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Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Fig. 2 | Large-scale Assessments in Education

Fig. 2

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. 2

Continuous-time Latent Curve Model with Structured Residuals. The CT-LCM-SR with four measurement occasions: Manifest scores \({x}_{jt}\) are represented by the squares. On the bottom of the squares, there is the trend process (standard linear growth-curve process with random effects for intercept and slope) accounting for differences in the initial values and trends. The continuous-time dynamic process, which accounts for the dynamic structure is represented on the top of the squares. Estimated parameters: \(int\) mean intercept, \({int}_{SD}\) variance of the random effects of the intercept, \(b\) mean growth rate, \({b}_{SD}\) SD of the random effects of the growth rate, \({Cor}_{int,b}\) intercept-growth correlation, \({T0dyn}_{SD}\) initial SD of the dynamic process; \(\mathbf{A}\) drift matrix, \(\mathbf{Q}\) diffusion matrix

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