Variable Speed Across Dimensions of Ability in the Joint Model for Responses and Response Times

Longitudinal joint modeling for assessing parallel interactive development of latent ability and processing speed using responses and response times

To measure the parallel interactive development of latent ability and processing speed using longitudinal item response accuracy (RA) and longitudinal response time (RT) data, we proposed three longitudinal joint modeling approaches from the structural equation modeling perspective, namely unstructured-covariance-matrix-based longitudinal joint modeling, latent growth curve-based longitudinal joint modeling, and autoregressive cross-lagged longitudinal joint modeling. The proposed modeling approaches can not only provide the developmental trajectories of latent ability and processing speed individually, but also exploit the relationship between the change in latent ability and processing speed through the across-time relationships of these two constructs. The results of two empirical studies indicate that (1) all three models are practically applicable and have highly consistent conclusions in terms of the changes in ability and speed in the analysis of the same data set, and (2) additional analysis of the RT data and acquisition of individual processing speed measurements can reveal the parallel interactive development phenomena that are difficult to detect using RA data alone. Furthermore, the results of our simulation study demonstrate that the proposed Bayesian Markov chain Monte Carlo estimation algorithm can ensure accurate model parameter recovery for all three proposed longitudinal joint models. Finally, the implications of our findings are discussed from the research and practice perspectives.

Joint modeling of action sequences and action time in computer-based interactive tasks

Process data refers to data recorded in computer-based assessments that reflect the problem-solving processes of participants and provide greater insight into how they solve problems. Action time, namely the amount of time required to complete a state transition, is also included in such data along with actions. In this study, an action-level joint model of action sequences and action time is proposed, in which the sequential response model (SRM) is used as the measurement model for action sequences, and a new log-normal action time model is proposed as the measurement model for action time. The proposed model can be regarded as an extension of the SRM by incorporating action time within the joint-hierarchical modeling framework and as an extension of the conventional item-level joint models in process data analysis. Results of the empirical and simulation studies demonstrated that the model setup was justified, model parameters could be interpreted, parameter estimates were accurate, and taking into account participants' action time further was beneficial for obtaining a deep understanding of participants' behavioral patterns. Overall, the proposed action-level joint model provides an innovative modeling framework for analyzing process data in computer-based assessments from the latent variable modeling perspective.