NRFUopt {PracTools}

Sample sizes for a nonresponse follow-up study

Description

Compute optimal values of the first-phase sample size and the second-phase sampling fraction in a two-phase sample.

Usage

NRFUopt(Ctot=NULL, c1, c2, theta, CV0=NULL, CVpop=NULL, N=Inf, type.sw)

Arguments

Ctot

total variable cost

c1

cost per unit in phase-1

c2

cost per unit in phase-2

theta

probability of response for each unit

CV0

target coefficient of variation for the estimated total or mean

CVpop

Unit coefficient of variation

N

Population size; default is Inf

type.sw

type of allocation; "cost" = target total variable cost, "cv" = target coefficient of variation

Details

NRFUopt computes the optimal values of the first-phase sample size and the second-phase sampling fraction in a two-phase sample. Both stages are assumed to be selected using simple random sampling without replacement. If type.sw="cost", the optima are computed for a target total, expected cost across both phases. If type.sw="cv", the optima are computed for a target coefficient of variation for an estimated mean.

Value

List object with values:

allocation

type of allocation: either "fixed cost" or "fixed CV"

"Total variable cost"

expected total cost: fixed cost if type.sw="cost" or computed cost if type.sw="cv"; unrounded sample sizes are used in calculation

"Response rate"

first-phase response rate

CV

anticipated coefficient of variation (CV) if type.sw="cost" or target CV if type.sw="cv"

v.opt

optimal fraction of first-phase nonrespondents to select for second-phase follow-up

n1.opt

optimal number of units to sample at first-phase

"Expected n2"

expected number of respondents obtained at second-phase

"srs sample for same cv"

size of single-phase simple random sample (srs) needed to obtain same CV as the two-phase sample

"Cost Ratio: Two phase to srs"

ratio of expected cost for two-phase sample to cost of single-phase srs

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Saerndal, C.E., Swensson, B., and Wretman, J. (1992, examples 15.4.4 and 15.4.5). Model Assisted Survey Sampling. New York: Springer.

Valliant, R., Dever, J., Kreuter, F. (2018, chap.17). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

Examples

    # optima for fixed target CV
NRFUopt(Ctot=NULL, c1=50, c2=200, theta=0.5, CV0=0.05, CVpop=1, type.sw = "cv")
    # optima for fixed total cost
NRFUopt(Ctot=100000, c1=50, c2=200, theta=0.5, CV0=NULL, CVpop=1, type.sw = "cost")