svyrecvar               package:survey               R Documentation

_V_a_r_i_a_n_c_e _e_s_t_i_m_a_t_i_o_n _f_o_r _m_u_l_t_i_s_t_a_g_e _s_u_r_v_e_y_s

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

     Compute the variance of a total under multistage sampling, using a
     recursive descent algorithm.

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

     svyrecvar(x, clusters, stratas,fpcs, postStrata = NULL,
     lonely.psu = getOption("survey.lonely.psu"),
     one.stage=getOption("survey.ultimate.cluster"))

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

       x: Matrix of data or estimating functions

clusters: Data frame or matrix with cluster ids for each stage

 stratas: Strata for each stage 

    fpcs: Information on population and sample size for each stage,
          created by 'as.fpc'

postStrata: post-stratification information as created by
          'postStratify' or 'calibrate' 

lonely.psu: How to handle strata with a single PSU

one.stage: If 'TRUE', compute a one-stage (ultimate-cluster) estimator

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

     The main use of this function is to compute the variance of the
     sum of a set of estimating functions under multistage sampling. 
     The sampling is assumed to be simple or stratified random sampling
     within clusters at each stage except perhaps the last stage.  The
     variance of a statistic is computed from the variance of
     estimating functions as described by Binder (1983).

     Use 'one.stage=FALSE' for compatibility with other software that
     does not perform multi-stage calculations, and set
     'options(survey.ultimate.cluster=TRUE)' to make this the default.

     The idea of a recursive algorithm is due to Bellhouse (1985).
     Texts such as Cochran (1977) and Sarndal et al (1991) describe the
     decomposition of the variance into a single-stage between-cluster
     estimator and a within-cluster estimator, and this is applied
     recursively.

     If 'one.stage' is a positive integer it specifies the number of
     stages of sampling to use in the recursive estimator.

     If 'pps="brewer"', standard errors are estimated using Brewer's
     approximation for PPS without replacement, option 2 of those
     described by Berger (2004). The 'fpc' argument must then be
     specified in terms of sampling fractions, not population sizes (or
     omitted, but then the 'pps' argument would have no effect and the
     with-replacement standard errors would be correct).

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

     A covariance matrix

_N_o_t_e:

     A simple set of finite population corrections will only be exactly
     correct when each successive stage uses simple or stratified
     random sampling without replacement.  A correction under general
     unequal probability sampling (eg PPS) would require joint
     inclusion probabilities (or, at least, sampling probabilities for
     units not included in the sample), information not generally
     available.

     The quality of Brewer's approximation is excellent in Berger's
     simulations, but the accuracy may vary depending on the sampling
     algorithm used.

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

     Bellhouse DR (1985) Computing Methods for Variance Estimation in
     Complex Surveys. Journal of Official Statistics. Vol.1, No.3, 1985

     Berger, Y.G. (2004), A Simple Variance Estimator for Unequal
     Probability Sampling Without Replacement. Journal of Applied
     Statistics, 31, 305-315.

     Binder, David A. (1983).  On the variances of asymptotically
     normal estimators from complex surveys.  International Statistical
     Review, 51, 279-292.

     Brewer KRW (2002) Combined Survey Sampling Inference (Weighing
     Basu's Elephants)  [Chapter 9]

     Cochran, W. (1977)  Sampling Techniques. 3rd edition. Wiley.

     Sarndal C-E, Swensson B, Wretman J (1991) Model Assisted Survey
     Sampling. Springer.

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

     'svrVar' for replicate weight designs

     'svyCprod' for a description of how variances are estimated at
     each stage

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

     data(mu284)
     dmu284<-svydesign(id=~id1+id2,fpc=~n1+n2, data=mu284)
     svytotal(~y1, dmu284)

     data(api)
     # two-stage cluster sample
     dclus2<-svydesign(id=~dnum+snum, fpc=~fpc1+fpc2, data=apiclus2)
     summary(dclus2)
     svymean(~api00, dclus2)
     svytotal(~enroll, dclus2,na.rm=TRUE)

     # two-stage `with replacement'
     dclus2wr<-svydesign(id=~dnum+snum, weights=~pw, data=apiclus2)
     summary(dclus2wr)
     svymean(~api00, dclus2wr)
     svytotal(~enroll, dclus2wr,na.rm=TRUE)

