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Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Fig. 3 | Large-scale Assessments in Education

Fig. 3

From: A primer on continuous-time modeling in educational research: an exemplary application of a continuous-time latent curve model with structured residuals (CT-LCM-SR) to PISA Data

Fig. 3

Combination of trend (A) and dynamics (B) in the CT-LCM-SR (C) in comparison to a CT-AR(1) model (D). Same simulated data as used in Fig. 1. Panel A CT-LCM-SR-implied trend. Panel B continuous-time dynamic process of the residuals. Panel C Putting trend and dynamic process together. Panel D A standard CT-AR(1) model, which ignores any trend in the data. Black solid lines visualize model implied expected trajectories (given past observations). The model implied predictions of the CT-LCM-SR (Panel C) are a combination of the static trend component (Panel A) and the autoregressive structure of the residuals over time as reflected by the CT auto-effect (Panel B). The dynamic part gives information on how much of the deviation from the trend on time T is expected to be carried over to future states with growing time intervals. A mean-reverting process is shown, which means that the CT auto effect is negative (corresponding to DT autoregressive effects between 0 and 1 for every time interval)

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