Power Analysis for Randomized Response

power.rr.test is used to conduct power analysis for randomized response survey designs.

power.rr.test(p, p0, p1, q, design, n = NULL, r, presp, presp.null =
NULL, sig.level, prespT, prespC, prespT.null = NULL, prespC.null, power =
NULL, type = c("one.sample", "two.sample"), alternative = c("one.sided",
"two.sided"), solve.tolerance = .Machine$double.eps)

Arguments

p	The probability of receiving the sensitive question (Mirrored Question Design, Unrelated Question Design); the probability of answering truthfully (Forced Response Design); the probability of selecting a red card from the 'yes' stack (Disguised Response Design).
p0	The probability of forced 'no' (Forced Response Design).
p1	The probability of forced 'yes' (Forced Response Design).
q	The probability of answering 'yes' to the unrelated question, which is assumed to be independent of covariates (Unrelated Question Design).
design	Call of design (including modified designs) used: "forced-known", "mirrored", "disguised", "unrelated-known", "forced-unknown", and "unrelated-unknown".
n	Number of observations. Exactly one of 'n' or 'power' must be NULL.
r	For the modified designs only (i.e. "forced-unknown" for Forced Response with Unknown Probability and "unrelated-unknown" for Unrelated Question with Unknown Probability), r is the proportion of respondents allocated to the first group, which is the group that is directed to answer the sensitive question truthfully with probability p as opposed to the second group which is directed to answer the sensitive question truthfully with probability 1-p.
presp	For a one sample test, the probability of possessing the sensitive trait under the alternative hypothesis.
presp.null	For a one sample test, the probability of possessing the sensitive trait under the null hypothesis. The default is NULL meaning zero probability of possessing the sensitive trait.
sig.level	Significance level (Type I error probability).
prespT	For a two sample test, the probability of the treated group possessing the sensitive trait under the alternative hypothesis.
prespC	For a two sample test, the probability of the control group possessing the sensitive trait under the alternative hypothesis.
prespT.null	For a two sample test, the probability of the treated group possessing the sensitive trait under the null hypothesis. The default is NULL meaning there is no difference between the treated and control groups, specifically that prespT.null is the same as prespC.null, the probability of the control group possessing the sensitive trait under the null hypothesis.
prespC.null	For a two sample test, the probability of the control group possessing the sensitive trait under the null hypothesis.
power	Power of test (Type II error probability). Exactly one of 'n' or 'power' must be NULL.
type	One or two sample test. For a two sample test, the alternative and null hypotheses refer to the difference between the two samples of the probabilities of possessing the sensitive trait.
alternative	One or two sided test.
solve.tolerance	When standard errors are calculated, this option specifies the tolerance of the matrix inversion operation solve.

Value

power.rr.test contains the following components (the inclusion of some components such as the design parameters are dependent upon the design used):

n

Point estimates for the effects of covariates on the randomized response item.

r

Standard errors for estimates of the effects of covariates on the randomized response item.

presp

For a one sample test, the probability of possessing the sensitive trait under the alternative hypothesis. For a two sample test, the difference between the probabilities of possessing the sensitive trait for the treated and control groups under the alternative hypothesis.

presp.null

For a one sample test, the probability of possessing the sensitive trait under the null hypothesis. For a two sample test, the difference between the probabilities of possessing the sensitive trait for the treated and control groups under the null hypothesis.

sig.level

Significance level (Type I error probability).

power

Power of test (Type II error probability).

type

One or two sample test.

alternative

One or two sided test.

Details

This function allows users to conduct power analysis for randomized response survey designs, both for the standard designs ("forced-known", "mirrored", "disguised", "unrelated-known") and modified designs ("forced-unknown", and "unrelated -unknown").

References

Blair, Graeme, Kosuke Imai and Yang-Yang Zhou. (2015) "Design and Analysis of the Randomized Response Technique." Journal of the American Statistical Association. Available at http://graemeblair.com/papers/randresp.pdf.

Examples

## Calculate the power to detect a sensitive item proportion of .2
## with the forced design with known probabilities of 2/3 in truth-telling group,
## 1/6 forced to say "yes" and 1/6 forced to say "no" and sample size of 200.

power.rr.test(p = 2/3, p1 = 1/6, p0 = 1/6, n = 200,
             presp = .2, presp.null = 0,
             design = "forced-known", sig.level = .01,
             type = "one.sample", alternative = "one.sided")
#> $design
#> [1] "forced-known"
#> 
#> $n
#> [1] 200
#> 
#> $r
#> NULL
#> 
#> $presp
#> [1] 0.2
#> 
#> $presp.null
#> [1] 0
#> 
#> $sig.level
#> [1] 0.01
#> 
#> $power
#> [1] 0.9868872
#> 
#> $type
#> [1] "one.sample"
#> 
#> $alternative
#> [1] "one.sided"
#> 
				       
# NOT RUN {
## Find power varying the number of respondents from 250 to 2500 and 
## the population proportion of respondents possessing the sensitive 
## trait from 0 to .15

presp.seq <- seq(from = 0, to = .15, by = .0025)
n.seq <- c(250, 500, 1000, 2000, 2500)
power <- list()
for(n in n.seq) {
    power[[n]] <- rep(NA, length(presp.seq))
    for(i in 1:length(presp.seq))
        power[[n]][i] <- power.rr.test(p = 2/3, p1 = 1/6, p0 = 1/6, n = n,
                                       presp = presp.seq[i], presp.null = 0,
                                       design = "forced-known", sig.level = .01,
                                       type = "one.sample",
                                       alternative = "one.sided")$power
    }

## Replicates the results for Figure 2 in Blair, Imai, and Zhou (2014)
# }