svyquantile {survey} | R Documentation |
Compute quantiles for data from complex surveys.
## S3 method for class 'survey.design': svyquantile(x, design, quantiles, alpha=0.05, ci=FALSE, method = "linear", f = 1, interval.type=c("Wald","score"), na.rm=FALSE,...) ## S3 method for class 'svyrep.design': svyquantile(x, design, quantiles, method ="linear", interval.type=c("probability","quantile"), f = 1, return.replicates=FALSE,...) ## S3 method for class 'svyquantile': SE(object,...)
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? |
na.rm |
Remove NA s? |
... |
arguments for future expansion |
object |
Object returned by svyquantile.survey.design |
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. This is the method of
Woodruff (1952).
If interval.type="score"
we use a method described by Binder
(1991) and due originally to Francisco and Fuller (1986), 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. It is much
slower, and Dorfman & Valliant (1993) suggest it is not any more accurate.
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 valid for BRR and Fay's method, and for some bootstrap-based
designs, but not for jackknife-based designs.
interval.type="quantile"
gives these replication-based
standard errors. The default, interval.type="probability"
computes confidence on the probability scale and then transforms
back to quantiles, the equivalent of interval.type="Wald"
for
survey.design
objects (with alpha=0.05
).
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
.
By default, svyquantile
interpolates between the two nearest
observed values to obtain a quantile. This is the almost universal practice outside
survey statistics, but software for survey analysis often does not
interpolate. Interpolation is discussed in the help for
quantile
; svyquantile
uses type 4 of the 9 methods
described there. For type 1 quantiles, the inverse of the weighted right-continuous
empirical cdf, specify method="constant"
and f=0
.
Thomas Lumley
Binder DA (1991) Use of estimating functions for interval estimation from complex surveys. Proceedings of the ASA Survey Research Methods Section 1991: 34-42
Dorfman A, Valliant R (1993) Quantile variance estimators in complex surveys. Proceedings of the ASA Survey Research Methods Section. 1993: 866-871
Francisco CA, Fuller WA (1986) Estimation of the distribution function with a complex survey. Technical Report, Iowa State University.
Shao J, Tu D (1995) The Jackknife and Bootstrap. Springer.
Woodruff RS (1952) Confidence intervals for medians and other position measures. JASA 57, 622-627.
svydesign
, svymean
,
as.svrepdesign
, svrepdesign
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) #stratified sample, replicate weights # interval="probability" is necessary for jackknife weights rstrat<-as.svrepdesign(dstrat) svyquantile(~api00, rstrat, c(.25,.5,.75), interval="probability") # 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, interval="quantile")