svyrecvar  R Documentation 
Compute the variance of a total under multistage sampling, using a recursive descent algorithm.
svyrecvar(x, clusters, stratas,fpcs, postStrata = NULL,
lonely.psu = getOption("survey.lonely.psu"),
one.stage=getOption("survey.ultimate.cluster"))
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 
postStrata 
poststratification information as created by

lonely.psu 
How to handle strata with a single PSU 
one.stage 
If 
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 multistage 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 singlestage betweencluster estimator and a withincluster 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
withreplacement standard errors would be correct).
A covariance matrix
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.
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, 305315.
Binder, David A. (1983). On the variances of asymptotically normal estimators from complex surveys. International Statistical Review, 51, 279292.
Brewer KRW (2002) Combined Survey Sampling Inference (Weighing Basu's Elephants) [Chapter 9]
Cochran, W. (1977) Sampling Techniques. 3rd edition. Wiley.
Sarndal CE, Swensson B, Wretman J (1991) Model Assisted Survey Sampling. Springer.
svrVar
for replicate weight designs
svyCprod
for a description of how variances are
estimated at each stage
data(mu284)
dmu284<svydesign(id=~id1+id2,fpc=~n1+n2, data=mu284)
svytotal(~y1, dmu284)
data(api)
# twostage cluster sample
dclus2<svydesign(id=~dnum+snum, fpc=~fpc1+fpc2, data=apiclus2)
summary(dclus2)
svymean(~api00, dclus2)
svytotal(~enroll, dclus2,na.rm=TRUE)
# bootstrap for multistage sample
mrbclus2<as.svrepdesign(dclus2, type="mrb", replicates=100)
svytotal(~enroll, mrbclus2, na.rm=TRUE)
# twostage `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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