Im using manually calculated IPW, stabilized by prevalence of exposure (stabIPW) to achieve adequate balance and overlap .
I plan to perform a doubly robust RA model to estimate ATE.
Whilst IPWRA allow for incorporation of manual probability weights I am unclear if it is appropriate to include both the treatment assingment model (calculating IPW) and then including my manual weights as well
eg teffects ipwra (outcome model) (treatment assignment model) [pw=stabIPW]
my question is whether teffects ra (outcome equation) (exposure) [pw=IPW] is equivalent to teffects ipwra (outcome model) (treatment assignment model) if the treatment assignment model generating the manual IPW the same?
Illustration, indicates close but not identical:
webuse cattaneo2.dta, clear
codebook _all, compact
// generate binary birthweight at ~ 90 centile
su bweight,de
gen binbwt = 0
replace binbwt =1 if bweight >=4000
tab binbwt
// generate manual IPW (ipw_man )
logit mbsmoke mmarried mage prenatal1 fbaby medu
predict phat,pr
gen man_ipw=.
replace man_ipw= 1/phat if mbsmoke ==1
replace man_ipw= 1/(1-phat) if mbsmoke ==0
// teffects ra weighted by IPW
teffects ra (binbwt mmarried mage prenatal1 fbaby medu, logit) ///
(mbsmoke) [pw=man_ipw] ,ate
Treatment-effects estimation Number of obs = 4,642
Estimator : regression adjustment
Outcome model : logit
Treatment model: none
----------------------------------------------------------------------------------------
| Robust
binbwt | Coefficient std. err. z P>|z| [95% conf. interval]
-----------------------+----------------------------------------------------------------
ATE |
mbsmoke |
(Smoker vs Nonsmoker) | -.0558386 .0129927 -4.30 0.000 -.0813037 -.0303735
-----------------------+----------------------------------------------------------------
POmean |
mbsmoke |
Nonsmoker | .1173439 .0052618 22.30 0.000 .1070309 .1276569
----------------------------------------------------------------------------------------
// teffects ipwa and calculation of ps & ipw
teffects ipwra (binbwt mmarried mage prenatal1 fbaby medu, logit) ///
(mbsmoke mmarried mage prenatal1 fbaby medu ) ,ate
predict te_ps , ps
gen te_ipw=.
replace te_ipw= 1/te_ps if mbsmoke ==1
replace te_ipw= 1/(1-te_ps) if mbsmoke ==0
Treatment-effects estimation Number of obs = 4,642
Estimator : IPW regression adjustment
Outcome model : logit
Treatment model: logit
----------------------------------------------------------------------------------------
| Robust
binbwt | Coefficient std. err. z P>|z| [95% conf. interval]
-----------------------+----------------------------------------------------------------
ATE |
mbsmoke |
(Smoker vs Nonsmoker) | -.0531514 .0145424 -3.65 0.000 -.0816539 -.0246489
-----------------------+----------------------------------------------------------------
POmean |
mbsmoke |
Nonsmoker | .1192232 .0052657 22.64 0.000 .1089026 .1295439
----------------------------------------------------------------------------------------
// teffects ipwra weighted as well by manual ipw
teffects ipwra (binbwt mmarried mage prenatal1 fbaby medu, logit) ///
(mbsmoke mmarried mage prenatal1 fbaby medu ) [pw=man_ipw],ate
Treatment-effects estimation Number of obs = 4,642
Estimator : IPW regression adjustment
Outcome model : logit
Treatment model: logit
----------------------------------------------------------------------------------------
| Robust
binbwt | Coefficient std. err. z P>|z| [95% conf. interval]
-----------------------+----------------------------------------------------------------
ATE |
mbsmoke |
(Smoker vs Nonsmoker) | -.0557366 .0129586 -4.30 0.000 -.081135 -.0303382
-----------------------+----------------------------------------------------------------
POmean |
mbsmoke |
Nonsmoker | .1171227 .0052589 22.27 0.000 .1068155 .1274299
----------------------------------------------------------------------------------------
// comparison of manual and teffects ps and ipw
tabstat phat te_ps man_ipw te_ipw, stats(n mean sd min max) col(stat) longstub
Variable | N Mean SD Min Max
-------------+--------------------------------------------------
phat | 4642 .1861267 .1111502 .0587356 .7320087
te_ps | 4642 .8138733 .1111502 .2679913 .9412644
man_ipw | 4642 1.972293 1.978859 1.062401 16.82916
te_ipw | 4642 6.52958 4.15462 1.063175 17.02545
----------------------------------------------------------------
Given the output similarities is teffects ra with manual ipw weights essentially the ipwra 'automated' model?
Any guidance or advice, especially when using tailored stabilized weights would be appreciated
with thanks
Richard Hiscock
I plan to perform a doubly robust RA model to estimate ATE.
Whilst IPWRA allow for incorporation of manual probability weights I am unclear if it is appropriate to include both the treatment assingment model (calculating IPW) and then including my manual weights as well
eg teffects ipwra (outcome model) (treatment assignment model) [pw=stabIPW]
my question is whether teffects ra (outcome equation) (exposure) [pw=IPW] is equivalent to teffects ipwra (outcome model) (treatment assignment model) if the treatment assignment model generating the manual IPW the same?
Illustration, indicates close but not identical:
webuse cattaneo2.dta, clear
codebook _all, compact
// generate binary birthweight at ~ 90 centile
su bweight,de
gen binbwt = 0
replace binbwt =1 if bweight >=4000
tab binbwt
// generate manual IPW (ipw_man )
logit mbsmoke mmarried mage prenatal1 fbaby medu
predict phat,pr
gen man_ipw=.
replace man_ipw= 1/phat if mbsmoke ==1
replace man_ipw= 1/(1-phat) if mbsmoke ==0
// teffects ra weighted by IPW
teffects ra (binbwt mmarried mage prenatal1 fbaby medu, logit) ///
(mbsmoke) [pw=man_ipw] ,ate
Treatment-effects estimation Number of obs = 4,642
Estimator : regression adjustment
Outcome model : logit
Treatment model: none
----------------------------------------------------------------------------------------
| Robust
binbwt | Coefficient std. err. z P>|z| [95% conf. interval]
-----------------------+----------------------------------------------------------------
ATE |
mbsmoke |
(Smoker vs Nonsmoker) | -.0558386 .0129927 -4.30 0.000 -.0813037 -.0303735
-----------------------+----------------------------------------------------------------
POmean |
mbsmoke |
Nonsmoker | .1173439 .0052618 22.30 0.000 .1070309 .1276569
----------------------------------------------------------------------------------------
// teffects ipwa and calculation of ps & ipw
teffects ipwra (binbwt mmarried mage prenatal1 fbaby medu, logit) ///
(mbsmoke mmarried mage prenatal1 fbaby medu ) ,ate
predict te_ps , ps
gen te_ipw=.
replace te_ipw= 1/te_ps if mbsmoke ==1
replace te_ipw= 1/(1-te_ps) if mbsmoke ==0
Treatment-effects estimation Number of obs = 4,642
Estimator : IPW regression adjustment
Outcome model : logit
Treatment model: logit
----------------------------------------------------------------------------------------
| Robust
binbwt | Coefficient std. err. z P>|z| [95% conf. interval]
-----------------------+----------------------------------------------------------------
ATE |
mbsmoke |
(Smoker vs Nonsmoker) | -.0531514 .0145424 -3.65 0.000 -.0816539 -.0246489
-----------------------+----------------------------------------------------------------
POmean |
mbsmoke |
Nonsmoker | .1192232 .0052657 22.64 0.000 .1089026 .1295439
----------------------------------------------------------------------------------------
// teffects ipwra weighted as well by manual ipw
teffects ipwra (binbwt mmarried mage prenatal1 fbaby medu, logit) ///
(mbsmoke mmarried mage prenatal1 fbaby medu ) [pw=man_ipw],ate
Treatment-effects estimation Number of obs = 4,642
Estimator : IPW regression adjustment
Outcome model : logit
Treatment model: logit
----------------------------------------------------------------------------------------
| Robust
binbwt | Coefficient std. err. z P>|z| [95% conf. interval]
-----------------------+----------------------------------------------------------------
ATE |
mbsmoke |
(Smoker vs Nonsmoker) | -.0557366 .0129586 -4.30 0.000 -.081135 -.0303382
-----------------------+----------------------------------------------------------------
POmean |
mbsmoke |
Nonsmoker | .1171227 .0052589 22.27 0.000 .1068155 .1274299
----------------------------------------------------------------------------------------
// comparison of manual and teffects ps and ipw
tabstat phat te_ps man_ipw te_ipw, stats(n mean sd min max) col(stat) longstub
Variable | N Mean SD Min Max
-------------+--------------------------------------------------
phat | 4642 .1861267 .1111502 .0587356 .7320087
te_ps | 4642 .8138733 .1111502 .2679913 .9412644
man_ipw | 4642 1.972293 1.978859 1.062401 16.82916
te_ipw | 4642 6.52958 4.15462 1.063175 17.02545
----------------------------------------------------------------
Given the output similarities is teffects ra with manual ipw weights essentially the ipwra 'automated' model?
Any guidance or advice, especially when using tailored stabilized weights would be appreciated
with thanks
Richard Hiscock
