Longitudinal CFA with multicollinearity
Message/Author
 Isaac Petersen posted on Wednesday, September 26, 2012 - 12:28 pm
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.

 Bengt O. Muthen posted on Wednesday, September 26, 2012 - 5:33 pm
I assume that you have one factor at each time point. I can't think of a way to reduce the factor correlation over time beyond what you have done. If the factors are so highly correlated over time, is there really any change in their means to motivate a longitudinal study?
 Isaac Petersen posted on Tuesday, October 02, 2012 - 7:06 am
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.

 Isaac Petersen posted on Tuesday, October 02, 2012 - 7:08 am
Sorry about the repost. Not sure why it did that..

At the indicator level, we find a good amount of change in the slope over time (mean-level decreases). I'm surprised the latent variable correlations are so high. The within-time correlations of the indicators range from .23 to .67, and the cross-time correlations of the indicators range from .52 to .69.
 Linda K. Muthen posted on Tuesday, October 02, 2012 - 10:08 am