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I have pre - post data on quality of life, depression, and self-esteem. I hypothesize that changes in self-esteem from pre to post cause changes in depression, which in turn cause changes in quality of life, from pre to post.

This looks to me like two separate multiple regressions, but I am unsure whether this could be combined into a single analysis or what it's the same. I don't know what kind of analysis would be best to answer my hypothesis.

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By 'predicts' do you mean 'is one of the causes of'? If so, you do indeed have a mediation relationship, for which there are dedicated regression models. – conjugateprior Jul 8 '14 at 12:19
Yes, @conjugateprior, I mean A "causes" B, and B "causes" C. But, would it be necessary for A to be somehow related to C? Because I anticipate that relationship to be weak, or at least shadowed by the precense of B. – Irving Jul 8 '14 at 12:34
If the relationship between A and C becomes negligible when controlling for the relationship between B and C, that's a big part of establishing mediation. There should be some relationship between A and C though, if B relates to both... – Nick Stauner Jul 8 '14 at 12:39
You can model this using a Bayesian network. – Zhubarb Jul 8 '14 at 13:23
No it wouldn't be necessary. There's some discussion of the relevant assumptions here. – conjugateprior Jul 8 '14 at 23:06
up vote 3 down vote accepted

Sounds like a job for structural equation modeling. Changes can be modeled as latent variables, used to predict one another, and lined up in a chain as you've described. For an introduction to latent change modeling, see McArdle (2009); it's quite readable and thorough. Given three latent change variables, you can use one to predict the next, and that next to predict the last. That's a fairly simple structural equation model, and is effectively a fully mediated regression model of the first change predicting the last. You may also want to test for an unmediated predictive relationship between self-esteem change and quality of life change. It shouldn't be hard to find a basic introduction to mediated regression path models, but if it is, you can ask a new question about that (if there isn't one out there already).

McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual Review of Psychology, 60, 577–605.

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