# NRFUopt: Sample sizes for a nonresponse follow-up study In PracTools: Tools for Designing and Weighting Survey Samples

 NRFUopt R Documentation

## 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")

```

PracTools documentation built on Aug. 17, 2022, 5:06 p.m.