svyquantile              package:survey              R Documentation

_Q_u_a_n_t_i_l_e_s _f_o_r _s_a_m_p_l_e _s_u_r_v_e_y_s

_D_e_s_c_r_i_p_t_i_o_n:

     Compute quantiles for data from complex surveys.

_U_s_a_g_e:

     ## 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", interval.type=c("probability","quantile"), f = 1,
      return.replicates=FALSE,...)
     ## S3 method for class 'svyquantile':
     SE(object,...)

_A_r_g_u_m_e_n_t_s:

       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'

_D_e_t_a_i_l_s:

     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 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 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').

_V_a_l_u_e:

     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'.

_A_u_t_h_o_r(_s):

     Thomas Lumley

_R_e_f_e_r_e_n_c_e_s:

     Binder DA (1991) Use of estimating functions for interval
     estimation from complex surveys. _Proceedings of the ASA Survey
     Research Methods Section_  1991: 34-42

     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.

_S_e_e _A_l_s_o:

     'svydesign', 'svymean', 'as.svrepdesign', 'svrepdesign'

_E_x_a_m_p_l_e_s:

       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")

      

