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Re: st: BRR and svy command (with mean bootstrap weights)

From (Jeff Pitblado, StataCorp LP)
Subject   Re: st: BRR and svy command (with mean bootstrap weights)
Date   Wed, 18 Oct 2006 09:44:14 -0500

Alan Diener <> asks how to get -svy brr- to work with
bootstrap weights:

> In Stata Version 9, it is possible to use the svy command with balance
> repeated replication (BRR) weights in the case of privacy-conscious data
> sets. i.e. data sets which do not provide variables that identify the PSUs
> and strata, but instead provide, for example, bootstrap weights that can be
> used to estimate the appropriate standard errors.

> In previous versions of Stata this type of analysis was possible with the
> BSWREG ado file.

I'll just add a short example of how easy this is in Stata 9.  Suppose the
sampling weight variable is named -sampwt- and the bootstrap weight variables
are named -bsw1-, -bsw2-, ..., -bsw6000- (for 6000 bootstrap weight
variables), then the -svyset- command looks like the following (assuming that
only the bootstrap weight variables start with 'bsw'):

	. svyset [pw=sampwt], brrweight(bsw*) vce(brr)

Then all the following -svy- estimation commands will use the bootstrap weight
variables (via -svy brr-) to perform the variance estimation.

> However, there are data sets in which the bootstrap weights provided are
> actually *mean* bootstrap weights. For example, 500 bootstrap weights may
> be provided, but each one is the mean of 12 weights (i.e. there were
> originally 6000 bootstrap weights created, but only 500 are provided). The
> BSWREG command is able to take mean bootstrap weights into account with the
> cmeansb option.

> Does anybody know if it is possible consider *mean* bootstrap weights with
> the svy command in Stata 9?

> (not taking the fact that they are mean bootstrap weights into
> consideration results in SE estimates that are biased downwards)

Yes, this is possible in Stata 9.  You must use Fay's adjustment to account
for the fact that the weight variables are 'mean bootstrap' weight variables.

In the example proposed by Alan, 500 mean bootstrap weight variables were
generated by taking the mean of the original 6000 bootstrap weight variables
partitioned into groups of size 12 (6000/12 = 500).  The Fay's adjustment is
a function of how many weight variables were used in the mean.

Let K denote the value of Fay's adjustment, and C be the number of weight
variables used in the mean (e.g. C = 12).  Then the formula for Fay's
adjustment is

	K = 1 - 1/sqrt(C)

For Alan's example, I would suggest something like the following in Stata 9:

	. local fay = 1 - 1/sqrt(12)
	. svyset [pw=sampwt], brrweight(bsw*) vce(brr) fay(`fay')


The fact that you can use -svy brr- with bootstrap weights was first brought
to my attention in an online article I read by Owen Phillips.

Phillips, Owen.  2004. Using bootstrap weights with WesVar and SUDAAN. The
	Research Data Centres Information and Technical Bulletin. 1(2): 6-15.

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