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Dual-frame and multi-frame surveys

multiframe.Rd

Given a list of samples from K different sampling frames and information about which observations are in which frame, constructs an object representing the whole multi-frame sample. If an unit is in the overlap of multiple frames in the population it is effectively split into multiple separate units and so the weight is split if it is sampled. To optimise the split of frame weights, see reweight

Usage

multiframe(designs, overlaps, estimator = c("constant", "expected"), theta = NULL)

Arguments

designs

List of survey design objects

overlaps

list of matrices. Each matrix has K columns indicating whether the observation is in frames 1-K. For the 'constant'-type estimator, this is binary. For the expected estimator the entry in row i and column k is the weight or probability that observation i would have had if sampled from frame k. (weights if all >=1, probabilities if all <=1)

estimator

"constant" specifies Hartley's estimators in which the partition of weights is the same for each observation. "expected" weights each observation by the reciprocal of the expected number of times it is sampled; it is the estimator proposed by Bankier and by Kalton and Anderson.

theta

Scale factors adding to 1 for splitting the overlap between frames

Details

It is not necessary that the frame samples contain exactly the same variables or that they are in the same order, although only variables present in all the samples can be used. It is important that factor variables existing across more than one frame sample have the same factor levels in all the samples.

All these estimators assume sampling is independent between frames, and that any observation sampled more than once is present in the dataset each time it is sampled.

Value

Object of class multiframe

References

Bankier, M. D. (1986) Estimators Based on Several Stratified Samples With Applications to Multiple Frame Surveys. Journal of the American Statistical Association, Vol. 81, 1074 - 1079.

Hartley, H. O. (1962) Multiple Frames Surveys. Proceedings of the American Statistical Association, Social Statistics Sections, 203 - 206. Hartley, H. O. (1974) Multiple frame methodology and selected applications. Sankhya C, Vol. 36, 99 - 118.

Kalton, G. and Anderson, D. W. (1986) Sampling Rare Populations. Journal of the Royal Statistical Society, Ser. A, Vol. 149, 65 - 82.

See also

svydesign, reweight

For a simple introduction: Metcalf P and Scott AJ (2009) Using multiple frames in health surveys. Stat Med 28:1512-1523

For general reference: Lohr SL, Rao JNK. Inference from dual frame surveys. Journal of the American Statistical Association 2000; 94:271-280.

Lohr SL, Rao JNK. Estimation in multiple frame surveys. Journal of the American Statistical Association 2006; 101:1019-1030.

Examples

data(phoneframes)
A_in_frames<-cbind(1, DatA$Domain=="ab")
B_in_frames<-cbind(DatB$Domain=="ba",1)

Bdes_pps<-svydesign(id=~1, fpc=~ProbB, data=DatB,pps=ppsmat(PiklB))
Ades_pps <-svydesign(id=~1, fpc=~ProbA,data=DatA,pps=ppsmat(PiklA))

## optimal constant (Hartley) weighting
mf_pps<-multiframe(list(Ades_pps,Bdes_pps),list(A_in_frames,B_in_frames),theta=0.74) 
svytotal(~Lei,mf_pps)
#>     total     SE
#> Lei 53251 1285.5
svymean(~Lei, mf_pps)
#>       mean    SE
#> Lei 22.488 0.365

svyby(~Lei, ~Size, svymean, design=mf_pps)
#>   Size      Lei        se
#> 1    1 17.24798 0.7854292
#> 2    2 20.00846 1.0267183
#> 3    3 22.83538 0.5414836
#> 4    4 26.09760 0.6669667
#> 5    5 29.27000 0.1872848
svytable(~Size+I(Lei>20), mf_pps,round=TRUE)
#>     I(Lei > 20)
#> Size FALSE TRUE
#>    1    38    9
#>    2   164  168
#>    3   138  401
#>    4    34  345
#>    5     0   26