svyquantile.RdEstimates quantiles and confidence intervals for them. This function was completely re-written for version 4.1 of the survey package, and has a wider range of ways to define the quantile. See the vignette for a list of them.
svyquantile(x, design, quantiles, ...)
# S3 method for survey.design
svyquantile(x, design, quantiles, alpha = 0.05,
interval.type = c("mean", "beta","xlogit", "asin","score"),
na.rm = FALSE, ci=TRUE, se = ci,
qrule=c("math","school","shahvaish","hf1","hf2","hf3",
"hf4","hf5","hf6","hf7","hf8","hf9"),
df = NULL, ...)
# S3 method for svyrep.design
svyquantile(x, design, quantiles, alpha = 0.05,
interval.type = c("mean", "beta","xlogit", "asin","quantile"),
na.rm = FALSE, ci = TRUE, se=ci,
qrule=c("math","school","shahvaish","hf1","hf2","hf3",
"hf4","hf5","hf6","hf7","hf8","hf9"),
df = NULL, return.replicates=FALSE,...)A one-sided formula describing variables to be used
Design object
Numeric vector specifying which quantiles are requested
Specified confidence interval coverage
See Details below
Remove missing values?
Return an estimated confidence interval and standard error?
Rule for defining the quantiles: either a character string specifying one of the built-in rules, or a function
Degrees of freedom for confidence interval estimation: NULL specifies degf(design)
Return replicate estimates of the quantile (only for interval.type="quantile")
For future expansion
The pth quantile is defined as the value where the estimated cumulative
distribution function is equal to p. As with quantiles in
unweighted data, this definition only pins down the quantile to an
interval between two observations, and a rule is needed to interpolate.
The default is the mathematical definition, the lower end of the
quantile interval; qrule="school" uses the midpoint of the
quantile interval; "hf1" to "hf9" are weighted analogues of
type=1 to 9 in quantile. See the vignette
"Quantile rules" for details and for how to write your own.
By default, confidence intervals are estimated using Woodruff's (1952) method,
which involves computing the quantile, estimating a confidence interval
for the proportion of observations below the quantile, and then
transforming that interval using the estimated CDF. In that context,
the interval.type argument specifies how the confidence interval
for the proportion is computed, matching svyciprop. In
contrast to oldsvyquantile, NaN is returned if a confidence
interval endpoint on the probability scale falls outside [0,1].
There are two exceptions. For svydesign objects,
interval.type="score" asks for the Francisco & Fuller confidence
interval based on inverting a score test. According to Dorfmann &
Valliant, this interval has inferior performance to the "beta"
and "logit" intervals; it is provided for compatibility.
For replicate-weight designs, interval.type="quantile" ask for an
interval based directly on the replicates of the quantile. This interval
is not valid for jackknife-type replicates, though it should perform well for
bootstrap-type replicates, BRR, and SDR.
The df argument specifies degrees of freedom for a t-distribution
approximation to distributions of means. The default is the design degrees of
freedom. Specify df=Inf to use a Normal distribution (eg, for compatibility).
When the standard error is requested, it is estimated by dividing the
confidence interval length by the number of standard errors in a t
confidence interval with the specified alpha. For example, with
alpha=0.05 and df=Inf the standard error is estimated as the confidence
interval length divided by 2*1.96.
An object of class "newsvyquantile", except that with a
replicate-weights design and interval.type="quantile" and
return.replicates=TRUE it's an object of class "svrepstat"
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.
Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in statistical packages, The American Statistician 50, 361-365.
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.
data(api)
## population
quantile(apipop$api00,c(.25,.5,.75))
#> 25% 50% 75%
#> 565 667 761
## one-stage cluster sample
dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
rclus1<-as.svrepdesign(dclus1)
bclus1<-as.svrepdesign(dclus1,type="boot")
svyquantile(~api00, dclus1, c(.25,.5,.75))
#> $api00
#> quantile ci.2.5 ci.97.5 se
#> 0.25 552 492 627 31.47166
#> 0.5 652 561 714 35.66788
#> 0.75 719 696 777 18.88300
#>
#> attr(,"hasci")
#> [1] TRUE
#> attr(,"class")
#> [1] "newsvyquantile"
svyquantile(~api00, dclus1, c(.25,.5,.75),interval.type="beta")
#> $api00
#> quantile ci.2.5 ci.97.5 se
#> 0.25 552 502 637 31.47166
#> 0.5 652 555 717 37.76599
#> 0.75 719 689 762 17.01801
#>
#> attr(,"hasci")
#> [1] TRUE
#> attr(,"class")
#> [1] "newsvyquantile"
svyquantile(~api00, rclus1, c(.25,.5,.75))
#> $api00
#> quantile ci.2.5 ci.97.5 se
#> 0.25 552 482 629 34.26914
#> 0.5 652 552 720 39.16473
#> 0.75 719 691 781 20.98111
#>
#> attr(,"hasci")
#> [1] TRUE
#> attr(,"class")
#> [1] "newsvyquantile"
svyquantile(~api00, rclus1, c(.25,.5,.75),interval.type="quantile")
#> Warning: Jackknife replicate weights may not give valid standard errors for quantiles
#> $api00
#> quantile ci.2.5 ci.97.5 se
#> 0.25 552 452.3926 651.6074 46.44163
#> 0.5 652 558.8913 745.1087 43.41162
#> 0.75 719 679.4477 758.5523 18.44116
#>
#> attr(,"hasci")
#> [1] TRUE
#> attr(,"class")
#> [1] "newsvyquantile"
svyquantile(~api00, bclus1, c(.25,.5,.75),interval.type="quantile")
#> $api00
#> quantile ci.2.5 ci.97.5 se
#> 0.25 552 473.6719 630.3281 36.52023
#> 0.5 652 573.4258 730.5742 36.63496
#> 0.75 719 675.2491 762.7509 20.39872
#>
#> attr(,"hasci")
#> [1] TRUE
#> attr(,"class")
#> [1] "newsvyquantile"
svyquantile(~api00+ell, dclus1, c(.25,.5,.75), qrule="math")
#> $api00
#> quantile ci.2.5 ci.97.5 se
#> 0.25 552 492 627 31.47166
#> 0.5 652 561 714 35.66788
#> 0.75 719 696 777 18.88300
#>
#> $ell
#> quantile ci.2.5 ci.97.5 se
#> 0.25 16 8 23 3.496851
#> 0.5 26 25 30 1.165617
#> 0.75 37 34 43 2.098111
#>
#> attr(,"hasci")
#> [1] TRUE
#> attr(,"class")
#> [1] "newsvyquantile"
svyquantile(~api00+ell, dclus1, c(.25,.5,.75), qrule="school")
#> $api00
#> quantile ci.2.5 ci.97.5 se
#> 0.25 552 492 627 31.47166
#> 0.5 652 561 714 35.66788
#> 0.75 719 696 777 18.88300
#>
#> $ell
#> quantile ci.2.5 ci.97.5 se
#> 0.25 16 8 23 3.496851
#> 0.5 26 25 30 1.165617
#> 0.75 37 34 43 2.098111
#>
#> attr(,"hasci")
#> [1] TRUE
#> attr(,"class")
#> [1] "newsvyquantile"
svyquantile(~api00+ell, dclus1, c(.25,.5,.75), qrule="hf8")
#> $api00
#> quantile ci.2.5 ci.97.5 se
#> 0.25 552.1667 491.6476 627.1866 31.59731
#> 0.5 652.0000 559.9436 714.5300 36.03772
#> 0.75 718.6667 691.5805 777.1490 19.94800
#>
#> $ell
#> quantile ci.2.5 ci.97.5 se
#> 0.25 16 8 23.0000 3.496851
#> 0.5 26 25 30.0000 1.165617
#> 0.75 37 34 43.2537 2.157253
#>
#> attr(,"hasci")
#> [1] TRUE
#> attr(,"class")
#> [1] "newsvyquantile"