On Thu, 19 Jul 2007, Fluss wrote:
> Hello!
> I am using for logistic regression in survey data the svyglm procedure.
> I wondered how does the strata effect estimates SE (in addition to the
> weights given proportional to population size).
> I know that for simple regression measurements of each strata is assumed to
> have different variance.
> But in a logistic model this is not the case.
It is simpler (and more complicated) than that. The survey package uses
the same formula for nearly all designs and estimators, so it doesn't
have to handle special cases like estimating separate stratum variances
for stratified models.
For a population total the variance estimator is just the Horvitz-Thompson
estimator. Other estimators are defined by the estimating equations they
solve, so the mean solves
sum_i w_i(x_i-mu) = 0
and logistic regression solves
sum_i w_ix_i(y_i-mu_i) = 0
We now compute the Horvitz-Thompson estimator for the sum of the
estimating functions (V) and also the population total of the derivative
of the estimating functions (D). The variance of the estimator is
D^{-1}VD^{-1}
The standard reference for this in the survey literature seems to be
Binder, David A. (1983). On the variances of asymptotically
normal estimators from complex surveys. International Statistical
Review, 51, 279-292.
which is in the References section of help(svyrecvar).
-thomas
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