We wanted to ask you for some help understanding the causes leading to a correlation greater than 1 between the slope and quadratic factors.
Our linear model (unconditional) fit was modest and there was evidence to look at the quadratic form. We ran the quadratic model and results came back with a correlation between S and Q > 1. In searching through other posts on the Mplus site and several references in articles and books (including Bollen and Curran, “Latent Curve Models”) this problem appears somewhat common, but it was not clear in these references why the correlations are so high.
We thought that since the time points (0 and 1) would be the same when squared in the quadratic factor as in the linear factor that this might cause the high correlation, so following guidelines in the M+ manual and elsewhere, we tried a different centering and different parameter values for time, but the correlation between S and Q for both of these models still came back as greater than 1.
We did run a model allowing the time scores to be estimated and the model fit much better, but we still wanted to understand what causes the high correlations. Could you offer some input?
I think the main reason is that the time scores are the same for the time points with time scores of zero and one. You can try centering the times scores at the middle time point, that is, have the time score of zero there.