Introductory And Intermediate Growth Models - Mplus

Latent Growth Model ParametersFor Three Time PointsLinear growth over three time points, no covariates.Free parameters in the H 1 unrestricted model:• 3 means and 6 variances-covariancesFree parameters in the H 0 growth model(8 parameters, 1 d.f.)• Means of intercept and slope growth factors• Variances of intercept and slope growth factors• Covariance of intercept and slope growth factors• Residual variances for outcomesFixed parameters in the H 0 growth model:• Intercepts of outcomes at zero• Loadings for intercept growth factor at one• Loadings for slope growth factor at time scores• Residual covariances for outcomes at zero51Growth Model Means And Variancesy ti = η 0i + η 1i x t + ε ti ,x t = 0, 1, …, T – 1.Expectation (mean; E) and variance (V):E(y ti)E (y ti ) = E (η 0i ) + E (η 1i ) x t ,V (y ti ) = V (η 0i ) + V (η 1i ) x t+ 2x t Cov (η 0i , η 1i ) + V (ε ti )2V(y ti)} E(η 1i)} V(η 1i)} E(η 0i } ) V(η 0i )0 1 2 3 4t0 1 2 3 4V(ε ti ) constant over tCov(η 0 , η 1 ) = 0t5226