mean comparison with sample weights (pweight)

[Daniel Graeber]

Dear all,

I want to perform mean comparisons across groups. I also want to apply sample weights (pweight). That works fine. Now, I want to allow for unequal variances across groups as a robustness check. I want to do this with sample weights. But I did not find any command that allows this procedure with sample weights. Thus, I performed a regression, including two groups, with a group indicator as regressor. Further, I apply analytic weights and robust standard errors.

Is my solution appropriate? Thank you very much.

Best

Daniel

[Carlo Lazzaro]

Daniel:
you may want to consider something along the following lines (please note that -pweight- are usually applied in survey statistics):

use "C:\Program Files\Stata16\ado\base\a\auto.dta"

. g prob=22/74 if foreign==1
(52 missing values generated)

. replace prob=52/74 if foreign==0
(52 real changes made)

. tab prob

       prob |      Freq.     Percent        Cum.
------------+-----------------------------------
   .2972973 |         22       29.73       29.73
   .7027027 |         52       70.27      100.00
------------+-----------------------------------
      Total |         74      100.00

. regress price mpg [pw=1/prob]
(sum of wgt is 147.9999997686673)

Linear regression                               Number of obs     =         74
                                                F(1, 72)          =      14.72
                                                Prob > F          =     0.0003
                                                R-squared         =     0.2356
                                                Root MSE          =     2508.4

------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -222.8268   58.08595    -3.84   0.000     -338.619   -107.0346
       _cons |   11197.55   1417.579     7.90   0.000     8371.659    14023.44
------------------------------------------------------------------------------

.

[Joro Kolev]

Yes, you can use -regress- to do this, however I do not see why you should be switching from pw to aw, just keep on using pw and add the robust option.

Or you can declare your data as survey data, as explained here:

https://stats.idre.ucla.edu/stata/fa...h-survey-data/

[Daniel Graeber]

Thanks Carlo and Joro. I will switch to probability weights then. You convinced me. On a note: I already treid both and results change in the third or fourth digit. But I assume probability weights are closer to the truth then.

Best

Daniel

[Daniel Graeber]

Daniel:
you may want to consider something along the following lines (please note that -pweight- are usually applied in survey statistics):

use "C:\Program Files\Stata16\ado\base\a\auto.dta"

. g prob=22/74 if foreign==1
(52 missing values generated)

. replace prob=52/74 if foreign==0
(52 real changes made)

. tab prob

prob | Freq. Percent Cum.
------------+-----------------------------------
.2972973 | 22 29.73 29.73
.7027027 | 52 70.27 100.00
------------+-----------------------------------
Total | 74 100.00

. regress price mpg [pw=1/prob]
(sum of wgt is 147.9999997686673)

Linear regression Number of obs = 74
F(1, 72) = 14.72
Prob > F = 0.0003
R-squared = 0.2356
Root MSE = 2508.4

------------------------------------------------------------------------------
| Robust
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg | -222.8268 58.08595 -3.84 0.000 -338.619 -107.0346
_cons | 11197.55 1417.579 7.90 0.000 8371.659 14023.44
------------------------------------------------------------------------------

.

Interesting,...... In your example, pweight and (aweight & robust) deliver the same results. Fascinating.

[daniel klein]

Interesting,...... In your example, pweight and (aweight & robust) deliver the same results. Fascinating.

Well, pweights and aweights generally result in the same point estimates*; robust standard errors are based on the score/predicted values, which are based on those point estimates; using pweight implies vce(robust).


Edit: * This is not really true, e.g., estimating totals; see [U] 20.24 Weighted estimation

[Carlo Lazzaro]

Thanks, Daniel:
I was late to the party!

[Daniel Graeber]

Well, pweights and aweights generally result in the same point estimates*; robust standard errors are based on the score/predicted values, which are based on those point estimates; using pweight implies vce(robust).


Edit: * This is not really true, e.g., estimating totals; see [U] 20.24 Weighted estimation

Thanks, I was referring to the standard errors ;-).