survey (version 2.9-1)

svyquantile: Quantiles for sample surveys

Description

Compute quantiles for data from complex surveys.

Usage

## S3 method for class 'survey.design':
svyquantile(x, design, quantiles, alpha=0.05, ci=FALSE, method = "linear", f = 1, interval.type=c("Wald","score"),...)
## S3 method for class 'svyrep.design':
svyquantile(x, design, quantiles, method =
"linear", f = 1, return.replicates=FALSE,...)
## S3 method for class 'svyquantile':
SE(object,...)

Arguments

x

A formula, vector or matrix

design

survey.design or svyrep.design object

quantiles

Quantiles to estimate

method

see approxfun

f

see approxfun

ci

Compute a confidence interval (relatively slow)?

alpha

Level for confidence interval

interval.type

See Details below

return.replicates

Return the replicate means?

...

arguments for future expansion

object

Object returned by svyquantile.survey.design

Value

• returns a list whose first component is the quantiles and second component is the confidence intervals. For replicate weight designs, returns an object of class svyrepstat.

Details

Interval estimation for quantiles is complicated, because the influence function is not continuous. Linearisation cannot be used, and only some replication weight designs give valid results. For survey.design objects the computation is controlled by interval.type. If "Wald", a 95% Wald confidence interval is constructed for the proportion below the estimated quantile. The inverse of the estimated CDF is used to map this to a confidence interval for the quantile. If interval.type="score" we use the method of Francisco-Fuller, which corresponds to inverting a robust score test. At the upper and lower limits of the confidence interval, a test of the null hypothesis that the cumulative distribution function is equal to the target quantile just rejects. This was the default before version 2.9 and should be more accurate, but is much slower. Standard errors are computed from these confidence intervals by dividing the confidence interval length by 2*qnorm(alpha/2). For replicate-weight designs, ordinary replication-based standard errors are computed. These are typically not valid for the JK1 and JKn jackknife designs. They are valid for BRR and Fay's method, and for some bootstrap-based designs.

References

Binder DA (1991) Use of estimating functions for interval estimation from complex surveys. Proceedings of the ASA Survey Research Methods Section 1991: 34-42 Shao J, Tu D (1995) The Jackknife and Bootstrap. Springer.

See Also

svydesign, svymean, as.svrepdesign, svrepdesign

Examples

data(api)
  ## population
  quantile(apipop$api00,c(.25,.5,.75))

  ## one-stage cluster sample
  dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
  svyquantile(~api00, dclus1, c(.25,.5,.75),ci=TRUE)

  dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
  (qapi<-svyquantile(~api00, dclus1, c(.25,.5,.75),ci=TRUE, interval.type="score"))
  SE(qapi)

  #stratified sample
  dstrat<-svydesign(id=~1, strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
  svyquantile(~api00, dstrat, c(.25,.5,.75),ci=TRUE)


  # BRR method
  data(scd)
  repweights<-2*cbind(c(1,0,1,0,1,0), c(1,0,0,1,0,1), c(0,1,1,0,0,1),
              c(0,1,0,1,1,0))
  scdrep<-svrepdesign(data=scd, type="BRR", repweights=repweights)
  svyquantile(~arrests+alive, design=scdrep, quantile=0.5)