set obs 1000
set seed 12345678
gen z=cond(uniform()<0.5,1,2)
gen y=invnorm(uniform())
replace y=y+5 if z==2


histogram y, bin(20) frequency


capture program drop mixing2
program define mixing2
version 11.0
args lj xb xb2 lo1 ls1 ls2
tempvar f1 f2 p s1 s2
quietly gen double `s1'=exp(`ls1')
quietly gen double `s2'=exp(`ls2')
quietly gen double `p'=1/(1+exp(-`lo1'))
quietly gen double `f1'=exp(-0.5*(($ML_y1-`xb')/`s1')^2)/(sqrt(2*_pi)*`s1')
quietly gen double `f2'=exp(-0.5*(($ML_y1-`xb2')/`s2')^2)/(sqrt(2*_pi)*`s2')
quietly replace `lj'=ln(`p'*`f1'+(1-`p')*`f2')
end
ml model lf mixing2 (xb1:  y=)  /xb2 /lo1 /lsd1 /lsd2
ml init 1 6  0 0.2 -0.2, copy
ml maximize







program myprobit
version 11
args lnf theta1
quietly replace `lnf' = ln(normal(`theta1')) if $ML_y1==1
quietly replace `lnf' = ln(normal(-`theta1')) if $ML_y1==0
end


g z_bin=(z==2)
ml model lf myprobit (z_bin = y)
ml maximize

probit  z_bin y