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st: Constraints in the MLE and delta method


From   Beatrice Crozza <beatrice.crozza@gmail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   st: Constraints in the MLE and delta method
Date   Sun, 26 Jun 2011 18:40:52 +0100

Dear All,

thanks to Maarten now I know how to insert a constraint in a MLE.

However, if I use the delta method for my parameters, I don't know how to do.

This is the MLE:

program define myprog

args lnf a d m e g p

tempvar ma md mm  me mg mp am dm omm em

quietly gen double `am'=exp(`a')/(1+exp(`a'))
quietly gen double `dm'=exp(`d')/(1+exp(`d'))
quietly gen double `omm'=exp(`m')
quietly gen double `em'=exp(`e')
quietly gen double `ma'=1-`am'
quietly gen double `md'=1-`dm'
quietly gen double `mm'=1-`omm'
quietly gen double `me'=1-`em'
quietly gen double `mg'=1-`g'
quietly gen double `mp'=1-`p'

quietly replace
`lnf'=ln((`am')*(`dm')*((((`mm')+(`omm')*(`em')*(`g'))^x1)*(((`omm')+(`mm')*(`em')*(`p'))^x2)*(((`mm')*(`em')*(`me'))^x3)*(((`mmo')*(`em')*(`mg'))^x4)*(((`mm')*(`mp'))^x5)*(((`mmo')*(`eo'))^x6)))

end

ml model lf myprog (a:) (d:) (m:) (e:) (g:) (p:),  technique(bfgs)
constraint(1-2)

ml check
ml search
ml maximize, difficult

nlcom (a: exp([am]_b[_cons])/(1+exp([am]_b[_cons])))
nlcom (d: exp([dm]_b[_cons])/(1+exp([dm]_b[_cons])))




If I do:
constraint 1 [a]_cons=[d]_cons is not correct because these are not
the correct values coming from the delta method.

Could you please help me?

Thanks,
Bea
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