Obtaining weighted means and SDs using -tebalance summarize- after -teffects ipw-

[Philip Jones]

Dear all,

I am performing some observational research which uses IPTW and the -teffects ipw- package.

After performing the analysis, I am using the -tebalance summarize- command to obtain the standardized differences, as so:

quietly webuse cattaneo2, clear

quietly teffects ipw (bweight) (mbsmoke foreign alcohol mage medu fage fedu, logit)

 
tebalance summarize mage alcohol

  Covariate balance summary
                                                   Raw     Weighted
                          -----------------------------------------
                          Number of obs =        4,642      4,642.0
                          Treated obs   =          864      2,238.7
                          Control obs   =        3,778      2,403.3
                          -----------------------------------------

  -----------------------------------------------------------------
                  |Standardized differences          Variance ratio
                  |        Raw    Weighted           Raw   Weighted
  ----------------+------------------------------------------------
             mage |   -.300179   -.0893001      .8818025   .8381985
          alcohol |   .3222725   -.0033769      4.509207   .9828912
  -----------------------------------------------------------------

but does anyone know how to get the actual weighted means and SDs (or weighted numbers/percentages for binary variables)?

I have attached a figure showing what I am trying to achieve.

The columns to the right show the weighted numbers and percentages (for binary variables) and weighted means/SDs (for continuous variables), and these are the numbers I would like to get.


My attempt has been to use each demographic variable that I am interested in as an "outcome" in the -teffects ipw- analysis and use the POMs as the weighted means.

. teffects ipw (mage) (mbsmoke foreign alcohol mage medu fage fedu, logit), pom

Iteration 0:   EE criterion =  3.138e-17  
Iteration 1:   EE criterion =  1.339e-29  

Treatment-effects estimation                    Number of obs     =      4,642
Estimator      : inverse-probability weights
Outcome model  : weighted mean
Treatment model: logit
------------------------------------------------------------------------------
             |               Robust
        mage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
POmeans      |
     mbsmoke |
  nonsmoker  |   26.45739   .0842272   314.12   0.000     26.29231    26.62247
     smoker  |   25.96681   .1190025   218.20   0.000     25.73357    26.20005
------------------------------------------------------------------------------

I think this is correct for the weighted means, but I am unsure how to go from the robust SEs given to SDs. But since SE = SD / sqrt(n), perhaps it is just multiplying the SE by the square root of the number of observations in the weighted sample?

For example:

. di sqrt(2403.3) * .0842272
4.1291091

for the control group above, and

. di sqrt(2238.7) * .1190025
5.6305917

for the treatment group

Can anyone help?

Many thanks, Phil

[Philip Jones]

Alternatively, I thought for the continuous variables I could tackle the situation manually, as so:

. * manually calculate inverse-probability weights:
quietly logit mbsmoke foreign alcohol mage medu fage fedu

quietly predict double ps if e(sample)

quietly gen double ipw = 1.mbsmoke/ps + 0.mbsmoke/(1-ps)



 * use -mean- to get weighted means
 
mean mage [pw=ipw] if e(sample), over(mbsmoke)

Mean estimation                   Number of obs   =      4,642

    nonsmoker: mbsmoke = nonsmoker
       smoker: mbsmoke = smoker

--------------------------------------------------------------
        Over |       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
mage         |
   nonsmoker |   26.45739   .0979118      26.26544    26.64934
      smoker |   25.96681   .1983074      25.57803    26.35558
--------------------------------------------------------------

. estat sd

    nonsmoker: mbsmoke = nonsmoker
       smoker: mbsmoke = smoker

-------------------------------------
        Over |       Mean   Std. Dev.
-------------+-----------------------
mage         |
   nonsmoker |   26.45739    7.183891
      smoker |   25.96681    3.258869
-------------------------------------

[Philip Jones]

Joerg Luedicke (StataCorp) Do you have any advice on this issue? Thank you.

[Joerg Luedicke (StataCorp)]

Hi Philip,

You would simply use the sample standard deviation of the weighted means, where the weights are the normalized inverse-probability weights. It would also be possible to calculate the standard deviations from the standard errors, but those should be non-robust standard errors then. However, there is no need for going this route as you could simply use summarize with iweights here:

. * Data:
. webuse cattaneo2, clear
(Excerpt from Cattaneo (2010) Journal of Econometrics 155: 138-154)
. 
. * Model:
. qui teffects ipw (bweight) (mbsmoke foreign alcohol mage medu fage fedu)
. 
. * IPWs:
. predict double ps, ps tlevel(1)
. gen double ipw = 1.mbsmoke/ps + 0.mbsmoke/(1-ps)
. 
. * Normalizing weights:
. sum ipw, mean
. qui replace ipw = ipw/r(mean)
. 
. * Inverse probability weighted means and SDs:
. bysort mbsmoke: summarize mage alcohol [iw=ipw]

-------------------------------------------------------------------------------
-> mbsmoke = nonsmoker

    Variable |     Obs      Weight        Mean   Std. Dev.       Min        Max
-------------+-----------------------------------------------------------------
        mage |   3,778  2403.34515    26.45739    5.73034         13         45
     alcohol |   3,778  2403.34515    .0346019   .1828073          0          1

-------------------------------------------------------------------------------
-> mbsmoke = smoker

    Variable |     Obs      Weight        Mean   Std. Dev.       Min        Max
-------------+-----------------------------------------------------------------
        mage |     864  2238.65485    25.96681   5.246309         14         43
     alcohol |     864  2238.65485    .0339872   .1812367          0          1

This corresponds to the calculations of the standardized mean differences from tebalance summarize:

. webuse cattaneo2, clear
(Excerpt from Cattaneo (2010) Journal of Econometrics 155: 138-154)

. qui teffects ipw (bweight) (mbsmoke foreign alcohol mage medu fage fedu)
. predict double ps, ps tlevel(1)
. gen double ipw = 1.mbsmoke/ps + 0.mbsmoke/(1-ps)
. sum ipw, mean
. qui replace ipw = ipw/r(mean)
. sum mage if mbsmoke == 0 [iw=ipw]

    Variable |     Obs      Weight        Mean   Std. Dev.       Min        Max
-------------+-----------------------------------------------------------------
        mage |   3,778  2403.34515    26.45739    5.73034         13         45

. scalar Vc = r(Var)
. scalar Mc = r(mean)
. sum mage if mbsmoke == 1 [iw=ipw]

    Variable |     Obs      Weight        Mean   Std. Dev.       Min        Max
-------------+-----------------------------------------------------------------
        mage |     864  2238.65485    25.96681   5.246309         14         43

. scalar Vt = r(Var)
. scalar Mt = r(mean)
. scalar stddiff_ipw = (scalar(Mt)-scalar(Mc))/sqrt((scalar(Vt)+scalar(Vc))/2)
. display %8.7f scalar(stddiff_ipw)
-0.0893001

. tebalance summarize mage

  Covariate balance summary
                                                   Raw     Weighted
                          -----------------------------------------
                          Number of obs =        4,642      4,642.0
                          Treated obs   =          864      2,238.7
                          Control obs   =        3,778      2,403.3
                          -----------------------------------------

  -----------------------------------------------------------------
                  |Standardized differences          Variance ratio
                  |        Raw    Weighted           Raw   Weighted
  ----------------+------------------------------------------------
             mage |   -.300179   -.0893001      .8818025   .8381985
  -----------------------------------------------------------------

I hope this helps!

Joerg

[Philip Jones]

Joerg,

What a superb answer! Thank you so much for taking the time. I really hope this will benefit someone else too.

[Mo hady]

Thanks Joerg,

I was wondering how to generate baseline characteristics for categorical variables displaying n(%) after PS.

[Mohamed Nachid Boussiala]

. teffects ipw ($Y) ($A $W), atet
. predict double ps, ps tlevel(1)
. gen double ipw = 1.$A + (0.$A/(1-ps))* ps
. sum ipw, mean
. replace ipw = ipw/r(mean)

. sum $Y if $A == 0 [iw=ipw]
. scalar Vc = r(Var)
. scalar Mc = r(mean)

. sum $Y if $A == 1 [iw=ipw]
. scalar Vt = r(Var)
. scalar Mt = r(mean)
. scalar stddiff_ipw = (scalar(Mt)-scalar(Mc))/sqrt((scalar(Vt)+scalar(Vc))/2)
. display %8.7f scalar(stddiff_ipw)
. tebalance summarize $Y