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Is it possible have an SES where the component equations are probabilistic, say, logit or probit? I am evaluating a number of quality metrics of services provided by a number of providers. The metrics are binary (pass/fail quality certification). The obvious approach would appear to be to estimate the logit/probit equations, conditional upon provider characteristics, jointly in something like an SUR, but I can't find anything like that in the discrete choice literature.

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    $\begingroup$ Formally you can do, but from practical point of view are the discrete choice variables endogenously related in your model? It would be nice to hear a complete story, and in this ad hoc case it will be more or less clear if it is relevant. The estimation algorithm probably will be slow, since you have to deal with full (limited) information maximum likelihood method estimating the parameters. $\endgroup$ – Dmitrij Celov Apr 16 '11 at 17:01
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This is possible. The type of model you need is called multivariate probit. For a textbook treatment you can refer to Greene's Econometric Analysis.

However, from the computational point of view, these models can be laborious. Convergence can be slow or can even fail.

Multivariate probit models are implemented in R and in Stata.

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I am also trying to find a solution to it. But the current available (user-written in stata) command is so slow that I got no solution. A simple solution I am using is the propensity score matching method that solves selective treatment effect. it works only when you have large observations. The estimated variance is tricky. so you have to estimate relative risk that has a neat variance estimator and convert the relative risk (rr) to probability change as a result of the other binary variable (the treatment variable). The confidence interval is not available although you can test the significance of the using rr. The Heckman model only estimate effect of a treatment (binary variable) on continuous output.

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  • $\begingroup$ Velcome to our site! But you should try to write a bit more explicit response, defining terms (such as "propensity score matching method") or at least some references $\endgroup$ – kjetil b halvorsen Jun 12 '14 at 18:11
  • $\begingroup$ What's there to define in propensity score matching? That's like asking someone to define instrumental variables :) $\endgroup$ – Andy Jun 12 '14 at 18:18

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