A Multiprocess ExampleWhile there are several software packages on the market which support multilevel modeling, none offers aML's capabilities to mix outcome types in multiprocess (multi-equation) settings. Consider a simple Heckman selection model. The continuous outcome of interest is modeled by a linear model:
The model equations are specified in an intuitive manner following their mathematical representations. Residuals u and v are correlated across equations because they are defined as part of the same distribution and have the same "draw."define regressor set AlphaX; var = <list of variables>; define regressor set BetaX; var = <list of variables>; define normal distribution; dim=2; name=u; name=v; probit model; outcome = z; model = regressor set AlphaX + residual(draw=1, ref=u); continuous model; keep if (z>0); outcome = y; model = regressor set BetaX + residual(draw=1, ref=v);
The example readily generalizes to other types of outcomes and to multilevel models. For example, you may estimate Heckman-type probit selection models ("heckprob" models), multilevel Heckman selection models, and further embed such models into a larger system of equations. Similarly, multivariate heterogeneity may be correlated across equations.
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