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How can I estimate a model where

Y ~ X1 + X2 + X3

X1 ~ Z1 + Z2

X2 ~ Z1 + Z2

X3 ~ Z1 + Z2

where Y may/may not be correlated with Z1 and Z2. Is there a R procedure that I could use to estimate the model.

Thanks a lot for your help.

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You can try R-package "sem".

It should contain functions for above mentioned analysis.

Do you want to test if some of the variables do not appear in some of the equations above?

You can have 14 parameters when you have only 5 observed variables and four equations simultenously to be estimated. I think you have to impose some prior restrictions to the values of some parameters, otherwise this system of equations cannot be estimated.

Structural equations are usually estimated jointly with maximum likelihood method, equation by equation estimation with ordinary least squares leads to biased and inconsistent results.

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  • $\begingroup$ Thank you. Can you tell me how SEM is different from Seemingly Unrelated regression? $\endgroup$ – oblixram Sep 25 '13 at 17:51
  • $\begingroup$ Is there any way apart from SEM to do this. Could I regress equation 2 to 4 individually and get the predicted value which I could then use to estimate the new beta's from regression equation 1? $\endgroup$ – oblixram Sep 25 '13 at 18:41

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