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Table 5 Parameter Estimates of the 3-Class Solution in the TRacking Adolescent Individuals’ Lives Survey (TRAILS), The Netherlands, 2001–2017

From: Variance constraints strongly influenced model performance in growth mixture modeling: a simulation and empirical study

Model Parameter Class 1   Class 2   Class 3  
   Mean Variance Mean Variance Mean Variance
0: Unconstrained Intercept 0.358 0.024 0.325 0.008 0.145 0.009
  Linear Slope 0.087 0.001 0.008 0.001 0.005 0.001
  Quadratic Slope −0.033 0a −0.048 0a −0.024 0a
  Cubic slope 0.003 0a 0.008 0a 0.004 0a
  T1 0.038 0.049 0.01
  T2 0.04 0.03 0.008
  T3 0.041 0.019 0.01
  T4 0.059 0.01 0.002
  T5 0.05 0.006 0.001
  T6 0.049 0.011 0.001
1A: Residual variance time constrained Intercept 0.460 0.012 0.283 0.008 0.136 0.011
Linear Slope 0.078 0.003 0.039 0.001 0.024 0.001
Quadratic Slope −0.039 0a − 0.042 0a − 0.03 0a
Cubic slope 0.004 0a 0.006 0a 0.004 0a
T1 0.058 0.023 0.005
T2 0.058 0.023 0.005
T3 0.058 0.023 0.005
T4 0.058 0.023 0.005
T5 0.058 0.023 0.005
T6 0.058 0.023 0.005
1B: Residual variance classes constrained Intercept 0.352 0.026 0.265 0.022 0.369 0.037
Linear Slope 0.078 0.003 0.019 0.001 0.089 0.003
Quadratic Slope −0.07 0a −0.033 0a 0.023 0a
Cubic slope 0.012 0a 0.004 0a − 0.008 0a
T1 0.034 0.034 0.034
  T2 0.029 0.029 0.029
  T3 0.028 0.028 0.028
  T4 0.027 0.027 0.027
  T5 0.026 0.026 0.026
  T6 0.005 0.005 0.005
1C: Random effects constrained Intercept 0.282 0.013 0.466 0.013 0.234 0.013
Linear Slope 0.073 0.001 0.091 0.001 −0.023 0.001
Quadratic Slope −0.048 0a −0.033 0a − 0.025 0a
Cubic slope 0.006 0a 0.004 0a 0.005 0*
T1 0.027 0.067 0.031
T2 0.029 0.061 0.013
  T3 0.027 0.057 0.011
  T4 0.028 0.094 0.003
  T5 0.023 0.09 0.001
  T6 0.03 0.075 0.004
Model 2A:
Residual variance Constrained time and classes
Intercept 0.302 0.021 0.223 0.006 0.715 0.021
Linear Slope 0.105 0.001 0.043 0.000b −0.142 0.000b
Quadratic Slope −0.034 0a −0.045 0a −0.029 0a
Cubic slope 0.004 0a 0.006 0a 0.007 0a
T1 0.028 0.028 0.028
T2 0.028 0.028 0.028
  T3 0.028 0.028 0.028
  T4 0.028 0.028 0.028
  T5 0.028 0.028 0.028
  T6 0.028 0.028 0.028
2B: Random effects and residual variance time constrained Intercept 0.463 0.01 0.323 0.01 0.148 0.01
Linear Slope 0.094 0.001 0.04 0.001 0.026 0.001
Quadratic Slope −0.033 0a −0.044 0a −0.032 0a
Cubic slope 0.003 0a 0.006 0a 0.005 0a
T1 0.073 0.029 0.006
T2 0.073 0.029 0.006
T3 0.073 0.029 0.006
T4 0.073 0.029 0.006
  T5 0.073 0.029 0.006
  T6 0.073 0.029 0.006
2C: Random effects and residual variance classes constrained Intercept 0.273 0.018 0.491 0.018 0.397 0.018
Linear Slope 0.019 0.001 0.469 0.001 −0.074 0.001
Quadratic Slope −0.032 0a −0.261 0a 0.099 0a
Cubic slope 0.005 0a 0.032 0a −0.015 0a
T1 0.037 0.037 0.037
T2 0.023 0.023 0.023
T3 0.026 0.026 0.026
  T4 0.033 0.033 0.033
  T5 0.017 0.017 0.017
  T6 0.027 0.027 0.027
  1. aThese variances were manually set to be equal to zero
  2. bThese variances were estimated to be very close to zero, which led to a warning that the covariance matrix was not positive definite. Nevertheless, the variances were not set to be equal to zero, in order to keep the model comparable to other models