sysuse auto, clear
* Probit MLE
probit foreign weight mpg
estat classification

margins, dydx(mpg)
margins, dydx(mpg) atmeans
centile
margins, dydx(mpg) at(weight=3190 mpg=20)

* Logit MLE
logit foreign weight mpg
estat classification

* LPM robust
reg foreign weight mpg, vce(robust)
predict p

gen pp = p > .5
tabulate pp foreign

gen var = p*(1-p)
summarize var, detail
* GLS truncated
reg foreign weight mpg [aweight=1/var] if p>0
predict pgls
replace pp = pgls > .5
tabulate pp foreign

* GLS censored
replace p = .01 if p < .01
replace var=p*(1-p)
reg foreign weight mpg [aweight=1/var] 
predict pglsc
replace pp = pglsc > .5
tabulate pp foreign

* Specification Tests
probit foreign weight mpg
predict pt, pr
predict ind, xb

replace var = pt*(1-pt)
gen res = foreign - pt
gen fxb = normalden(ind)
gen x2 = mpg*fxb
gen x3 = weight*fxb
gen z = price*fxb*ind

reg res fxb x2 x3 z [aweight=1/var], noconst
scalar LM1 = e(N)*e(r2)
scalar p1 = chi2tail(1,LM1)

gen ind2=ind*ind

reg res fxb x2 x3 ind2 [aweight=1/var]