I'm currently working on a cross-lagged mixed effects model of the following form:
Here, the "i" refer to random subjects and therefore we have subject-specific dynamic effects.
This model can be fitted with linear mixed modeling software, but this is only possible when Y and Z are measured.
In practice however, Y and Z may be latent constructs, measured by several indicators. (in my example, Y and Z are depression and self-esteem, each measured by several strongly correlated indicators.)
As far as I know, currently no methods exist to combine the dynamic random effects and the latent constructs (at least not in an easy way / within the frequentist framework).
Therefore, my question is: does any of you have an idea if this is possible in any way and, if yes, how it could be implemented.
The easier problem can be rephrased as: how can Y_i = b_i * X_i with X and Y latent and b_i subject specific be modeled.
At the workshop of prof. Boker at the IMPS conference, this question was also raised (in a less clear way I must admit) and subject-specific moderators were mentioned as a possible way to do this.