Hi all. So I'm taking a look at a dataset of about 200 individuals, each with a number of variables measured 50 times longitudinally. A lot of these variables are scored on a scale of 0-100, which 'seems' to have created large differences in scale usage - differences that are no doubt normally there with a 0-10 scale but are probably emphasised now. If the measurement model were equivalent across individuals, then the structural model is clearly not anyway, so I have a similar issue, or probably both measurement and structural differences. Nevertheless, I want to estimate the dynamic parameters which characterise the processes, using autoregressive / cross regressive type models.
I see a few easy options:
Estimate all parameters separately for every individual - but this will badly overfit and I expect?? parameters to become relatively meaningless.
Constrain parameters governing relationships in time across the sample, free the intercept, latent and manifest error variances across individuals (though still constrained over time). This is probably better, but again, I suspect this will overfit, and I've seen similar overfit heavily bias dynamic parameters.
a somewhat trickier option I don't have much confidence in would be to generate an additional manifest variable, such as 'variance', treat it as perfectly measured, and use it as a definition variable (along with an estimated param for the moderating relationship) moderating the variance parameters I need moderated.
I think my ideal solution is random variance parameters - do I need to go and learn how to write up my problem in Stan (bayesian), are there potentially good solutions possible within OpenMx I haven't considered, or are perhaps some of those I have considered more workable than I suspect? Would love to hear any thoughts, thanks!