I am trying to fit a longitudinal CFA with 3 indicators at each of 4 time points, with a 1 year time lag. The model runs fine when I have 3 time points, but the model fails when I add the fourth time point. It appears that the model may fail because of multicollinearity among the latent factors (the correlation between the latent factors at T3 and T4 = .996). I have already specified the within-indicator residual covariances across time, but it does not solve the problem. Here are the correlations of the 4 latent vars:
lag T=1: .988, .990, .996
lag T=2: .976, .967
lag T=3: .937
Any ideas for how to specify the longitudinal CFA given the high correlation among the latent variables across time? The 3 indicators represent questionnaires by three raters: mothers, teachers, and fathers.
Thanks in advance!