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st: GLLAMM: selection model with endogenous regressor


From   "Marcello Morciano (MED)" <M.Morciano@uea.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: GLLAMM: selection model with endogenous regressor
Date   Fri, 9 Nov 2012 17:12:35 +0000

Dear Statalist,
 
I would like use GLLAMM for estimating a Heckman model (heckprob) with an endogenous covariate in the selection equation. I am still trying to understand the "language" of Gllamm to which I'm not used to.
Thanks to Sophia and Alfonso's (http://www.stata-journal.com/article.html?article=st0107 ) I am able to reproduce results of a heckprob model with GLLAMM. Thanks to Sophia and Xiaohui's paper (http://www.stata-journal.com/article.html?article=st0129 ) I am able to implement a MIMIC model with GLAMM.
I wondering whether I can combine these 2 pieces in a Full information maximum likelihood, instead of applying the Murphy-Topel estimator required in adopting a limited information maximum likelihood, two-step procedure for estimating the following model (in GLLAMM language):
 
 
*** MIMIC model
eq load: d1-d7
eq f1:  female age dhs2 dhs3 dhs4 dhs5
#delimit ;
gllamm score d2-d7, i(idauniq) eqs(load) geqs(f1)  link(logit) family(binom) pweight(wt)  adapt nip(30) iterate(100) difficult
#delimit cr
 
where d1-d7 are binary indicators of the latent construct EndVAR_d, and f1 is the vector of covariates for which the conditional mean of EndVAR_d is assumed to vary (the first factor is constrained to unity for identification).
 
*** SELECTION MODEL
eq fac: end cv
constraint def 1 [id1_1]end=1
eq load: d1-d7
 
#delimit ;
gllamm resp  Ewalk_c Esit_c age_c female_c cons_c EndVAR_d female_d dhs2_d dhs3_d dhs4_d dhs5_d age_d cons_d, i(id)  weightf(wt)
constr(1) from(startv) long family(binom binom) nr(2,1)
link(probit probit) fv(vartype) lv(vartype) nocons
eq(fac) adapt nip(16)      copy;
#delimit cr
 
Where *_c variables are covariates in the main model; *_d are covariates in the selection model (EndVAR_d included).
 
My questions are:
1)How data should be organized, given the fact that to fit a model in GLLAMM, all responses must be stacked in one variable?
2)How the model should be specified in GLLAMM?
3)Are you aware of any application of this type? 
 
Many thanks in advance for your attention.


Marcello 



Marcello Morciano

Research Fellow, Health Economics Group, Faculty of Medicine and Health Sciences
University of East Anglia, Norwich Research Park, Norwich NR4 7TJ
Tel: +44 (0) 1603 591074; Fax: +44 (0) 1603 593604; email: m.morciano@uea.ac.uk  
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