survey (version 3.1)

calibrate: G-calibration (GREG) estimators

Description

G-calibration (GREG) estimators generalise post-stratification and raking by calibrating a sample to the marginal totals of variables in a linear regression model. This function reweights the survey design and adds additional information that is used by svyrecvar to reduce the estimated standard errors.

Usage

calibrate(design,...)
## S3 method for class 'survey.design2':
calibrate(design, formula, population,stage=NULL,lambda=NULL,...)
## S3 method for class 'svyrep.design':
calibrate(design, formula, population, compress=NA,lambda=NULL,...)

Arguments

design

survey design object

formula

model formula for calibration model

population

Vectors of population column totals for the model matrix in the calibration model, or list of such vectors for each cluster.

compress

compress the resulting replicate weights if TRUE or if NA and weights were previously compressed

stage

See Details below

lambda

Coefficients for variance in calibration model (see Details below)

...

options for other methods

Value

• A survey design object.

Details

In a model with two-stage sampling population totals may be available for the PSUs actually sampled, but not for the whole population. In this situation, calibrating within each PSU reduces with second-stage contribution to variance. This generalizes to multistage sampling. The stage argument specifies which stage of sampling the totals refer to. Stage 0 is full population totals, stage 1 is totals for PSUs, and so on. The default, stage=NULL is interpreted as stage 0 when a single population vector is supplied and stage 1 when a list is supplied. If lambda=NULL the calibration model has constant variance. The model must explicitly or implicitly contain an intercept. If lambda is not NULL it specifies a linear combination of the columns of the model matrix and the calibration variance is proportional to that linear combination.

References

Sarndal CA, Swensson B, Wretman J. "Model Assisted Survey Sampling". Springer. 1991.

Rao JNK, Yung W, Hidiroglou MA (2002) Estimating equations for the analysis of survey data using poststratification information. Sankhya 64 Series A Part 2, 364-378.

See Also

postStratify, rake

Examples

data(api)
dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)

pop.totals<-c(`(Intercept)`=6194, stypeH=755, stypeM=1018)

## For a single factor variable this is equivalent to
## postStratify

(dclus1g<-calibrate(dclus1, ~stype, pop.totals))

svymean(~api00, dclus1g)
svytotal(~enroll, dclus1g)
svytotal(~stype, dclus1g)


## Now add sch.wide
(dclus1g2 <- calibrate(dclus1, ~stype+sch.wide, c(pop.totals, sch.wideYes=5122)))

svymean(~api00, dclus1g2)
svytotal(~enroll, dclus1g2)
svytotal(~stype, dclus1g2)

## Finally, calibrate on 1999 API and school type

(dclus1g3 <- calibrate(dclus1, ~stype+api99, c(pop.totals, api99=3914069)))

svymean(~api00, dclus1g3)
svytotal(~enroll, dclus1g3)
svytotal(~stype, dclus1g3)

## Same syntax with replicate weights
rclus1<-as.svrepdesign(dclus1)

(rclus1g3 <- calibrate(rclus1, ~stype+api99, c(pop.totals, api99=3914069)))

svymean(~api00, rclus1g3)
svytotal(~enroll, rclus1g3)
svytotal(~stype, rclus1g3)

## Ratio estimators
dstrat<-svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
rstrat<-as.svrepdesign(dstrat)

svytotal(~api.stu,dstrat)

common<-svyratio(~api.stu, ~enroll, dstrat, separate=FALSE)
sep<-svyratio(~api.stu,~enroll, dstrat,separate=TRUE)
stratum.totals<-list(E=1877350, H=1013824, M=920298)
predict(sep, total=stratum.totals)
predict(common, total=do.call("sum",stratum.totals))

pop<-colSums(model.matrix(~stype*enroll-1,model.frame(~stype*enroll,apipop)))
pop
## common ratio
dstratg1<-calibrate(dstrat,~enroll-1, pop[4], lambda=1)
svytotal(~api.stu, dstratg1)
rstratg1<-calibrate(rstrat,~enroll-1, pop[4], lambda=1)
svytotal(~api.stu, rstratg1)

## similar (but not identical) to separate ratio.
dstratg2<-calibrate(dstrat,~stype*enroll-1, pop,lambda=c(0,0,0,1,0,0))
svytotal(~api.stu,dstratg2)