multiframe  R Documentation 
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 multiframe 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
multiframe(designs, overlaps, estimator = c("constant", "expected"), theta = NULL)
designs 
List of survey design objects 
overlaps 
list of matrices. Each matrix has K columns indicating whether the
observation is in frames 1K. For the 'constant'type estimator, this is
binary. For the 
estimator 

theta 
Scale factors adding to 1 for splitting the overlap between frames 
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.
Object of class multiframe
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.
svydesign
, reweight
For a simple introduction: Metcalf P and Scott AJ (2009) Using multiple frames in health surveys. Stat Med 28:15121523
For general reference: Lohr SL, Rao JNK. Inference from dual frame surveys. Journal of the American Statistical Association 2000; 94:271280.
Lohr SL, Rao JNK. Estimation in multiple frame surveys. Journal of the American Statistical Association 2006; 101:10191030.
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)
svymean(~Lei, mf_pps)
svyby(~Lei, ~Size, svymean, design=mf_pps)
svytable(~Size+I(Lei>20), mf_pps,round=TRUE)
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