svyrecvar: Variance estimation for multistage surveys

Description

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

Usage

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

Arguments

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

Value

A covariance matrix

Details

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.

References

Bellhouse DR (1985) Computing Methods for Variance Estimation in Complex Surveys. Journal of Official Statistics. Vol.1, No.3, 1985 Binder, David A. (1983). On the variances of asymptotically normal estimators from complex surveys. International Statistical Review, 51, 279-292.

Cochran, W. (1977) Sampling Techniques. 3rd edition. Wiley. Sarndal C-E, Swensson B, Wretman J (1991) Model Assisted Survey Sampling. Springer.

Examples

Run this code

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)

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