R: Quantiles for sample surveys

svyquantile {survey} | R Documentation

## 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","betaWald"), na.rm=FALSE,se=ci,
       ties=c("discrete","rounded"), df=Inf,...)
    ## 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,...)
    ## 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; needed for `svyby`)
`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. `Inf` requests a Normal distribution, `NULL` uses `degf`. Not relevant for `type="betaWald"`
`return.replicates` | Return the replicate means?
`na.rm` | Remove `NA`s?
`...` | arguments for future expansion
`object` | Object returned by `svyquantile.survey.design`

### Details

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.

### 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`.

### Author(s)

Thomas Lumley

### 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

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.

### See Also

`svykm` for quantiles of survival curves

`svyciprop` for confidence intervals on proportions.

### 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)
      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")

[Package survey version 3.32-1 Index]