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Re: st: sampling query


From   Steven Samuels <sjsamuels@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: sampling query
Date   Thu, 27 Jan 2011 16:54:54 -0500


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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