withReplicates: Compute variances by replicate weighting

Description

Given a function or expression computing a statistic based on sampling weights, withReplicates evaluates the statistic and produces a replicate-based estimate of variance. vcov.svrep.design produces the variance estimate from a set of replicates and the design object.

Usage

withReplicates(design, theta,..., return.replicates=FALSE)
# S3 method for svyrep.design
withReplicates(design, theta, rho = NULL, ..., 
     scale.weights=FALSE, return.replicates=FALSE)
# S3 method for svrepvar
withReplicates(design, theta,  ...,  return.replicates=FALSE)
# S3 method for svrepstat
withReplicates(design, theta,  ...,  return.replicates=FALSE)
# S3 method for svyimputationList
withReplicates(design, theta,  ...,  return.replicates=FALSE)
# S3 method for svyrep.design
vcov(object, replicates, centre,...)

Value

If return.replicates=FALSE, the weighted statistic, with the variance matrix as the "var" attribute. If

return.replicates=TRUE, a list with elements theta for the usual return value and replicates for the replicates.

Arguments

design: A survey design with replicate weights (eg from svrepdesign) or a suitable object with replicate parameter estimates
theta: A function or expression: see Details below
rho: If design uses BRR weights, rho optionally specifies the parameter for Fay's variance estimator.
...: Other arguments to theta
scale.weights: Divide the probability weights by their sum (can help with overflow problems)
return.replicates: Return the replicate estimates as well as the variance?
object: The replicate-weights design object used to create the replicates
replicates: A set of replicates
centre: The centering value for variance calculation. If object$mse is TRUE this is the result of estimation using the sampling weights, and must be supplied. If object$mse is FALSE the mean of the replicates is used and this argument is silently ignored.

Details

The method for svyrep.design objects evaluates a function or expression using the sampling weights and then each set of replicate weights. The method for svrepvar objects evaluates the function or expression on an estimated population covariance matrix and its replicates, to simplify multivariate statistics such as structural equation models.

For the svyrep.design method, if theta is a function its first argument will be a vector of weights and the second argument will be a data frame containing the variables from the design object. If it is an expression, the sampling weights will be available as the variable .weights. Variables in the design object will also be in scope. It is possible to use global variables in the expression, but unwise, as they may be masked by local variables inside withReplicates.

For the svrepvar method a function will get the covariance matrix as its first argument, and an expression will be evaluated with .replicate set to the variance matrix.

For the svrepstat method a function will get the point estimate, and an expression will be evaluated with .replicate set to each replicate. The method can only be used when the svrepstat object includes replicates.

The svyimputationList method runs withReplicates on each imputed design (which must be replicate-weight designs).

Examples

Run this code

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)

a<-svyratio(~alive, ~arrests, design=scdrep)
print(a$ratio)
print(a$var)
withReplicates(scdrep, quote(sum(.weights*alive)/sum(.weights*arrests)))
withReplicates(scdrep, function(w,data)
sum(w*data$alive)/sum(w*data$arrests))

data(api)
dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
rclus1<-as.svrepdesign(dclus1)
varmat<-svyvar(~api00+api99+ell+meals+hsg+mobility,rclus1,return.replicates=TRUE)
withReplicates(varmat, quote( factanal(covmat=.replicate, factors=2)$unique) )


data(nhanes)
nhanesdesign <- svydesign(id=~SDMVPSU, strata=~SDMVSTRA, weights=~WTMEC2YR, nest=TRUE,data=nhanes)
logistic <- svyglm(HI_CHOL~race+agecat+RIAGENDR, design=as.svrepdesign(nhanesdesign),
family=quasibinomial, return.replicates=TRUE)
fitted<-predict(logistic, return.replicates=TRUE, type="response")
sensitivity<-function(pred,actual) mean(pred>0.1 & actual)/mean(actual)
withReplicates(fitted, sensitivity, actual=logistic$y)

if (FALSE) {
library(quantreg)
data(api)
## one-stage cluster sample
dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
## convert to bootstrap
bclus1<-as.svrepdesign(dclus1,type="bootstrap", replicates=100)

## median regression
withReplicates(bclus1, quote(coef(rq(api00~api99, tau=0.5, weights=.weights))))
}


## pearson correlation
dstrat <- svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
bstrat<- as.svrepdesign(dstrat,type="subbootstrap")

v <- svyvar(~api00+api99, bstrat, return.replicates=TRUE)
vcor<-cov2cor(as.matrix(v))[2,1]
vreps<-v$replicates
correps<-apply(vreps,1, function(v) v[2]/sqrt(v[1]*v[4]))

vcov(bstrat,correps, centre=vcor)