Re: st: Sample weights: Combining strata estimates to get one overall estimate

[Steven Samuels <sjsamuels@gmail.com>]

Rahul,

Just -svyset- your data with the poststrata() and postweight() options. The following code illustrates this and shows how to do it by hand.

**********CODE BEGINS*********
sysuse auto, clear
gen postwx=2000 if foreign==0 //total pop for Domestic
replace postwx= 1000 if foreign==1 //total pop for Foreign
svyset _n [pw=turn], strata(foreign)
svy: tab foreign, count
// sum of weights: 2155 for Domestic 779 Foreign
svyset _n [pw=turn], strata(foreign) poststrata(foreign) postweight(postwx)
svy: tab foreign, count
// Post-stratification "by hand":
gen new_wt= (2000/2155)*turn if foreign==0
replace new_wt =(1000/779)*turn if foreign==1
svyset _n [pw=new_wt], strata(foreign)
svy: tab foreign, count
**********CODE ENDS*********

The totals used (2000, 1000 here) need not be actual totals, but numbers that are close and maintain the correct proportions. In analysis of 2005-2006 data from India, for example, I used totals from the 2001 Census of India.

Disproportionate stratum sample sizes by themselves will not cause problems. In a survey that samples all stages with PPS, the sum of weights in a stratum is an independent estimate of the stratum's population size.

For a good reference on weighting, see Chapter 8 of Sharon Lohr 2009. Sampling: Design and Analysis. Pacific Grove, CA: Brooks Cole Publishing Company. After you have looked at that, I encourage you to "rake" (post-stratify simultaneously) other factors, such as urban/rural totals, age/gender totals, village size. In Stata you can do this with -survwgt rake-, contained in Nick Winter's -svr- package at SSC.

Steve

Steven J. Samuels
Consulting Statistician
18 Cantine's Island
Saugerties, NY 12477 USA
Voice: 845-246-0774
Fax: 206-202-4783 
sjsamuels@gmail.com



On Apr 7, 2011, at 12:09 PM, Rahul wrote:

Dear Statalist,

I had a weighting related question. I am developing weights for household
sample survey in State of Karnataka in India.

In our sampling design we divide the state into four strata (regions) and
> pick districts (biggest sampling unit within the region) within the stratas
> randomly. Then we divide each district into rural and urban strata. We do
> random sampling using Population proportion to size sampling at stages below
> this in picking taluks (biggest administrative unit in a district) and then
> villages (our FSU's).
> 
> We have developed weights for each region [which are all inverse
> of probability of selection at each stage of sampling] separately. So we get
> weighted rural estimate for Region 1,2,3 and 4. We need to combine these
> four estimates to get an estimate at the rural state level.
> 
> The stratification is disproportionate i.e. each strata's sample size is
> not exactly proportional to its share in the overall population of the
> state. In some strata the proportion of sample of
> the overall state sample is greater than its corresponding proportion
> of strata population to the total population. These are off by a few
> percentage points. We are assuming if they were similar we needn't make any
> adjustment and the State overall estimate is just simple combination of each
> strata's estimate.
> 
> How should we combine the strata estimates? Do we need to make
> the correction for disproportionate ?. Is it needed and in what form?. Can
> we just multiply the correction term with the probability weight which we
> are providing stata?
> 
> the step above would give me two estimates rural and urban estimates at
> the state level. rural/urban is also a strata. To combine this and get
> one estimate at the state level do we have to multiply by some factor?.
> 
> In short, our question is how to combine strata level estimates to get
> one overall estimate - especially in case where we have disproportionate
> stratification.
> 
> I would appreciate any help in this regards.
> 
> thanks
> rahul
> 
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