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

[Rahul <rahul.lahoti@gmail.com>]

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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