Relvariance components for 3-stage sample

Description

Compute components of relvariance for a sample design where primary sampling units (PSUs) are selected with ppswr and secondary sampling units (SSUs) and elements within SSUs are selected via srs. The input is an entire sampling frame.

Usage

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BW3stagePPS(X, pp, psuID, ssuID)

Arguments

X

data vector; length is the number of elements in the population.

pp

vector of one-draw probabilities for the PSUs; length is number of PSUs in population.

psuID

vector of PSU identification numbers. This vector must be as long as X. Each element in a given PSU should have the same value in psuID. PSUs must be in the same order as in X.

ssuID

vector of SSU identification numbers. This vector must be as long as X. Each element in a given SSU should have the same value in ssuID. PSUs and SSUs must be in the same order as in X. ssuID should have the form psuID||(ssuID within PSU)

.

Details

BW3stagePPS computes the between and within population relvariance components appropriate for a three-stage sample in which PSUs are selected with varying probabilities and with replacement. SSUs and elements within SSUs are selected by simple random sampling. The components are appropriate for approximating the relvariance of the pwr-estimator of a total when the same number of SSUs are selected within each PSU, and the same number of elements are selected within each sample SSU. The function requires that an entire sampling frame of PSUs and elements be input. (Use BW2stagePPSe if only a sample of PSUs, SSUs, and elements is available.)

Value

List with values:

B

between PSU unit relvariance

W

within PSU unit relvariance computed as if the sample were two-stage

W2

unit relvariance among SSU totals

W3

unit relvariance among elements within PSU/SSUs

unit relvar

unit relvariance for population

k1

ratio of B^2 + W^2 to unit relvariance

k2

ratio of W_{2}^2 + W_{3}^2 to unit relvariance

delta1

homogeneity measure among elements within PSUs estimated as B^2/(B^2+W^2)

delta2

homogeneity measure among elements within SSUs estimated as W_{2}^2/(W_{2}^2 + W_{3}^2)

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Hansen,M.H., Hurwitz,W.N., and Madow,W.G. (1953, chap. 9, p.211). Sample Survey Methods and Theory, Vol.I. John Wiley & Sons.

Saerndal, C.E., Swensson, B., and Wretman, J. (1992, p.149). Model Assisted Survey Sampling. Springer.

Valliant, R., Dever, J., Kreuter, F. (2013, sect. 9.2.4). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

See Also

BW2stagePPS, BW2stagePPSe, BW2stageSRS, BW3stagePPSe

Examples

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data(MDarea.pop)
MDsub <- MDarea.pop[1:100000,]
M <- length(unique(MDsub$PSU))
    # srs/srs/srs design
pp.PSU <- rep(1/M,M)
BW3stagePPS(X=MDsub$y1, pp=pp.PSU, psuID=MDsub$PSU, ssuID=MDsub$SSU)
    # ppswr/srs/srs design
pp.PSU <- table(MDsub$PSU) / nrow(MDsub)
BW3stagePPS(X=MDsub$y1, pp=pp.PSU, psuID=MDsub$PSU, ssuID=MDsub$SSU)

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