I'm trying to model the effect of a time-independent predictor on the parameters of a dual latent change score model (in discrete time). My predictor is the cohort to which the subjects belong. The groups (cohorts) of individuals in my data have different values for the parameters (e.g., different self-feedbacks, mean and variance of the slope...). I managed to successfully account for cohort effects on means, variances, and regression parameters, just using mxPaths. However, the covariance between the initial state of the system and the slope also changes across cohorts, and that's where I'm stuck.
How can I account for cohort effects on a covariance parameter in SEM using a RAM type model? Is it possible to manipulate the S matrix to include this effect? I've tried it but with 15 repeated measures it gets a bit cumbersome to work with these matrices, and I'm not even sure if thats the right way to go.
Thank you in advance!
Pablo.