/*This ado file gives the log likelihood function used in interval regressions for the SGT distribution. For use with grouped data. It works with gintreg.ado v 1 Author--Jacob Orchard Update--8/8/2016*/ program intllf_sgt_group version 13 args lnf mu lambda sigma p q tempvar Fu Fl zu zl qui gen double `Fu' = . qui gen double `Fl' = . qui gen double `zu' = . qui gen double `zl' = . *Point data tempvar x s l y qui gen double `x' = $ML_y1 - (`mu') if $ML_y1 != . & $ML_y2 != . /// & $ML_y1 == $ML_y2 qui gen double `s' = exp(`sigma') if $ML_y1 != . & $ML_y2 != . /// & $ML_y1 == $ML_y2 qui gen double `l' = (exp(`lambda')-1)/(exp(`lambda')+1) if $ML_y1 /// != . & $ML_y2 != . & $ML_y1 == $ML_y2 qui gen double `y' = (2 * `s' * `l' * `q'^(1/`p') * exp(lngamma(2/`p') /// + lngamma(`q' - 1/`p') - lngamma(1/`p' + /// `q')))/exp(lngamma(1/`p') + lngamma(`q') - /// lngamma(1/`p' + `q')) if $ML_y1 != . & /// $ML_y2 != . & $ML_y1 == $ML_y2 qui replace `lnf' = ln(`p') - ln(2) - `sigma' - (ln(`q')/`p') - /// (lngamma(1/`p') + lngamma(`q') - lngamma(1/`p' /// + `q')) - (1/`p' + `q') * ln(1 + abs(`x' + /// `y')^`p'/(`q' * `s'^`p' * (1 + `l' * sign(`x' + /// `y'))^`p')) if $ML_y1 != . & $ML_y2 != . & /// $ML_y1 == $ML_y2 *Interval data qui replace `zu' = abs($ML_y2 - `mu')^`p'/(abs($ML_y2 - `mu')^`p' + /// `q'*`sigma'^`p'*(1+`lambda'*sign($ML_y2 -`mu'))^`p') /// if $ML_y1 != . & $ML_y2 != . & $ML_y1 != $ML_y2 qui replace `Fu' = .5*(1-`lambda') + .5*(1+`lambda'*sign($ML_y2- /// `mu'))*sign($ML_y2 - `mu')*ibeta(1/`p',`q',`zu') /// if $ML_y1 != . & $ML_y2 != . & $ML_y1 != $ML_y2 qui replace `zl' = abs($ML_y1 - `mu')^`p'/(abs($ML_y1 - `mu')^`p' + /// `q'*`sigma'^`p'*(1+`lambda'*sign($ML_y1 -`mu'))^`p') /// if $ML_y1 != . & $ML_y2 != . & $ML_y1 != $ML_y2 qui replace `Fl' = .5*(1-`lambda') + .5*(1+`lambda'*sign($ML_y1- /// `mu'))*sign($ML_y1 - `mu')*ibeta(1/`p',`q',`zl') /// if $ML_y1 != . & $ML_y2 != . & $ML_y1 != $ML_y2 qui replace `lnf' = log(`Fu' -`Fl') if $ML_y1 != . & $ML_y2 != . & /// $ML_y1 != $ML_y2 *Bottom coded data qui replace `zl' = abs($ML_y1 - `mu')^`p'/(abs($ML_y1 - `mu')^`p' + /// `q'*`sigma'^`p'*(1+`lambda'*sign($ML_y1 -`mu'))^`p') /// if $ML_y1 != . & $ML_y2 == . qui replace `Fl' = .5*(1-`lambda') + .5*(1+`lambda'*sign($ML_y1- /// `mu'))*sign($ML_y1 - `mu')*ibeta(1/`p',`q',`zl') /// if $ML_y1 != . & $ML_y2 == . qui replace `lnf' = log(1-`Fl') if $ML_y1 != . & $ML_y2 == . *Top coded data qui replace `zu' = abs($ML_y2 - `mu')^`p'/(abs($ML_y2 - `mu')^`p' + /// `q'*`sigma'^`p'*(1+`lambda'*sign($ML_y2 -`mu'))^`p') /// if $ML_y2 != . & $ML_y1 == . qui replace `Fu' = .5*(1-`lambda') + .5*(1+`lambda'*sign($ML_y2- /// `mu'))*sign($ML_y2 - `mu')*ibeta(1/`p',`q',`zu') /// if $ML_y2 != . & $ML_y1 == . qui replace `lnf' = log(`Fu') if $ML_y2 != . & $ML_y1 == . *Missing values qui replace `lnf' = 0 if $ML_y2 == . & $ML_y1 == . *Group frequency qui replace `lnf' = `lnf'*$group_per end