Three regressions in one Lavaan model

[Michal Levinsky]

Hello everyone,

I have three regressions with the same independent variables. Each regression has a different dependent variable - the dependent variables measured within the same person, and reflect different but slightly related aspects. like this:

Model->' y1 ~ x1 + x2 + x3 + x4 + x5 + x6'

Model->' y1 ~ x1 + x2 + x3 + x4 + x5 + x6'

Model->' y1 ~ x1 + x2 + x3 + x4 + x5 + x6'

I was thinking of putting everything into one SEM model, because the dependent variables are related (but as mentioned, they are different aspects so I can not create one latent variable with them). I thought about this:

Model-> '

y1 ~ x1 + x2 + x3 + x4 + x5 + x6

y2 ~ x1 + x2 + x3 + x4 + x5 + x6

y3 ~ x1 + x2 + x3 + x4 + x5 + x6

'

Is it right to do so? What does Lavaan give me beyond examining each equation individually? Does it take into account the associations between the dependent variables?

Additionally, If there are any more ideas I would be grateful to know:)

Thanks a lot!

[Edward Rigdon]

     By default, I believe, lavaan will estimate residual covariances among your dependent variables. In addition, your estimated standard errors will be more correct. Putting the equations together would also give you the possibility of imposing constraints on parameters across regressions, if that is of interest.
     This appears to be an example of "seemingly unrelated regressions," and you might find more information searching for that term.

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[Michal Levinsky]

Thank you so much! that is very helpful! appreciate your answer. I have a few more questions, hope you (or someone) can help me...:
1. so I ran all three within an SEM model. Should I report the covariances between any two dependents?
2. If so, with standardized or the unstandardized coefficient?
3. Is entering the three regressions to Lavaan is enough for terming the analysis SUR ("seemingly unrelated regressions")?
4. Each of my equations contains exactly the same independent variables. Is it still "seemingly unrelated regressions"?
Thank you!

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