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random variance parameters, or approximations of such?

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CharlesD's picture
Joined: 04/30/2013 - 11:05
random variance parameters, or approximations of such?

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!

mhunter's picture
Joined: 07/31/2009 - 15:26

Hi Charles,

There's no doubt you're on the cutting edge here. To my knowledge there is no ready-made, or agreed-upon, solution. More and more, I believe the problem of measuring and modeling multiple individuals at many occasions on several variables is one of the burgeoning fundamental challenges in this field.

Estimating a separate model for each individual is a standard approach, and one that is made easier by having the SEM software operate inside a full programming environment like R. This would overfit in the sense that you're not capitalizing on the likely shared information between individuals, and rather treating them all separately and independently. Having some parameters common to all individuals and others estimated separately for each person is a nice compromise. It's a nice combination of relatively easy and relatively accurate.

I'm not completely clear on what the definition variable method you suggested would entail.

The random variance parameter method, depending on how it's done, should be possible but not easy in OpenMx currently. OpenMx can fit "random intercept" types of multilevel SEMs as state space models following the method of Fei Gu and colleagues in their recent MBR publication: "A Computationally Efficient State Space Approach to Estimating Multilevel Regression Models and Multilevel Confirmatory Factor Models"; . In your situation, you'd have your standard autoregression model for each individual as the "Within" model, and some other possibly atheoretical "Between" model for the cluster-level (i.e. individual-level as opposed to time/occasion-level) model. The "Between" model would account for the individual intercepts and variances. If you'd like to pursue this option, I can share some code examples with you that should help get you started. There's currently one example checked into the trunk here:

Hopefully this helps!

Mike Hunter

CharlesD's picture
Joined: 04/30/2013 - 11:05
Thanks Mike, nice to hear

Thanks Mike, nice to hear your thoughts on the issue. At some point I expect I'll want to use the state space approach, and good to know that it easily incorporates a multilevel aspect. I just have a wide format approach at present, so can deal with the between structure of the intercepts a bit easier. This 'between persons structure of the variance and or dynamic parameters' issue has been going around my head for a while, but this dataset seems to really require some thinking on it. Either that or a new approach to the questions, of course...