[R] R

[Thomas Lumley]

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