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,
       aggregate.stage=NULL, stage=0, variance=NULL,
       bounds=c(-Inf,Inf), calfun=c("linear","raking","logit"),
       maxit=50,epsilon=1e-7,verbose=FALSE,force=FALSE,...)
## S3 method for class 'svyrep.design':
calibrate(design, formula, population,compress=NA,
       aggregate.index=NULL, variance=NULL, bounds=c(-Inf,Inf),
       calfun=c("linear","raking","logit"),
       maxit=50, epsilon=1e-7, verbose=FALSE,force=FALSE, ...)
## S3 method for class 'twophase':
calibrate(design, phase=2,formula, population,
       calfun=c("linear","raking","logit","rrz"),...)
grake(mm,ww,calfun,eta=rep(0,NCOL(mm)),bounds,population,epsilon, verbose,maxit)

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. Required except for two-phase designs

compress

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

stage

See Details below

variance

Coefficients for variance in calibration model (see Details below)

aggregate.stage

An integer. If not NULL, make calibration weights constant within sampling units at this stage.

aggregate.index

A vector or one-sided formula. If not NULL, make calibration weights constant within levels of this variable

bounds

Bounds for the calibration weights, optional except for calfun="logit"

...

options for other methods

calfun

Calibration function: see below

maxit

Number of iterations

epsilon

tolerance in matching population total

verbose

print lots of uninteresting information

force

Return an answer even if the specified accuracy was not achieved

phase

Phase of a two-phase design to calibrate (only phase=2 currently implemented.)

model matrix

vector of weights

eta

starting values for iteration

Value

A survey design object.

Details

If the population argument has a names attribute it will be checked against the names produced by model.matrix(formula) and reordered if necessary. This protects against situations where the (locale-dependent) ordering of factor levels is not what you expected. The calibrate function implements linear, bounded linear, raking, bounded raking, and logit calibration functions. All except unbounded linear calibration use the Newton-Raphson algorithm described by Deville et al (1993). This algorithm is exposed for other uses in the grake function. Unbounded linear calibration uses an algorithm that is less sensitive to collinearity. The calibration function may be specified as a string naming one of the three built-in functions or as an object of class calfun, allowing user-defined functions. See make.calfun for details.

Calibration with bounds, or on highly collinear data, may fail. If force=TRUE the approximately calibrated design object will still be returned (useful for examining why it failed). A failure in calibrating a set of replicate weights when the sampling weights were successfully calibrated will give only a warning, not an error.

For two-phase designs calfun="rrz" estimates the sampling probabilities using logistic regression as described by Robins et al (1994). estWeights will do the same thing.

Calibration may result in observations within the last-stage sampling units having unequal weight even though they necessarily are sampled together. Specifying aggegrate.stage ensures that the calibration weight adjustments are constant within sampling units at the specified stage; if the original sampling weights were equal the final weights will also be equal. The algorithm is as described by Vanderhoeft (2001, section III.D). Specifying aggregate.index does the same thing for replicate weight designs; a warning will be given if the original weights are not constant within levels of aggregate.index. In a model with two-phase 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. For unbounded linear calibration only, the variance in the calibration model may depend on covariates. If variance=NULL the calibration model has constant variance. The model must explicitly or implicitly contain an intercept. If variance 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.

The design matrix specified by formula (after any aggregation) must be of full rank, with one exception. If the population total for a column is zero and all the observations are zero the column will be ignored. This allows the use of factors where the population happens to have no observations at some level.

In a two-phase design, population may be omitted when phase=2, to specify calibration to the phase-one sample.

References

Deville J-C, Sarndal C-E, Sautory O (1993) Generalized Raking Procedures in Survey Sampling. JASA 88:1013-1020

Kalton G, Flores-Cervantes I (2003) "Weighting methods" J Official Stat 19(2) 81-97 Sarndal C-E, 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.

Robins JM, Rotnitzky A, Zhao LP. (1994) Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89, 846-866.

Vanderhoeft C (2001) Generalized Calibration at Statistics Belgium. Statistics Belgium Working Paper No 3. http://www.statbel.fgov.be/studies/paper03_en.asp

Examples

Run this code

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)

## Make weights constant within school district
(dclus1agg<-calibrate(dclus1, ~stype, pop.totals, aggregate=1))
svymean(~api00, dclus1agg)
svytotal(~enroll, dclus1agg)
svytotal(~stype, dclus1agg)


## 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)

(rclus1agg3 <- calibrate(rclus1, ~stype+api99, c(pop.totals,api99=3914069), aggregate.index=~dnum))

svymean(~api00, rclus1agg3)
svytotal(~enroll, rclus1agg3)
svytotal(~stype, rclus1agg3)

image(rclus1agg3)

###
## Bounded weights
range(weights(dclus1g3)/weights(dclus1))
(dclus1g3b <- calibrate(dclus1, ~stype+api99, c(pop.totals, api99=3914069),bounds=c(0.6,1.6)))
range(weights(dclus1g3b)/weights(dclus1))

svymean(~api00, dclus1g3b)
svytotal(~enroll, dclus1g3b)
svytotal(~stype, dclus1g3b)

## generalised raking
(dclus1g3c <- calibrate(dclus1, ~stype+api99, c(pop.totals,
    api99=3914069), calfun="raking"))
range(weights(dclus1g3c)/weights(dclus1))

(dclus1g3c <- calibrate(dclus1, ~stype+api99, c(pop.totals,
    api99=3914069), calfun=cal.raking))
range(weights(dclus1g3c)/weights(dclus1))

(dclus1g3d <- calibrate(dclus1, ~stype+api99, c(pop.totals,
    api99=3914069), calfun="logit",bounds=c(0.5,2.5)))
range(weights(dclus1g3d)/weights(dclus1))



## 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)
predict(common, total=3811472)

pop<-3811472
## equivalent to (common) ratio estimator
dstratg1<-calibrate(dstrat,~enroll-1, pop, variance=1)
svytotal(~api.stu, dstratg1)
rstratg1<-calibrate(rstrat,~enroll-1, pop, variance=1)
svytotal(~api.stu, rstratg1)

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