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Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 5 Parameter Estimates of the CT-AR(1) model, the Standard GCM and the CT-LCM-SR

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

Parameters (labelsa)

Processb

CT-AR(1)

GCM

CT-LCM-SR

Estimate

SE

p

Estimate

SE

p

Estimate

SE

p

Fixed effects

 Intercept (int)

Trend

469.73

6.02

 < .001

464.69

7.44

 < .001

464.80

7.37

 < .001

 Linear growth (b)

Trend

–

–

–

0.49

.45

.018

0.43

0.20

.037

 CT auto-effect (a)

Dynamic

− .19

0.05

 < .001

–

–

–

− 0.39

0.13

.003

Variance components

 Intercept SD (int_SD)

Trend

42.91

4.47

 < .001

54.56

5.52

 < .001

53.50

5.57

 < .001

 Growth SD (b_SD)

Trend

–

–

–

1.30

0.43

 < .001

1.06

0.32

.002

 Initial residual SD (T0dynSD)

Dynamic

26.25

4.42

 < .001

–

–

–

18.58

2.99

 < .001

 Residual (m_err) /Diffusion SD (q)

Residual / Dynamic

8.80

0.57

 < .001

10.65

0.70

 < .001

9.95

0.86

 < .001

Covariances

 Intercept-Growth (Cor_T0M_b)

Trend

–

–

–

− .55

.23

 < .001

− .61

.13

 < .001

  1. The parameter estimates of the CT-LCM-SR were already represented in Table 3 and are repeated here to facilitate comparisons
  2. aThe labels refer to the parameter labels used in Eq. 10 and 11 as well as in the presentation of the R code (p. 23) and Fig. 2
  3. bThis column indicates, which parameter belongs to which process component
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