Seemingly unrelated bivariate probit (BIPROBIT) using SEM?

[Kristof Cauder]

Dear Stata users! Is it in any way possible to estimate seemingly unrelated bivariate probit (BIPROBIT) using SEM (structura; equation modeling)?

There are examples of SUR estimation using SEM (http://www.stata.com/manuals13/semexample12.pdf), however in case of GSEM one cannot let errors to covariate. "For generalised responses, only the erros of Identity/Gaussian responses covary".

I will be grateful for any help

[Joseph Coveney]

Don't know the answer, but the following structural equation is suggested from the user's manual entry for biprobit at the set of equations introduced by "This derivation assumes that" in the Methods and Formulas section

webuse school
biprobit (private = logptax loginc years) (vote = logptax years), nolog
gsem (private <- logptax loginc years) (vote <- logptax years) ///
    (private@1 <- F1) (vote@1 <- F2), family(binomial) link(probit) ///
    variance(F1@1 F2@1) covariance(F1*F2) nolog
display in smcl as text "rho = " as result sign(_b[cov(F2,F1):_cons]) * sqrt(abs(_b[cov(F2,F1):_cons]))

The log-likelihood is the same and the Wald test statistics (and p-values etc.) are all the same for the explanatory variables. Values of the regression coefficients and their standard errors are greater in magnitude by a factor of sqrt(2), but you could start from there and explore further with the experts.