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.