Re: st: svy subpop option and e(sample)

[Steven Samuels <sjsamuels@gmail.com>]

Just to elaborate: with sub-populations, the ratio estimator of a mean with every sample member in numerator and denominator is necessary because the sample size of the subpopulation is random, not fixed. This extends to the regression estimators, as they are functions of means.  If you had use an -if- qualifier to restrict the analysis to black==1, e(sample) would work as you expect; the estimates would be the same; but the standard errors would be different.

Steve
sjsamuels@gmail.com

This is expected behavior, Richard.  Everyone contributes to the standard error, whether in the sub-population or not. For example, with n = 3 and X1 X2 in the supopulation and X3 not, let Z = 1 for those in the subpopulation, 0 if not. 

Then the mean of X is estimated by  (W1 + W2 + W3/(Z1 + Z2 + Z3), a ratio estimate, with Wi = Xi*Zi and  Variation in the mean is measured by variation between W's, which includes W3 =0.


Steve


On May 24, 2011, at 4:02 PM, Richard Williams wrote:

I've just noticed that the e(sample) option does not work the way I expect it to when using svy and the subpop option. Specifically, e(sample) codes everyone in the population as 1, whether they were in the subpopulation specified or not. I guess I can sort of kind of see a rationale for doing this (the whole population is used to compute the standard errors) but it has the potential to screw up your post-estimation analysis if you only wanted to do things with (what you thought) was the subpopulation you expected.

The following illustrates this. There are only 1086 cases in the subpopulation selected, but probabilities are computed for all 10,000 cases. That is, coefficients computed using only the black subpopulation are used to compute probabilities for the entire population:

. webuse nhanes2f, clear

. svy, subpop(black): ologit health age female
(running ologit on estimation sample)

Survey: Ordered logistic regression

Number of strata   =        30                 Number of obs      =      10000
Number of PSUs     =        60                 Population size    =  113285074
                                             Subpop. no. of obs =       1086
                                             Subpop. size       =   11189236
                                             Design df          =         30
                                             F(   2,     29)    =      29.87
                                             Prob > F           =     0.0000

------------------------------------------------------------------------------
           |             Linearized
    health |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       age |  -.0452349   .0063482    -7.13   0.000    -.0581996   -.0322703
    female |  -.3975887   .1336441    -2.97   0.006    -.6705263   -.1246511
-------------+----------------------------------------------------------------
     /cut1 |  -4.427029   .2976634   -14.87   0.000    -5.034939   -3.819119
     /cut2 |   -2.97326   .2848889   -10.44   0.000    -3.555081   -2.391439
     /cut3 |  -1.347426   .2497407    -5.40   0.000    -1.857465   -.8373876
     /cut4 |   -.214417   .2857434    -0.75   0.459    -.7979829    .3691488
------------------------------------------------------------------------------
Note: 1 stratum omitted because it contains no subpopulation members.

. predict p1 p2 p3 p4 p5 if e(sample)
(option pr assumed; predicted probabilities)
(337 missing values generated)

. sum p1 p2 p3 p4 p5

  Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
        p1 |     10000    .1362895    .0853605   .0286835   .3358028
        p2 |     10000    .2341256    .0876537   .0835067   .3482424
        p3 |     10000    .3367498    .0391877   .2327486   .3854614
        p4 |     10000    .1639109    .0712129   .0549047   .2749383
        p5 |     10000    .1289243    .0859123   .0284552   .3339704

I think one solution is to change the predict command to something like

predict p51 p52 p53 p54 p55 if e(sample) & black
predict p61 p62 p63 p64 p65 if e(sample) & `=e(subpop)'

But, are there others? Preferably simpler ones? And is this good behavior for e(sample) in the first place?

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

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