Re: st: sampling query

[Steven Samuels <sjsamuels@gmail.com>]

Rich,

You must compute these probabilities for every member of the combined  
sample, not just those selected in 2+ cohorts. If possible, your  
reading should include Section 11.2 "Duplicate Listings; Overlapping  
Frames" of Leslie Kish, Survey Sampling, Wiley, 1965.

Steve


Rich,

Look up "multiple frames". That's a more common term for samples in
which the ultimate unit can be reached through different trajectories
(say landline phone sample, cell phone sample, and area/personal visit
sample). The probabilities should be combined as

1 - Prob[ in the sample ] = product over k of (1-Prob[ reach the unit
through the k-th frame ] )

which for small probabilities leads to sum of selection probabilities.
You are totally right that the probability should go up rather than
down.

On Thu, Jan 27, 2011 at 10:37 AM, Richard Goldstein
<richgold@ix.netcom.com> wrote:
> all,
>
> I have received a report in which the report writer was stuck with the
> following design (already implemented before his involvement): a  
> number
> of "cohorts" were set up (22 of them in fact) and the definitions of
> these cohorts were not mutually exclusive (i.e., there was some  
> overlap
> in membership so that a given observation could appear in more than 1
> cohort); to calculate the probability weights, the report writer first
> calculated the probability of inclusion for each cohort (simply as n/N
> where n is sample size from cohort and N is population size of  
> cohort).
>
> For observations in more than one cohort, who were actually  
> selected, he
> then multiplied the inclusion probabilities of each cohort that
> observations was in. Since each inclusion probability is less than 1,
> the combined inclusion probability is smaller than the individual
> inclusion probabilities for the individual cohort. And then, of  
> course,
> the weights are greater for these people (since the weight is just the
> inverse of the inclusion probability).
>
> However, since these observations are in more than one cohort,  
> shouldn't
> the combined probability be greater for them (rather than smaller)?
>
> How should the combined inclusion probability be calculated?
>
> Or am I just wrong and the writer of the report is correct?
>
> Any references on dealing with overlapping "cohorts" would also be
> greatly appreciated.
>
> Rich
>
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--
Stas Kolenikov, also found at http://stas.kolenikov.name
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