< Construct a new weight within the stratum as the sample weight multiplied by the frequency> The correct formula for the new weights can be found in Chapter 6 of Shao and Tu (1996) "The Jackknife and the Bootstrap", Springer
Also in: " Keith Rust & Jon Rao have an overview article in Statistical Methods in Medical Research (1996 vol 5, pp 283-310) which review most of the literature and methods to that point (also see Shao & Tu's book Chapter 6). They also give the correct formula for the bootstrap weights. It is highly recommended in Rust & Rao (referring to Rao & Wu) that for bootstrap you select n(h)-1 out of n(h) PSUs in stratum h with replacement." If you select n(h)-1 out of n(h) PSUS in strata h the new weight should be: New-weight = Old-weight * frequency PSU is selected * n(h) / (n(h) - 1) So if you randomly select 1 out 2 PSUs you double the weight because of the factor n(h) / (n(h) - 1). This method is basically randomly building BRR replicates (in a 2-per design) so it is like an inefficient BRR and the number of bootstrap replicates needed may depend on both the statistic being estimated and the number of replicates in a fully balanced BRR set. Bob -----Original Message----- From: Fred Rohde [mailto:[EMAIL PROTECTED] Sent: Wednesday, April 14, 2004 9:46 AM To: Thomas Lumley Cc: [EMAIL PROTECTED] Subject: Re: [R] Complex sample variances I think I've figured out a way to do a bootstrap variance estimate of a quantile. I need to work out the code, but this is the algorithm (for a stratified cluster sample): Make a list of the stratum values for the sample For each stratum value, Make a list of the PSU values within that stratum Sample n-1 PSU values with replacement Get the frequency of PSU values selected Attach the frequency to the sample elements within the stratum by PSU Construct a new weight within the stratum as the sample weight multiplied by the frequency Once the new weight is generated in all stratum, get the quantile estimate(s) from svyquantile using the new weight Repeat another 99 times to build 100 bootstrap replicates Get the standard deviation of the replicate estimates as the variance What do you think? It's kind of general. For stratified non-clustered samples, the selections would be done on sample elements, not on PSUs, and for non-stratified cluster cluster designs, the PSU selections would be done across the whole sample, not by stratum. I'm not that up with bootstrapping however. I'm not sure how to set/save the seed values so running the procedure again on the same dataset will produce the same variance. Fred Thomas Lumley <[EMAIL PROTECTED]> wrote: On Mon, 12 Apr 2004, Fred Rohde wrote: > Thanks. I'll update the survey package. Sudaan does the standard > errors on quantiles using Taylor series. If I can hunt down the formula > it uses, could you add that to svyquantile? If I can bring myself to believe it. Computing standard errors for the normal approximation to the median is not easy even in simple random samples. -thomas > Fred > > Thomas Lumley wrote: > On Mon, 12 Apr 2004, Fred Rohde wrote: > > > Hello, > > Is there a way to get complex sample variances in the survey package on > > summary statistics other than means? If not, can they be added to a > > future version? It would be be great to have them on totals, quantiles, > > ratios, and tables (eg row percent, columns percent, etc). > > > > svytotal() and svyratio() will do this for totals and ratios if you have a > new enough version. At the moment the easiest way to get row or column > percentages is to think of them them as ratios of means of binary > variables and use svyratio(). > > Quantiles are more difficult, since neither Taylor series nor jackknife > approaches work. > > -thomas > > > --------------------------------- > Do you Yahoo!? Thomas Lumley Assoc. Professor, Biostatistics [EMAIL PROTECTED] University of Washington, Seattle --------------------------------- [[alternative HTML version deleted]] ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html