Calibration (GREG) estimators
Description
Calibration, generalized raking, or GREG estimators generalise poststratification 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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  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=1e7,verbose=FALSE,force=FALSE,trim=NULL,...)
## 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=1e7, verbose=FALSE,force=FALSE,trim=NULL, ...)
## 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, or list of formulas for each margin 
population 
Vectors of population column totals for the model matrix in the calibration model, or list of such vectors for each cluster, or list of tables for each margin. Required except for twophase designs 
compress 
compress the resulting replicate weights if

stage 
See Details below 
variance 
Coefficients for variance in calibration model (see Details below) 
aggregate.stage 
An integer. If not 
aggregate.index 
A vector or onesided formula. If not 
bounds 
Bounds for the calibration weights, optional
except for 
trim 
Weights outside this range will be trimmed to these bounds. 
... 
options for other methods 
calfun 
Calibration function: see below 
maxit 
Number of iterations 
epsilon 
tolerance in matching population total. Either a single
number or a vector of the same length as 
verbose 
print lots of uninteresting information 
force 
Return an answer even if the specified accuracy was not achieved 
phase 
Phase of a twophase design to calibrate (only

mm 
model matrix 
ww 
vector of weights 
eta 
starting values for iteration 
Details
The formula
argument specifies a model matrix, and the
population
argument is the population column sums of this
matrix.
For the important special case where the calibration totals are (possibly
overlapping) marginal tables of factor variables, as in classical
raking, the formula
and population
arguments may be
lists in the same format as the input to rake
.
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
(localedependent) ordering of factor levels is not what you expected.
Numerical instabilities may result if the sampling weights in the
design
object are wrong by multiple orders of magnitude. The
code now attempts to rescale the weights first, but it is better for
the user to ensure that the scale is reasonable.
The calibrate
function implements linear, bounded linear,
raking, bounded raking, and logit calibration functions. All except
unbounded linear calibration use the NewtonRaphson 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 builtin
functions or as an object of class calfun
, allowing
userdefined 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.
When calibration to the desired set of bounds is not possible, another option is
to trim weights. To do this set bounds
to a looser set of bounds
for which calibration is achievable and set trim
to the tighter
bounds. Weights outside the bounds will be trimmed to the bounds, and
the excess weight distributed over other observations in proportion to
their sampling weight (and so this may put some other observations
slightly over the trimming bounds). The projection matrix used in computing
standard errors is based on the feasible bounds specified by the
bounds
argument. See also trimWeights
,
which trims the final weights in a design object rather than the
calibration adjustments.
For twophase 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 laststage 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 twostage 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 secondstage
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. Calibrating to PSU totals will fail (with a message
about an exactly singular matrix) for PSUs that have fewer
observations than the number of calibration variables.
For unbounded linear calibration only, the variance in the calibration
model may depend on covariates. If variance=NULL
the
calibration model has constant variance. 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 twophase design, population
may be omitted when
phase=2
, to specify calibration to the phaseone sample. If the
twophase design object was constructed using the more memoryefficient
method="approx"
argument to twophase
, calibration of the first
phase of sampling to the population is not supported.
Value
A survey design object.
References
Deville JC, Sarndal CE, Sautory O (1993) Generalized Raking Procedures in Survey Sampling. JASA 88:10131020
Kalton G, FloresCervantes I (2003) "Weighting methods" J Official Stat 19(2) 8197
Lumley T, Shaw PA, Dai JY (2011) "Connections between survey calibration estimators and semiparametric models for incomplete data" International Statistical Review. 79:200220. (with discussion 79:221232)
Sarndal CE, 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, 364378.
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, 846866.
Vanderhoeft C (2001) Generalized Calibration at Statistics Belgium. Statistics Belgium Working Paper No 3. http://statbel.fgov.be/nl/binaries/paper03%5B1%5D_tcm32535412.pdf
See Also
postStratify
, rake
for other ways
to use auxiliary information
twophase
and vignette("epi")
for an example of calibration in twophase designs
survey/tests/kalton.R
for examples replicating those in Kalton & FloresCervantes (2003)
make.calfun
for userdefined calibration distances.
trimWeights
to trim final weights rather than calibration adjustments.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108  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)
###
## 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)
## trimming
dclus1tr < calibrate(dclus1, ~stype+api99, c(pop.totals, api99=3914069),
bounds=c(0.5,2), trim=c(2/3,3/2))
svymean(~api00+api99+enroll, dclus1tr)
svytotal(~stype,dclus1tr)
range(weights(dclus1tr)/weights(dclus1))
rclus1tr < calibrate(rclus1, ~stype+api99, c(pop.totals, api99=3914069),
bounds=c(0.5,2), trim=c(2/3,3/2))
svymean(~api00+api99+enroll, rclus1tr)
svytotal(~stype,rclus1tr)
## Input in the same format as rake() for classical raking
pop.table < xtabs(~stype+sch.wide,apipop)
pop.table2 < xtabs(~stype+comp.imp,apipop)
dclus1r<rake(dclus1, list(~stype+sch.wide, ~stype+comp.imp),
list(pop.table, pop.table2))
gclus1r<calibrate(dclus1, formula=list(~stype+sch.wide, ~stype+comp.imp),
population=list(pop.table, pop.table2),calfun="raking")
svymean(~api00+stype, dclus1r)
svymean(~api00+stype, gclus1r)
## generalised raking
dclus1g3c < calibrate(dclus1, ~stype+api99, c(pop.totals,
api99=3914069), calfun="raking")
range(weights(dclus1g3c)/weights(dclus1))
(dclus1g3d < calibrate(dclus1, ~stype+api99, c(pop.totals,
api99=3914069), calfun=cal.logit, bounds=c(0.5,2.5)))
range(weights(dclus1g3d)/weights(dclus1))
## Ratio estimators are calibration estimators
dstrat<svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
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,~enroll1, pop, variance=1)
svytotal(~api.stu, dstratg1)
