Re: st: -svyset- methods to account for singleton PSUs

[Steve Samuels <sjsamuels@gmail.com>]

1) The -singleunit(certainty)- option should be specified whenever a
PSU was selected with certainty. To use it, create a separate stratum
for each such unit. If later stages of sampling are ignored in
-svyset- then this option ignores the contribution from later stage
units to standard errors and so will understate the standard error
slightly. Theorems 10.3 and 10.4, p. 286 of WG Cochran (1977)
Sampling Techniques, Wiley, shows that for SRS at all stages, the bias
from ignoring the later stages will be minimal: the denominator for
the later stage variance components is the total number of
observations at that stage, which can often be large.

In some designs, all strata contain only a single PSU and standard
errors are formed from differences in the squares of PSU means from
adjacent strata. See the new -svy sdr- command. When -svy sdr- is
used, the - singleunit()- option should have no effect.

The other two automatic options are intended for situations in which
one or more selected PSUs is missing from the stratum. This can occur
when the entire PSU is missing, or more commonly, when either there
are no members of a subpopulation in a PSU or when there are no
observations in the PSU with non-missing values of crucial variables.
In these cases, I prefer not to use either automatic option, but to
merge the single unit PSUs with PSUs in "adjacent" strata.

2) The singlunit(centered) option will usually yield an upwardly
biased estimate of standard error, as you surmise. If the absent PSUs
are missing at random, the contribution to (positive) bias will be
roughly proportional to the squared difference between stratum mean
and population mean, divided by sample size. However, if PSU
missingness is related to the magnitude of the study variables, the
bias could be negative. The amount bias in any one study will be
depend on the particulars.

3) The direction of the bias from the singleunit(scaled) option can be
positive or negative, not just negative as you expect. Again,
generalization is impossible and will depend on the particular
population, stratum, and reason for missingness of absent PSUs.


Steve


On Mon, Jul 5, 2010 at 10:14 AM, James Shaw <shawjw@gmail.com> wrote:
> Can anyone cite references that discuss the singleunit(centered) and
> singleunit(scaled) methods for accommodating singleton PSUs?  I would
> expect the certainty and scaled methods to yield downward-biased
> variance estimates and the centered method to yield upward-biased
> estimates.  However, it is not clear to me if and how the magnitudes
> of the biases differ among the methods.


-- 
Steven Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
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