Multilevel selection models using gllamm
Models for handling sample selection or informative missingness have been developed for both cross sectional and longitudinal or panel data. For cross sectional data, Heckman (1979) suggested a joint model for the response and sample selection processes where the disturbances of the processes are correlated. For longitudinal data, Hausman and Wise (1979) and Diggle and Kenward (1994) developed a model in which the continuous response (observed or unobserved), and possibly the lagged response, is a predictor of attrition or dropout. The Heckman model can be estimated using the heckman command in Stata and the Diggle-Kenward model is available in the Oswald package running in S-PLUS. Both models can also be estimated using gllamm with the advantage that the following three generalisations are possible. First, the models can be extended to multilevel settings where there may be unobserved heterogeneity between the clusters at the different levels in both the substantive and selection processes and where selection may operate at several levels. Second, the Heckman model can be modified for non-normal response processes. Third, both the Heckman and Diggle-Kenward models can be extended to situations where the substantive response is a latent variable measured by a number of indicators. I will show how the standard Heckman and Diggle-Kenward models are estimated in gllamm and give a examples of all three types of generalisation of these standard models. The research was carried out jointly with Anders Skrondal and Andrew Pickles.
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