Re: SV: st: Survey - raking - calibration - post stratification - calculating weights

[Steven Samuels <sjhsamuels@earthlink.net>]

--

Stas, I am envious of statisticians who draw samples from those  
lists.  This is a double sample and I agree with your advice: give  
everyone the weight for their age stratum:
                          weight1 = N_i/n_i
where "N" denotes population and "n" denotes sample size.  Kristian   
apparently thinks of the 5,000 person sample as his "population"; the  
figure that he linked to does not show the initial sampling step at  
all. He may not have access to  the one-year census counts. If he  
does not, I suggest that he use the N's from the 5,000.  I  suggest  
below that he also form  geographic categories and rake those, with  
population counts, if possible, otherwise with counts from the  
5,000.  I roughly calculate that with 5,000 in the first phase  
sample, bias in estimates and in standard errors will be small.

Kristian, here is how to simultaneously match the age distribution  
and the geographic distribution of the final sample to your  
population. (This is called "sample balancing" or "raking".)  Form  
age groups (agegp) and geographical groupings (geogp) and get the  
population counts(or percentages, see below) in each cell.

**************************CODE BEGINS**************************
* tot_agep =  total for population in participant age group (agegp)
* tot_geogp = total for population in participant geographical group  
(geogp)
**************************************************************

survwgt rake  weight1  ///
      by(agegp geogp) ///
      totvars(tot_agegp tot_geogp ///
      gen(weight2)
***************************CODE ENDS***************************


Raking can present problems, so so I suggest that you read http:// 
www.abtassociates.com/
presentations/raking_survey_data_2_JOS.pdf. If you cannot get  
population counts, perhaps you can get population percentages,  
multiply by 10 or 100 and  round to the nearest whole number (e.g.  
5.12% = 51 or 512), so that the population "size" is 1,000 or 10,000.  
For estimating means and proportions, these will yield nearly the  
same results as actual population counts. The Denmark census counts  
or percentages might be available only in larger age categories than  
the ones you used to draw the sample: say (60-64, 65-70,70-74). If  
so, use those for the raking calculations.

If you have, say, four geographical categories, you may be tempted to  
use  4 x 15 =60 stratification combinations.  However, with only 600  
people in the final sample, the numbers in individual cells will be  
too small for reliable estimation.

Theory for double sampling can be found in WG Cochran, 1973, Sampling  
Techniques, pp 117-119, 327-334,  or in most other texts.   
Unfortunately, raking will not completely solve the problem of non- 
response.

-Steven

On Dec 6, 2008, at 11:19 PM, Stas Kolenikov wrote:

> Steven,
>
> you might be shocked, but people in Nordic countries do have their
> population completely enumerated. Putting NJC's hat on :)), let me
> remind you that this is an international list, and different countries
> have different standards of how they collect and store their official
> data. Denmark has a register with an equivalent of SSN that makes it
> possible to combine the data three ways from economic, medical and
> social perspectives. That's a survey statistician and a
> microeconometrician dream... and they actually do have the capacity of
> drawing SRS. That is, the first 5000 were SRS of the population, and
> then Kristian continued a with stratified second phase sampling.
>
> I would probably just give everybody the weight = # in age group
> across Denmark (in some meaningfully defined period of the study) / #
> in age in group in the sample. If you treat sample groups as
> non-response adjustment cells, that's what this will probably boil
> down to after multiplication of three or so fractions.
> ches and help try:
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