[R] Three Stage Sampling of categorical variable using 'survey' in R

[Thomas Lumley]

On Wed, Sep 26, 2012 at 12:45 AM, Kristof <bostoen at irc.nl> wrote:

> 1) SURVEY DESIGN
> So far  I designed mainly two stage cluster surveys but never did a three
> stage cluster survey design. It seems that in the analysis only the PSU is
> taken into account and enumeration area. So whatever happens at the second
> stage seems irrelevant to the analysis which seem odd to me.

There are two issues here that aren't the same.

If you don't provide population size information the analysis depends
only on the PSU, strata, weights, and measurements. If the sample is
much smaller than the population, then even if you do provide
population size information the analysis essentially depends only on
the PSU, strata, weights, and measurements.

This doesn't mean that the design doesn't matter after stage 1, it
just means that the weights and the distribution of the measurements
tells you everything about the subsequent stages that you need to
know.  In particular, the variability in weight*data is important, and
different designs can give very different standard errors.

The same design principles apply at later stages of design as at stage
1:  stratifying on a variable correlated with the variable of interest
will increase precision, and the Neyman allocation formula still tells
you how to choose stratum sizes based on what you know about variance
and cost.   It's harder to optimize a multistage design because there
are many more options and which design is best will depend on a lot of
things you don't know, but it's not intrinsically different from
optimising a single-stage design.



> Our intention was to do a PPM at the first and the second stage and have
> same size takes  in each enumeration area.
> The design would be to select 50 out of 150 Upazila's (sub-districts) as
> PSU using probability proportionate to size.
> The second stage would be 6 village-groups out of an average of 250
> village-groups per Upazila using PPS
> use SRS to select 26 households in each of the 6 selected villages per
> Upazila. Total sample size 7800
> Household is the BSU and where we need to calculate information on the
> individual level we are confident to be able to correct the sample weights
> for that.

That sounds plausible


   -thomas


-- 
Thomas Lumley
Professor of Biostatistics
University of Auckland