subpop option with survey data

[Charlotte Rogers]

Hi,

I have complex survey data for the health outcomes of males and females in a population in two separate years. I am trying to obtain the variation in the health outcomes of the overall, female and male population between one and the other year. Strangely, when I perform this analysis using sample weights, the variation for the total population is smaller than that of the female population and smaller than that of the male population. This is unexpected and counterintuitive.

My code is:

svy, subpop(male): reg outcome year2
svy, subpop(female): reg outcome year2
svy, subpop(male): reg outcome year2

Can anyone help? thanks!

[Richard Williams]

First, I suspect your code is wrong as the first and third lines are identical. Second it would help to see your output so we could see what it is that concerns you. Use code tags to make the output legible; see point 12 in the FAQ.

[Charlotte Rogers]

Ok, so I hereby provide my code and stata output:

svyset [pweight=w_fstuwt], brrweight(w_fstr1-w_fstr80) vce(brr) fay(0.5) mse

svy brr: reg pv1r year2003

gen male=0
replace male=1 if female==0

svy brr, subpop(female): reg pv1r year2003
svy brr, subpop(male): reg pv1r year2003


BRR replications (80)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..............................

Survey: Linear regression                       Number of obs      =     11150
                                                Population size    = 73546.129
                                                Replications       =        80
                                                Design df          =        79
                                                F(   1,     79)    =     27.48
                                                Prob > F           =    0.0000
                                                R-squared          =    0.0114

------------------------------------------------------------------------------
             |                BRR *
     pv1r |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    year2003 |   23.33034   4.450639     5.24   0.000     14.47157    32.18912
       _cons |   411.6454   3.086953   133.35   0.000      405.501    417.7898
------------------------------------------------------------------------------

BRR replications (80)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..............................

Survey: Linear regression                       Number of obs      =     11150
                                                Population size    = 73546.129
                                                Subpop. no. of obs =      5579
                                                Subpop. size       = 38431.825
                                                Replications       =        80
                                                Design df          =        79
                                                F(   1,     79)    =     28.12
                                                Prob > F           =    0.0000
                                                R-squared          =    0.0138

------------------------------------------------------------------------------
             |                BRR *
     pv1r|      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    year2003 |   24.00183   4.526299     5.30   0.000     14.99245     33.0112
       _cons |   428.8713    3.07544   139.45   0.000     422.7498    434.9928
------------------------------------------------------------------------------

BRR replications (80)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..............................

Survey: Linear regression                       Number of obs      =     11150
                                                Population size    = 73546.129
                                                Subpop. no. of obs =      5571
                                                Subpop. size       = 35114.303
                                                Replications       =        80
                                                Design df          =        79
                                                F(   1,     79)    =     17.84
                                                Prob > F           =    0.0001
                                                R-squared          =    0.0111

------------------------------------------------------------------------------
             |                BRR *
     pv1r |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    year2003 |   24.07191   5.699001     4.22   0.000     12.72833    35.41548
       _cons |   392.1133   3.775034   103.87   0.000     384.5993    399.6273
------------------------------------------------------------------------------

As you can see, the regression for males and females points to a difference between years of around 24 points and the overall difference is 23.3.

[Charlotte Rogers]

I suspect that the problem comes from the weighting structure, but I don't see how.

[Richard Williams]

Shouldn't there be a dummy variable for gender in the pooled model?

[Charlotte Rogers]

That is not the problem I think

[Steve Samuels]

The phenomenon you observe is an example of Simpson's paradox: the gender-specific differences differ from the pooled difference. It will occur whenever the weighted sex ratio is not the same in the two years. In the example below, the year 1 year 2 difference is 2 for both genders, but 1.9 in the pooled data.

Thanks for the listing with code delimiters , but in the future, please also show the commands and results as they appear in the log. Otherwise, it is difficult to know immediately which command goes with which results.

. input year gender vmean count

          year     gender      vmean      count
  1. 1  1  3 45
  2. 1  2  5 55
  3. 2  1  5 50
  4. 2  2  7 50
  5. end
.
. tabulate  year gender  [fw = count]

           |        gender
      year |         1          2 |     Total
-----------+----------------------+----------
         1 |        45         55 |       100
         2 |        50         50 |       100
-----------+----------------------+----------
     Total |        95        105 |       200
.
. table   year gender [fw = count], c(mean vmean)

----------------------
          |   gender  
     year |    1     2
----------+-----------
        1 |    3     5
        2 |    5     7
----------------------

. table   year     [fw = count], c( mean vmean)  // pooled

-----------------------
     year | mean(vmean)
----------+------------
        1 |         4.1
        2 |           6
-----------------------