Quantiles for sample surveys
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","betaWald"), na.rm=FALSE,se=ci,
ties=c("discrete","rounded"), df=NULL,...)
## S3 method for class 'svyrep.design'
svyquantile(x, design, quantiles,
method ="linear", interval.type=c("probability","quantile"), f = 1,
return.replicates=FALSE, ties=c("discrete","rounded"),na.rm=FALSE,
alpha=0.05,df=NULL,...)
## S3 method for class 'svyquantile'
SE(object,...)x |
A formula, vector or matrix |
design |
|
quantiles |
Quantiles to estimate |
method |
see |
f |
see |
ci |
Compute a confidence interval? (relatively slow; needed for |
se |
Compute standard errors from the confidence interval length? |
alpha |
Level for confidence interval |
interval.type |
See Details below |
ties |
See Details below |
df |
Degrees of freedom for a t-distribution. |
return.replicates |
Return the replicate means? |
na.rm |
Remove |
... |
arguments for future expansion |
object |
Object returned by |
The definition of the CDF and thus of the quantiles is ambiguous in
the presence of ties. With ties="discrete" the data are
treated as genuinely discrete, so the CDF has vertical steps at tied
observations. With ties="rounded" all the weights for tied
observations are summed and the CDF interpolates linearly between
distinct observed values, and so is a continuous function. Combining
interval.type="betaWald" and ties="discrete" is (close
to) the proposal of Shah and Vaish(2006) used in some versions of SUDAAN.
Interval estimation for quantiles is complicated, because the
influence function is not continuous. Linearisation cannot be used
directly, and computing the variance of replicates is valid only for
some designs (eg BRR, but not jackknife). The interval.type
option controls how the intervals are computed.
For survey.design objects the default is
interval.type="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). For "betaWald" the same procedure is used, but the
confidence interval for the proportion is computed using the exact
binomial cdf with an effective sample size proposed by Korn &
Graubard (1998).
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 than "Wald", 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).
There is a confint method for svyquantile objects; it
simply extracts the pre-computed confidence interval.
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.
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
Korn EL, Graubard BI. (1998) Confidence Intervals For Proportions With Small Expected Number of Positive Counts Estimated From Survey Data. Survey Methodology 23:193-201.
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.
Shah BV, Vaish AK (2006) Confidence Intervals for Quantile Estimation from Complex Survey Data. Proceedings of the Section on Survey Research Methods.
Woodruff RS (1952) Confidence intervals for medians and other position measures. JASA 57, 622-627.
svykm for quantiles of survival curves
svyciprop for confidence intervals on proportions.
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)
svyquantile(~api00, dclus1, c(.25,.5,.75),ci=TRUE,interval.type="betaWald")
svyquantile(~api00, dclus1, c(.25,.5,.75),ci=TRUE,df=NULL)
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.type="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.type="quantile")
svyquantile(~arrests+alive, design=scdrep, quantile=0.5, interval.type="quantile",df=NULL)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.