[R] Complex surveys, properly computed SEs and non-parametric analyses

[Thomas Lumley]

On Sun, 15 Jul 2007, Tobias Verbeke wrote:
> The survey package of Thomas Lumley has very broad functionality for the
> analysis of data from complex sampling designs. Please find below the
> homepage of the package (which is available on CRAN):
>
> http://faculty.washington.edu/tlumley/survey/
>
> I don't think non-parametric one-way ANOVA is implemented

No.

> but quoting
> http://faculty.washington.edu/tlumley/survey/survey-wss.pdf
> "Many features of the survey package result from requests from
> unsatisfied users.
>
> For new methods the most important information is a reference
> that gives sufficient detail for implementation. A data set is nice
> but not critical."
>

Yes, and the details are especially non-obvious here.  The test won't be 
small-sample exact, AFAICS, and it isn't clear whether the idea is to add 
weights to the influence function for the signed-rank test or to replace 
it with a design-based estimate of a population quantity. Often these 
approaches are equivalent, but they won't be in this case. It wouldn't 
have occured to me that people would want this. `Non-parametric' isn't 
really a relevant idea since design-based inference assumes a completely 
known model for the sampling indicators and doesn't even treat the data as 
random variables.

All this goes to say that if there is a standard quantity that John wants, 
it will have resulted in part from a set of arbitrary decisions, and it 
won't be possible to reverse-engineer the estimator in the absence of a 
precise description.  This is in contrast to apparently more complicated 
analyses such as calibration estimators for Cox models in case-cohort
designs, which follow just by putting standard pieces together in an 
obvious way.


 	-thomas