinova & Maris, 2016; Bolsinova, De Boeck, & Tijmstra, 2017a; Meng, Tao, & Chang, 2015) have found violations of the conditional independence assumption and proposed models to accommodate this violation by modelling conditional dependence of responses and RTs within a framework of Item Response Theory (IRT). Despite the widespread usage of Cognitive Diagnostic Models as formative assessment tools, the conditional joint modelling of responses and RTs has not yet been explored in this framework. Therefore, this research proposes a conditional joint response and RT model in CDM with an extended reparametrized higher-order deterministic input, noisy ‘and’ gate (DINA) model for the response accuracy. The conditional dependence is modelled by incorporating item-specific effects of residual RT (Bolsinova et al., 2017a) on the slope and intercept of the accuracy model. The effects of ignoring the conditional dependence on parameter recovery is explored with a simulation study, and empirical data analysis is conducted to demonstrate the application of the proposed model. Overall, modelling the conditional dependence, when applicable, has increased the correct attribute classification rates and resulted in more accurate item response parameter estimates.