Dena Pastor posted on Thursday, July 15, 2010 - 12:55 pm
I am using Mplus to estimate a multivaraite LGM with two variables measured at 4 time points.Each variable is being modeled using a piecewise linear growth model with the 1st slopes capturing change between the 1st and 2nd time points and the 2nd slopes capturing change beyond the 2nd time point. For identification purposes, I am constraining the residual variances across time to be equal for each variable. I am obtaining an error message because the correlation between the variables’ 1st slopes is >1.0, as is the correlation between the variables’ 2nd slopes. If I allow the residuals to covary between variables at the same time points, the correlation between my 1st slopes is below 1.0 but the correlation for my 2nd slopes is not.
If you have a piecewise model for only 4 time points (never heard of that), how can you model a linear trend? You need at least 3 time points to model a linear trend, but when you have two pieces (as you said) you only have two time points for each piece. The recommendation is to have 4 time points for a growth model to have enough flexibility when it comes to modeling issues. So I would assume that one needs at least 8 time points for a piecewise growth model with two pieces. In general, your approach is right to let the residuals covary. But it might be that your model is too restrictive (equal residual variances over time) and this is due to the too complex piecewise model. The above mentioned (wrong!?) restriction, in turn, might have lead to the phenomenon, that covarying the residuals has not enough impact on the correlated slopes (i.e. buffering the correlation). But this is highly speculative.
Thanks Linda. So I am wrong in thinking that the model is identified if I allow the first slope growth variance to be freely estimated, but constrain the residuals variances associated with the indicators across time to be equal?
With two timepoints, the H1 model has 5 pieces of information: 2 means, 2 variances, and 1 covariance. The H0 model has two growth factors means, two growth factor variances, one growth factor covariance, and two residual variances. This is 7 parameters. Even if you hold the residual variances equal, the model is still not identified because there are six parameters.