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RE: st: Definition of strata and PSUs when svysetting

From   "Angel Rodriguez Laso" <>
To   <>
Subject   RE: st: Definition of strata and PSUs when svysetting
Date   Fri, 28 Mar 2008 15:40:45 +0100

Thank you for your answer, Stas.

I´ve tried both specifications and the first surprise was that Stata 9
ignores further stages when stage 1 is sampled with replacement. It was good
to come across this warning because in our survey sampling was without
replacement and the sampling fraction of the census tracts was quite high
(more than one third in some strata) what precludes assuming that selection
was with replacement.

The problem with using age groups as second stage strata is that being 3 the
number of people over 65 selected per census tract, whenever there are
missing values in the variables some strata become single-PSU (person)
strata, what prevents Stata from calculating standard errors. So, the two
specifications I´ve tried are:

svyset censustract [pweight=pondef], strata(area) fpc(#censustractsinarea)
svyset censustract [pweight=pondef], strata(area-by-age) fpc(#censustractsin

Not surprisingly standard errors with both specifications differ only in
some hundreths. I believe this is mainly due to the fact that in both cases
degrees of freedom are very large. This is something I want to check with
you: From the reading of Korn and Graubard "Analysis of health surveys" I´ve
understood that in complex surveys degrees of freedom are calculated as
#PSUs - #strata (624 for the first specification and 1244 for the second,
because Stata duplicates the number of census tracts because each of them
belongs to two different strata). I do not follow you very well when you
recommend doing a small simulation with census or simulated data to
ascertain degrees of freedom or when you state that Taylor series expansion
standard errors might be badly off with small samples. It´s usual practice
to work with such low numbers of individuals per PSU (10 in my case) and
I´ve never heard that there was a problem of a small sample size then.

Unfortunately, I don´t have enough knowledge to go for option 3.

To conclude, although both specifications yield similar results, I agree
with you that the second one implies linked selection of PSUs while the
first one is conceptually sounder. 

Ángel Rodríguez Laso
Institute of Public Health of the Region of Madrid

-----Mensaje original-----
[] En nombre de Stas Kolenikov
Enviado el: jueves, 27 de marzo de 2008 20:06
Asunto: Re: st: Definition of strata and PSUs when svysetting

I would say your first specificaiton makes better sense, even though
the design it produces is quite weird, and the degrees of freedom in
that design are strange (and 7 initial strata won't get you very far,
anyway). In Stata 10, that's doable with

svyset tract, strata(area) || person, strata(age_group)

if I am getting your design right.

In the second specification with region by age strata, you have some
sort of coupled sampling when selecting a PSU in one stratum implies
selecting a certain PSU in the another stratum linked by geography.
You could still analyze that, but you would need to get accurate
pairwise probabilities of selection to compute Horwitz-Thompson
estimator, and Grundy-Yates-Sen estimator of its variance (which I
don't think is implemented anywhere commercially as those higher order
probabilities of selection are rarely known; Jeff P, that might
produce a cutting edge addition to Stata's set of -svy- tools,
although I've no idea how to input and parse those :)). Any reasonably
high level book would have it (Kish, Cochran, Mary Thompson's books
spring to mind). For special cases, I think that can be programmed in
Mata. Let's call that option 3. Note that the naive implementation as

svyset tract, strata(area X age) || person

produces wrong probabilities of selection, and the variances are
likely to be understated, as there is more variability in this
specification than in your actual design.

If I were in your shoes, I would try both specifications you described
and see whether they are producing comparable substantive results.
Keep in mind that either way you are getting asymptotic Taylor series
expansion standard errors, and they might be badly
off with small samples like those you have. And I think you need to
worry about your degrees of freedom, not your number of PSUs; I would
do a small simulation to determine the approximate d.f.s for your main
variables -- from census data if you have it, or from simulated data
resembling the actual population. If I had infinite time to work on
that project (meaning, a week or two of devoted programming), I would
implement option 3 as the most proper.

On 3/25/08, Angel Rodriguez Laso <> wrote:
> Greetings to all members of the list,
>  I have the following questions on svysetting for an analysis of a complex
>  survey:
>  We have carried out a regional health population survey. We defined
>  initially as geographic areas in the region (n=7) and allocated to each
>  them a sample proportional to their population. But because we wanted to
>  over-represent the elderly, we set that the number of people over 65
>  sampled in all areas had to reach a minimum number. We didn't change the
>  sample size of people bellow 65 obtained through the proportional
>  allocation. Therefore the sampling fractions (and consequently the
>  are different for each area by age group (bellow/over 65) category.
>  Then we selected census tracts in each geographic area with probabilities
>  proportional to their total population, and randomly sampled 10
>  in those selected, always keeping the proportion 7 bellow 65 years/3 over
>  years, which was the regional overall age distribution after the
>  oversampling explained above. My first question is if strata should be
>  defined as geographic regions alone or as geographic area by age groups
>  (bellow/ over 65 years) (n=14) when svysetting. The first possibility
>  more reasonable, because census tracts were selected within geographic
>  areas, not within geographic-age groups areas. If this is correct, then
>  probably the way to svyset would be declaring geographic areas as first
>  stage strata, census tracts as first stage PSUs and age groups as second
>  stage strata.
>  Alternatively, if the answer is that strata should be defined as region
>  two age-groups categories, then the same census tract can belong to two
>  different strata (for example area A bellow 65/ area A over 65) depending
>  the age of the individual considered. If I svyset: strata (region by age
>  group categories) and PSU= census tracts, STATA interprets that there are
>  twice the number of PSUs than real census tracts are. Is that correct?
>  Many thanks.
>  Ángel Rodríguez Laso
>  Institute of Public Health of the Region of Madrid

Stas Kolenikov, also found at

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