calibrate {survey} | R Documentation

## Calibration (GREG) estimators

### Description

Calibration (or 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.)
`mm` | model matrix
`ww` | vector of weights
`eta` | starting values for iteration

### 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-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. 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 two-phase design, `population` may be omitted when `phase=2`, to specify calibration to the phase-one sample. If the two-phase design object was constructed using the more memory-efficient `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 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

### See Also

`postStratify`, `rake` for other ways to use auxiliary information

`twophase` and `vignette("epi")` for an example of calibration in two-phase designs

`survey/tests/kalton.R` for examples replicating those in Kalton & Flores-Cervantes (2003)

`make.calfun` for user-defined calibration distances.

### 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)

    ## 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 are calibration 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)

[Package survey version 3.19 Index]