Using weights in regression

[Yolanda Schmidt]

Hi everyone,
I want to run a regression using weights in stata. I already know which command to use : reg y v1 v2 v3 [pweight= weights]. But I would like to find out how stata exactly works with the weights and how stata weights the individual observations.
In the stata-syntax-file I have read the attached concept.

I tried to do the regression manually in stata by first weight all variables of observation i with sqrt(w_i) and then perform a multiple linear regression. However, I don't get the same results as when I do a regression by using the option [pweight = weights].
Does anyone know why the calculation is false and how stata considers the weights in the observations?

Thank you for your help!

[Joro Kolev]

You get different results because pweights and aweights are different. In the picture that you post you see it is aweight, and in your post you speak of pweight.

Here is an explanation of what is going on

https://www.stata.com/support/faqs/s...ry-statistics/

[Joro Kolev]

Here is another tutorial on weights in Stata. In short it is a bit of a headache to figure out 1. what you need to do (how to weight) 2. what Stata does 3. It all depends on the estimator.

https://www.parisschoolofeconomics.e...n-stata(1).pdf

[Andrew Musau]

Here is an example showing the equivalence in #1:

sysuse auto
keep in 1/10
keep mpg weight
gen w=_n^2
l, sep(10)
regress mpg weight [aweight=w]
gen wcons= sqrt(w)
gen wmpg= sqrt(w)*mpg
gen wweight= sqrt(w)*weight
regress wmpg wweight wcons, nocons

Res.:

. l, sep(10)

     +--------------------+
     | mpg   weight     w |
     |--------------------|
  1. |  22    2,930     1 |
  2. |  17    3,350     4 |
  3. |  22    2,640     9 |
  4. |  20    3,250    16 |
  5. |  15    4,080    25 |
  6. |  18    3,670    36 |
  7. |  26    2,230    49 |
  8. |  20    3,280    64 |
  9. |  16    3,880    81 |
 10. |  19    3,400   100 |
     +--------------------+

. regress mpg weight [aweight=w]
(sum of wgt is 385)

      Source |       SS           df       MS      Number of obs   =        10
-------------+----------------------------------   F(1, 8)         =    477.32
       Model |  95.5590801         1  95.5590801   Prob > F        =    0.0000
    Residual |  1.60158778         8  .200198473   R-squared       =    0.9835
-------------+----------------------------------   Adj R-squared   =    0.9815
       Total |  97.1606679         9  10.7956298   Root MSE        =    .44744

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |    -.00588   .0002691   -21.85   0.000    -.0065007   -.0052594
       _cons |   39.02116   .9195017    42.44   0.000     36.90078    41.14153
------------------------------------------------------------------------------

. regress wmpg wweight wcons, nocons

      Source |       SS           df       MS      Number of obs   =        10
-------------+----------------------------------   F(2, 8)         =   9418.14
       Model |  145183.339         2  72591.6694   Prob > F        =    0.0000
    Residual |  61.6611296         8   7.7076412   R-squared       =    0.9996
-------------+----------------------------------   Adj R-squared   =    0.9995
       Total |      145245        10     14524.5   Root MSE        =    2.7763

------------------------------------------------------------------------------
        wmpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     wweight |    -.00588   .0002691   -21.85   0.000    -.0065007   -.0052594
       wcons |   39.02116   .9195017    42.44   0.000     36.90078    41.14153
------------------------------------------------------------------------------

[Yolanda Schmidt]

You get different results because pweights and aweights are different. In the picture that you post you see it is aweight, and in your post you speak of pweight.

Here is an explanation of what is going on

https://www.stata.com/support/faqs/s...ry-statistics/

Thanks for the document, its very helpful.

But in the Instruction they mention:
Note that point estimates are the same than the one obtained using aweight

I also get the same results when i use pweights and aweights.

[Yolanda Schmidt]

Here is an example showing the equivalence in #1:

sysuse auto
keep in 1/10
keep mpg weight
gen w=_n^2
l, sep(10)
regress mpg weight [aweight=w]
gen wcons= sqrt(w)
gen wmpg= sqrt(w)*mpg
gen wweight= sqrt(w)*weight
regress wmpg wweight wcons, nocons

Res.:

. l, sep(10)

+--------------------+
| mpg weight w |
|--------------------|
1. | 22 2,930 1 |
2. | 17 3,350 4 |
3. | 22 2,640 9 |
4. | 20 3,250 16 |
5. | 15 4,080 25 |
6. | 18 3,670 36 |
7. | 26 2,230 49 |
8. | 20 3,280 64 |
9. | 16 3,880 81 |
10. | 19 3,400 100 |
+--------------------+

. regress mpg weight [aweight=w]
(sum of wgt is 385)

Source | SS df MS Number of obs = 10
-------------+---------------------------------- F(1, 8) = 477.32
Model | 95.5590801 1 95.5590801 Prob > F = 0.0000
Residual | 1.60158778 8 .200198473 R-squared = 0.9835
-------------+---------------------------------- Adj R-squared = 0.9815
Total | 97.1606679 9 10.7956298 Root MSE = .44744

------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | -.00588 .0002691 -21.85 0.000 -.0065007 -.0052594
_cons | 39.02116 .9195017 42.44 0.000 36.90078 41.14153
------------------------------------------------------------------------------

. regress wmpg wweight wcons, nocons

Source | SS df MS Number of obs = 10
-------------+---------------------------------- F(2, 8) = 9418.14
Model | 145183.339 2 72591.6694 Prob > F = 0.0000
Residual | 61.6611296 8 7.7076412 R-squared = 0.9996
-------------+---------------------------------- Adj R-squared = 0.9995
Total | 145245 10 14524.5 Root MSE = 2.7763

------------------------------------------------------------------------------
wmpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
wweight | -.00588 .0002691 -21.85 0.000 -.0065007 -.0052594
wcons | 39.02116 .9195017 42.44 0.000 36.90078 41.14153
------------------------------------------------------------------------------

Thank you! Now it works! I forgot to weight the constant.

[Enoch Ahuakesey]

how do i use weight(1) option in stata and how do i explain it?