Package 'cWise' reference manual

Title:	Crosswise Models for Sensitive Survey Questions
Description:	Implements a bias-corrected crosswise estimator and its extensions for sensitive survey questions. The methods are described in Atsusaka and Stevenson (2023). "A bias-corrected estimator for the crosswise model with inattentive respondents" <doi:10.1017/pan.2021.43>.
Authors:	Yuki Atsusaka [aut, cre], Kolbe Dumas [aut]
Maintainer:	Yuki Atsusaka <[email protected]>
License:	GPL-3
Version:	0.1.0
Built:	2026-09-29 10:41:00 UTC
Source:	https://github.com/yukiatsusaka/cwise

bc_est

Description

bc_est is used to apply a bias-corrected crosswise estimator to survey data.

Usage

bc_est(Y, A, p, p.prime, weight, data, seed = NULL)

bc.est(...)
bc_est(Y, A, p, p.prime, weight, data, seed = NULL)

bc.est(...)

Arguments

Y

a vector of binary responses in the crosswise question (Y=1 if TRUE-TRUE or FALSE-FALSE, Y=0 otherwise).

A

a vector of binary responses in the anchor question (A=1 if TRUE-TRUE or FALSE-FALSE, A=0 otherwise).

p

an auxiliary probability for the crosswise question.

p.prime

an auxiliary probability for the anchor question.

weight

an optional vector specifying sample weights in data.

data

a data frame containing information from the crosswise model (Y, A, weight).

seed

Optional integer used to reproduce the bootstrap uncertainty estimate. When supplied, the caller's random-number state is restored after the function returns.

...

Arguments passed to bc_est().

Value

A list with:

Results: A two-row matrix of naive and bias-corrected prevalence estimates, standard errors, and 95 percent confidence intervals.
Stats: A matrix containing the estimated attentive-response rate and the number of complete observations.

References

Atsusaka, Y. and Stevenson, R. T. (2023). The crosswise model for sensitive survey questions. doi:10.1017/pan.2021.43.

Examples

bc_est(Y=Y, A=A, p=0.15, p.prime=0.15, data=cmdata)
bc_est(Y=Y, A=A, weight=weight, p=0.15, p.prime=0.15, data=cmdata)
bc_est(Y=Y, A=A, p=0.15, p.prime=0.15, data=cmdata)
bc_est(Y=Y, A=A, weight=weight, p=0.15, p.prime=0.15, data=cmdata)

cmBound is used to apply a sensitivity analysis and visualize the sensitivity bounds for naive crosswise estimates. The sensitivity analysis assumes that inattentive respondents choose either response option with equal probability.

Usage

cmBound(lambda.hat, p, N, dq = NULL, N.dq = NULL)
cmBound(lambda.hat, p, N, dq = NULL, N.dq = NULL)

Arguments

lambda.hat

a value for the observed crosswise proportion: Prop(TRUE-TRUE or FALSE-FALSE).

p

an auxiliary probability for the crosswise question. It must be a single finite value strictly between 0 and 1, excluding 0.5.

N

a value for the number of survey respondents in the crosswise (and anchor) question.

dq

a value for a point estimate from direct questioning (if available).

N.dq

a value for the number of survey respondents in direct questioning (if available).

Value

A ggplot object visualizing the result of sensitivity analysis.

References

Atsusaka, Y. and Stevenson, R. T. (2023). The crosswise model for sensitive survey questions. doi:10.1017/pan.2021.43.

Examples

p <- cmBound(lambda.hat=0.6385, p=0.25, N=310, dq=0.073, N.dq=310)
p

p <- p + ggplot2::ggtitle("Sensitivity Analysis") +
         ggplot2::theme(plot.title = ggplot2::element_text(size=20, face="bold"))
p <- cmBound(lambda.hat=0.6385, p=0.25, N=310, dq=0.073, N.dq=310)
p

p <- p + ggplot2::ggtitle("Sensitivity Analysis") +
         ggplot2::theme(plot.title = ggplot2::element_text(size=20, face="bold"))

Simulated Crosswise Survey Data I

Description

Typical, artificially generated toy data set that comes with the binary response in the crosswise question (Y=1 if TRUE-TRUE or FALSE-FALSE, Y=0 otherwise), the binary response in the anchor question, sample weights, and auxiliary probabilities in the crosswise and anchor questions, respectively (these columns are only included here for an illustrative purpose).

Usage

data(cmdata)
data(cmdata)

Format

an object of class "data.frame"

Y: a binary indicator for the crosswise item (TRUE-TRUE or FALSE-FALSE) in the crosswise question
A: a binary indicator for the crosswise item (TRUE-TRUE or FALSE-FALSE) in the anchor question
p: an auxiliary probability in the crosswise question
p.prime: an auxiliary probability in the anchor question

References

This data set was artificially created for the cWise package.

Examples


data(cmdata)
head(cmdata)

data(cmdata)
head(cmdata)

Simulated Crosswise Survey Data II

Description

Typical, artificially generated toy data set that comes with the binary response in the crosswise question (Y=1 if TRUE-TRUE or FALSE-FALSE, Y=0 otherwise), the binary response in the anchor question, two covariates, and auxiliary probabilities in the crosswise and anchor questions, respectively (these columns are only included here for an illustrative purpose).

Usage

data(cmdata2)
data(cmdata2)

Format

an object of class "data.frame"

Y: a binary indicator for the crosswise item (TRUE-TRUE or FALSE-FALSE) in the crosswise question
female: A binary covariate representing being a female
age: A discrete covariate representing age
A: a binary indicator for the crosswise item (TRUE-TRUE or FALSE-FALSE) in the anchor question
p: an auxiliary probability in the crosswise question
p.prime: an auxiliary probability in the anchor question

References

This data set was artificially created for the cWise package.

Examples


data(cmdata2)
head(cmdata2)

data(cmdata2)
head(cmdata2)

Simulated Crosswise Survey Data III

Description

Typical, artificially generated toy data set that comes with the binary response in the crosswise question (Y=1 if TRUE-TRUE or FALSE-FALSE, Y=0 otherwise), the binary response in the anchor question, the outcome variable, two covariates, and auxiliary probabilities in the crosswise and anchor questions, respectively (these columns are only included here for an illustrative purpose).

Usage

data(cmdata3)
data(cmdata3)

Format

an object of class "data.frame"

V: an outcome variable
female: A binary covariate representing being a female
age: A discrete covariate representing age
Y: a binary indicator for the crosswise item (TRUE-TRUE or FALSE-FALSE) in the crosswise question
A: a binary indicator for the crosswise item (TRUE-TRUE or FALSE-FALSE) in the anchor question
p: an auxiliary probability in the crosswise question
p.prime: an auxiliary probability in the anchor question

References

This data set was artificially created for the cWise package.

Examples


data(cmdata3)
head(cmdata3)

data(cmdata3)
head(cmdata3)

cmpredict

Description

Perform a post-estimation prediction with uncertainty quantification via parametric bootstrap

Usage

cmpredict(
  out,
  newdata = NULL,
  zval = NULL,
  typical = NULL,
  nsim = 1000L,
  seed = NULL,
  draws = FALSE
)
cmpredict(
  out,
  newdata = NULL,
  zval = NULL,
  typical = NULL,
  nsim = 1000L,
  seed = NULL,
  draws = FALSE
)

Arguments

out

An output of cmreg.

newdata

A named data frame, list, or vector supplying values for every covariate in the fitted formula. A data frame returns one prediction row per row of 'newdata'.

zval

Optional named vector for one covariate to vary. Its name must match a formula variable; all remaining covariates are supplied through 'newdata' or 'typical'.

typical

Optional named vector or list of fixed covariate values. This is a convenience alternative to 'newdata' when used with 'zval'.

nsim

Number of parametric-bootstrap draws.

seed

Optional integer seed for reproducible bootstrap draws. When set, the caller's RNG state is restored before returning.

draws

If 'TRUE', attach the raw bootstrap draw matrix as a '"draws"' attribute on the returned data frame.

Value

A data frame with 'estimate', 'conf.low', and 'conf.high' columns, with one row for each prediction scenario. When 'draws = TRUE', its '"draws"' attribute contains the raw parametric-bootstrap matrix.

References

Atsusaka, Y. and Stevenson, R. T. (2023). The crosswise model for sensitive survey questions. doi:10.1017/pan.2021.43.

Examples

m <- cmreg(Y ~ female + age, anchor = A, p = 0.1, p.prime = 0.15,
           data = cmdata2)
predictions <- cmpredict(m, typical = c(age = 30),
                          zval = c(female = 0, female = 1))
predictions
m <- cmreg(Y ~ female + age, anchor = A, p = 0.1, p.prime = 0.15,
           data = cmdata2)
predictions <- cmpredict(m, typical = c(age = 30),
                          zval = c(female = 0, female = 1))
predictions

cmpredict_p

Description

Perform a post-estimation prediction with uncertainty quantification via parametric bootstrap

Usage

cmpredict_p(
  out,
  newdata = NULL,
  zval = NULL,
  typical = NULL,
  type = c("response", "link"),
  nsim = 1000L,
  seed = NULL,
  draws = FALSE
)

cmpredict.p(...)
cmpredict_p(
  out,
  newdata = NULL,
  zval = NULL,
  typical = NULL,
  type = c("response", "link"),
  nsim = 1000L,
  seed = NULL,
  draws = FALSE
)

cmpredict.p(...)

Arguments

out

An output of cmreg_p.

newdata

A named data frame, list, or vector supplying values for every covariate in the fitted formula. A data frame returns absent/present latent- trait scenarios for every row.

zval

Optional named vector for one covariate to vary. Its name must match a formula variable; all remaining covariates are supplied through 'newdata' or 'typical'.

typical

Optional named vector or list of fixed covariate values. This is a convenience alternative to 'newdata' when used with 'zval'.

type

Prediction scale: '"response"' (default) or '"link"'. The Gaussian outcome model has an identity link, so these are currently equal.

nsim

Number of parametric-bootstrap draws.

seed

Optional integer seed for reproducible bootstrap draws. When set, the caller's RNG state is restored before returning.

draws

If 'TRUE', attach the raw bootstrap draw matrix as a '"draws"' attribute on the returned data frame.

...

Arguments passed to cmpredict_p().

Value

A data frame with 'estimate', 'conf.low', and 'conf.high' columns. Each input scenario contributes an absent-trait row followed by a present- trait row. When 'draws = TRUE', its '"draws"' attribute contains the raw parametric-bootstrap matrix.

References

Atsusaka, Y. and Stevenson, R. T. (2023). The crosswise model for sensitive survey questions. doi:10.1017/pan.2021.43.

Examples

# Keep the fitted example small: this likelihood is deliberately
# computationally intensive and package examples run during CRAN checks.
example_data <- cmdata3[seq_len(30L), ]
m2 <- cmreg_p(V ~ age + female, crosswise = Y, anchor = A, p = 0.1,
              p.prime = 0.15, data = example_data, n.start = 1L)
predictions <- cmpredict_p(
  m2, newdata = data.frame(age = 30, female = 1), nsim = 20L, seed = 1L
)
predictions
# Keep the fitted example small: this likelihood is deliberately
# computationally intensive and package examples run during CRAN checks.
example_data <- cmdata3[seq_len(30L), ]
m2 <- cmreg_p(V ~ age + female, crosswise = Y, anchor = A, p = 0.1,
              p.prime = 0.15, data = example_data, n.start = 1L)
predictions <- cmpredict_p(
  m2, newdata = data.frame(age = 30, female = 1), nsim = 20L, seed = 1L
)
predictions

cmreg

Description

cmreg is used to run a regression with the latent sensitive trait as an outcome.

Usage

cmreg(
  formula,
  anchor,
  p,
  p.prime,
  data,
  start = NULL,
  n.start = 3L,
  control = list()
)
cmreg(
  formula,
  anchor,
  p,
  p.prime,
  data,
  start = NULL,
  n.start = 3L,
  control = list()
)

Arguments

formula

an object of class "formula": a symbolic description of the model to be fitted. Ex. Crosswise response ~ Covariates. The anchor response is supplied separately through 'anchor'.

anchor

Unquoted column name (or a single character column name) for the anchor response.

p

an auxiliary probability for the crosswise question.

p.prime

an auxiliary probability for the anchor question.

data

a data frame containing information from the crosswise model and covariates.

start

Optional numeric vector of starting values for the beta and theta parameters. By default, starts are derived from binomial GLMs for the observed crosswise and anchor responses.

n.start

Number of optimization starts, including the data-informed start.

control

A list of control settings passed to [stats::optim()]. 'fnscale' is fixed internally because the log-likelihood is maximized.

Value

An object of class 'cmreg', a list with:

Call: The matched model call.
Coefficients: A coefficient table for the latent-trait outcome model.
AuxiliaryCoef: A coefficient table for the anchor-response model.
VCV: The estimated variance-covariance matrix of all parameters.
estimates, std.errors: Named full-precision parameter estimates and standard errors.
logLik, n, convergence: The optimized log-likelihood, number of complete observations, and optimizer convergence code.

References

Atsusaka, Y. and Stevenson, R. T. (2023). The crosswise model for sensitive survey questions. doi:10.1017/pan.2021.43.

Examples

m <- cmreg(Y ~ female + age, anchor = A, p = 0.1, p.prime = 0.15,
           data = cmdata2)
m
m <- cmreg(Y ~ female + age, anchor = A, p = 0.1, p.prime = 0.15,
           data = cmdata2)
m

cmreg_p

Description

cmreg is used to run a regression with the latent sensitive trait as a predictor.

Usage

cmreg_p(
  formula,
  crosswise,
  anchor,
  p,
  p.prime,
  data,
  start = NULL,
  n.start = 3L,
  control = list()
)

cmreg.p(...)
cmreg_p(
  formula,
  crosswise,
  anchor,
  p,
  p.prime,
  data,
  start = NULL,
  n.start = 3L,
  control = list()
)

cmreg.p(...)

Arguments

formula

an object of class "formula": a symbolic description of the model to be fitted. Ex. Outcome ~ Covariates. The crosswise and anchor responses are supplied separately through 'crosswise' and 'anchor'.

crosswise

Unquoted column name (or a single character column name) for the crosswise response.

anchor

Unquoted column name (or a single character column name) for the anchor response.

p

an auxiliary probability for the crosswise question.

p.prime

an auxiliary probability for the anchor question.

data

a data frame containing information from the crosswise model, the outcome variable, and covariates.

start

Optional numeric vector of starting values on the reporting scale: beta, theta, gamma, crosswise effect, and a positive sigma. By default, starts are derived from GLM and least-squares fits to observed responses.

n.start

Number of optimization starts, including the data-informed start.

control

A list of control settings passed to [stats::optim()]. 'fnscale' is fixed internally because the log-likelihood is maximized.

...

Arguments passed to cmreg_p().

Value

An object of class 'cmreg_p' (and 'cmreg'), a list with:

Call: The matched model call.
Coefficients: A coefficient table for the Gaussian outcome model, including the latent-trait effect.
AuxiliaryCoef, AuxiliaryCoef2: Coefficient tables for the crosswise and anchor-response models, with the residual standard deviation.
VCV: The estimated variance-covariance matrix of all parameters.
estimates, std.errors: Named full-precision parameter estimates and standard errors.
logLik, n, convergence: The optimized log-likelihood, number of complete observations, and optimizer convergence code.

References

Atsusaka, Y. and Stevenson, R. T. (2023). The crosswise model for sensitive survey questions. doi:10.1017/pan.2021.43.

Examples

# Keep the fitted example small: this likelihood is deliberately
# computationally intensive and package examples run during CRAN checks.
example_data <- cmdata3[seq_len(30L), ]
m2 <- cmreg_p(V ~ age + female, crosswise = Y, anchor = A, p = 0.1,
              p.prime = 0.15, data = example_data, n.start = 1L)
m2
# Keep the fitted example small: this likelihood is deliberately
# computationally intensive and package examples run during CRAN checks.
example_data <- cmdata3[seq_len(30L), ]
m2 <- cmreg_p(V ~ age + female, crosswise = Y, anchor = A, p = 0.1,
              p.prime = 0.15, data = example_data, n.start = 1L)
m2

Print and summarise crosswise regression fits

Description

Print and summarise crosswise regression fits

Usage

## S3 method for class 'cmreg'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'cmreg'
summary(object, ...)

## S3 method for class 'summary.cmreg'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'cmreg'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'cmreg'
summary(object, ...)

## S3 method for class 'summary.cmreg'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

A 'cmreg' or 'cmreg_p' fit object.

digits

Number of significant digits to display.

...

Additional arguments, currently ignored.

object

A 'cmreg' or 'cmreg_p' fit object.

Value

'summary.cmreg()' returns a list containing the fit call, coefficient tables, log-likelihood, sample size, convergence code, and model type.

Simulate Survey Data and Compute Bias-Corrected Estimates

Description

Core simulation function that generates crosswise model data with inattentive respondents and computes bias-corrected prevalence estimates with bootstrap confidence intervals. This implements the methodology described in Appendix C5 for power analysis of the crosswise model.

Usage

sim_cwdata(
  N.sim = 500,
  sample,
  prevalence,
  p,
  p.prime,
  gamma,
  direct,
  verbose = TRUE
)

sim.cwdata(...)
sim_cwdata(
  N.sim = 500,
  sample,
  prevalence,
  p,
  p.prime,
  gamma,
  direct,
  verbose = TRUE
)

sim.cwdata(...)

Arguments

N.sim

Integer. Number of Monte Carlo simulations to run. Default is 500.

sample

Integer. Sample size per simulation (number of respondents).

prevalence

Numeric. True prevalence rate of the sensitive attribute (between 0 and 1).

p

Numeric. Probability for the randomization item in sensitive question (between 0 and 1).

p.prime

Numeric. Probability for the anchor question (non-sensitive, between 0 and 1).

gamma

Numeric. Proportion of attentive respondents (between 0 and 1).

direct

Numeric. Direct questioning estimate for comparison purposes (between 0 and 1).

verbose

Logical. If 'TRUE' (the default), display a progress bar while simulations run.

...

Arguments passed to sim_cwdata().

Details

The function implements the crosswise model with bias correction for inattentive respondents. For each simulation:

Generates attentive/inattentive status based on gamma
Simulates responses to sensitive question (crosswise format)
Simulates responses to anchor question (for estimating attention rate)
Computes naive crosswise estimate
Applies bias correction based on estimated inattention
Uses bootstrap (500 iterations) to compute 95% confidence intervals

The bias correction formula is:

$\hat{\pi}_{BC} = \hat{\pi}_{naive} - \hat{Bias}$

where the bias is estimated using the anchor question responses.

Value

A list containing:

Results: Named vector with summary statistics including average bias, RMSE, and coverage rates for both naive and bias-corrected estimators
BiasCorrectEst: Numeric vector of bias-corrected point estimates (sorted)
BiasCorrectLow: Numeric vector of lower bounds of 95% bootstrap CIs (sorted)
BiasCorrectHigh: Numeric vector of upper bounds of 95% bootstrap CIs (sorted)
EstimatedBias: Numeric vector of estimated bias values for each simulation
RelativeLengthCI: Numeric vector of relative CI lengths (bias-corrected vs naive)

References

Atsusaka and Stevenson (2023). Appendix C5: Sample Size Determination and Parameter Selection. doi:10.1017/pan.2021.43.

Examples


# Basic usage
result <- sim_cwdata(
  N.sim = 100,
  sample = 500,
  prevalence = 0.1,
  p = 0.1,
  p.prime = 0.1,
  gamma = 0.8,
  direct = 0.05
)
print(result$Results)


# Basic usage
result <- sim_cwdata(
  N.sim = 100,
  sample = 500,
  prevalence = 0.1,
  p = 0.1,
  p.prime = 0.1,
  gamma = 0.8,
  direct = 0.05
)
print(result$Results)

Simulate and Plot Panel C of Figure C7

Description

Runs Monte Carlo simulations using the bias-corrected crosswise model and creates a caterpillar plot showing sorted point estimates with bootstrap confidence intervals, replicating Panel C of Figure C7 in Atsusaka and Stevenson (2023).

Usage

sim_estimates(
  N.sim = 100,
  sample,
  prevalence,
  p,
  p.prime,
  gamma,
  direct,
  txcol = "dimgray",
  sim.results = NULL,
  verbose = TRUE
)

sim.estimates(...)
sim_estimates(
  N.sim = 100,
  sample,
  prevalence,
  p,
  p.prime,
  gamma,
  direct,
  txcol = "dimgray",
  sim.results = NULL,
  verbose = TRUE
)

sim.estimates(...)

Arguments

N.sim

Integer. Number of Monte Carlo simulations. Default is 100.

sample

Integer. Sample size per simulation.

prevalence

Numeric. True prevalence rate of the sensitive attribute.

p

Numeric. Randomization probability for the sensitive question.

p.prime

Numeric. Randomization probability for the anchor question.

gamma

Numeric. Proportion of attentive respondents (between 0 and 1).

direct

Numeric. Direct questioning estimate for comparison.

txcol

Character. Color for annotation text. Default: "dimgray".

sim.results

Optional list. Pre-computed output from sim_cwdata. If NULL (default), the simulation is run internally.

verbose

Logical. Passed to sim_cwdata() when a new simulation is needed. If TRUE (the default), a progress bar is displayed.

...

Arguments passed to sim_estimates().

Details

The plot displays:

Sorted bias-corrected point estimates as filled circles
Bootstrap 95% confidence intervals as vertical line segments
A horizontal reference line at 0
A horizontal reference line at the true prevalence prevalence (red)

Estimates are sorted in ascending order, creating a characteristic "fan" shape that reveals the distribution of estimates across simulations.

Text annotation positions are calibrated to N.sim = 100 and scale proportionally for other values.

If sim.results is supplied, all simulation parameters (N.sim, sample, p, p.prime, gamma, direct) are still used for the annotations, but no new simulation is run.

Value

Invisibly returns the simulation results list from sim_cwdata, containing BiasCorrectEst, BiasCorrectLow, BiasCorrectHigh, and summary Results.

References

Atsusaka and Stevenson (2023). Figure C7, Panel C. doi:10.1017/pan.2021.43.

Examples


# Replicate Panel C of Figure C7
sim_estimates(
  N.sim   = 100,
  sample  = 1000,
  prevalence = 0.1,
  p       = 0.1,
  p.prime = 0.1,
  gamma   = 0.8,
  direct  = 0.1
)

# Re-use pre-computed simulation results
res <- sim_cwdata(N.sim = 100, sample = 1000, prevalence = 0.1,
                  p = 0.1, p.prime = 0.1, gamma = 0.8, direct = 0.1)
sim_estimates(sample = 1000, prevalence = 0.1, p = 0.1, p.prime = 0.1,
              gamma = 0.8, direct = 0.1, sim.results = res)


# Replicate Panel C of Figure C7
sim_estimates(
  N.sim   = 100,
  sample  = 1000,
  prevalence = 0.1,
  p       = 0.1,
  p.prime = 0.1,
  gamma   = 0.8,
  direct  = 0.1
)

# Re-use pre-computed simulation results
res <- sim_cwdata(N.sim = 100, sample = 1000, prevalence = 0.1,
                  p = 0.1, p.prime = 0.1, gamma = 0.8, direct = 0.1)
sim_estimates(sample = 1000, prevalence = 0.1, p = 0.1, p.prime = 0.1,
              gamma = 0.8, direct = 0.1, sim.results = res)

Compute Statistical Power for a Fixed Sample Size

Description

Computes statistical power for a one-sided hypothesis test of H0: pi <= pi0 versus H1: pi > pi0 at a given fixed sample size. This is useful when researchers already know their sample size and want to assess the power they can expect from their study.

Usage

sim_power(
  N.sim,
  sample,
  pi.null,
  pi.alt,
  p,
  p.prime,
  gamma,
  direct,
  verbose = TRUE
)

sim.power(...)
sim_power(
  N.sim,
  sample,
  pi.null,
  pi.alt,
  p,
  p.prime,
  gamma,
  direct,
  verbose = TRUE
)

sim.power(...)

Arguments

N.sim

Integer. Number of Monte Carlo simulations. Larger values provide more stable power estimates but increase computation time.

sample

Integer. The fixed sample size (number of respondents) to evaluate.

pi.null

Numeric. Prevalence rate under the null hypothesis (pi0). Can be 0 or a value from direct questioning.

pi.alt

Numeric. True prevalence rate under the alternative hypothesis (pi1). Must be greater than pi.null.

p

Numeric. Probability for the randomization item in the sensitive question. Values between 0.1 and 0.3 are typical.

p.prime

Numeric. Probability for the anchor question (non-sensitive).

gamma

Numeric. Proportion of attentive respondents (between 0 and 1). For example, 0.8 means 80% of respondents are attentive.

direct

Numeric. Direct questioning estimate for comparison purposes.

verbose

Logical. If TRUE (the default), report progress messages and show progress bars for the two underlying simulations.

...

Arguments passed to sim_power().

Details

The function implements the power calculation based on the Wald test:

$Power = \Phi\left(\frac{\pi_1 - \pi_0 + z_\alpha \tilde{\sigma}_0}{\tilde{\sigma}_1}\right)$

where:

$\Phi$ is the cumulative distribution function of the standard normal
$z_\alpha$ is derived from the simulated null distribution
$\tilde{\sigma}_0$ and $\tilde{\sigma}_1$ are simulated standard errors under H0 and H1 respectively

The function runs sim_cwdata() twice: once under H0 using pi.null and once under H1 using pi.alt, to estimate the sampling distributions at the specified sample size.

Value

A numeric scalar representing the estimated statistical power (probability of correctly rejecting H0 when H1 is true) at the given sample size.

Note

This function can take considerable time to run depending on N.sim and sample size. For quick exploration, use smaller N.sim values (for example, 100 to 500). For publication-quality results, use N.sim >= 2000.

References

Atsusaka and Stevenson (2023). Appendix C5: Sample Size Determination and Parameter Selection. doi:10.1017/pan.2021.43.

Examples

# Compute power at a fixed sample size of 1000

pwr <- sim_power(
  N.sim  = 500,
  sample = 1000,
  pi.null = 0,
  pi.alt  = 0.1,
  p       = 0.1,
  p.prime = 0.1,
  gamma   = 0.8,
  direct  = 0.02
)
cat(sprintf("Estimated power: %.3f\n", pwr))


# Compute power at a fixed sample size of 1000

pwr <- sim_power(
  N.sim  = 500,
  sample = 1000,
  pi.null = 0,
  pi.alt  = 0.1,
  p       = 0.1,
  p.prime = 0.1,
  gamma   = 0.8,
  direct  = 0.02
)
cat(sprintf("Estimated power: %.3f\n", pwr))

Determine Sample Size for Desired Coverage Properties

Description

Tests multiple sample sizes to determine which achieves desired confidence interval coverage properties. Specifically, it calculates what percentage of 95% confidence intervals (1) exclude zero and (2) include the direct estimate. This helps researchers choose a sample size that provides sufficient precision.

Usage

sim_power_N(N.sim = 50, prevalence, p, p.prime, gamma, direct, verbose = TRUE)

sim.power.N(...)
sim_power_N(N.sim = 50, prevalence, p, p.prime, gamma, direct, verbose = TRUE)

sim.power.N(...)

Arguments

N.sim

Integer. Number of Monte Carlo simulations per sample size. Default is 50. Larger values provide more stable estimates but increase computation time.

prevalence

Numeric. True prevalence rate of the sensitive attribute (between 0 and 1).

p

Numeric. Probability for the randomization item in sensitive question.

p.prime

Numeric. Probability for the anchor question (non-sensitive).

gamma

Numeric. Proportion of attentive respondents (between 0 and 1).

direct

Numeric. Direct questioning estimate for comparison purposes.

verbose

Logical. If TRUE (the default), display a progress bar while sample sizes are evaluated.

...

Arguments passed to sim_power_N().

Details

This function is useful for planning studies where researchers want to:

Distinguish the estimated prevalence from zero with high confidence
Obtain narrow confidence intervals for precise estimation
Compare crosswise estimates with direct questioning estimates

For each sample size, the function:

Simulates N.sim datasets using the crosswise model
Computes bias-corrected estimates with bootstrap 95% CIs
Calculates what percentage of CIs contain zero
Calculates what percentage of CIs contain the direct estimate

A progress bar displays simulation progress.

Value

A data frame with three columns:

SampleSize: Sample sizes tested: 100, 500, 1000, 1500, 2000, 2500, 3000
CoverageZero: Percentage of 95% CIs that include zero. Lower values indicate better precision (CIs exclude zero).
CoverageDirect: Percentage of 95% CIs that include the direct estimate. Values near 95% suggest good agreement with direct questioning.

Note

Low CoverageZero values indicate CIs that reliably exclude zero (good for establishing that prevalence is non-zero)
CoverageDirect near 95% suggests consistency between crosswise and direct questioning approaches
This function uses 500 bootstrap iterations per simulation

References

Atsusaka and Stevenson (2023). Appendix C5: Sample Size Determination and Parameter Selection. doi:10.1017/pan.2021.43.

Examples

# Find sample size needed to reliably exclude zero

result <- sim_power_N(
  N.sim = 50,
  prevalence = 0.1,
  p = 0.1,
  p.prime = 0.1,
  gamma = 0.8,
  direct = 0.05
)

print(result)

# Visualize results
plot(result$SampleSize, result$CoverageZero,
     type = "b", xlab = "Sample Size",
     ylab = "% of CIs Including Zero",
     main = "Precision vs Sample Size")


# Find sample size needed to reliably exclude zero

result <- sim_power_N(
  N.sim = 50,
  prevalence = 0.1,
  p = 0.1,
  p.prime = 0.1,
  gamma = 0.8,
  direct = 0.05
)

print(result)

# Visualize results
plot(result$SampleSize, result$CoverageZero,
     type = "b", xlab = "Sample Size",
     ylab = "% of CIs Including Zero",
     main = "Precision vs Sample Size")

Package 'cWise'

Help Index

bc_est

Description

Usage

Arguments

Value

References

See Also

Examples

cmBound

Description

Usage

Arguments

Value

References

See Also

Examples

Simulated Crosswise Survey Data I

Description

Usage

Format

References

Examples

Simulated Crosswise Survey Data II

Description

Usage

Format

References

Examples

Simulated Crosswise Survey Data III

Description

Usage

Format

References

Examples

cmpredict

Description

Usage

Arguments

Value

References

See Also

Examples

cmpredict_p

Description

Usage

Arguments

Value

References

See Also

Examples

cmreg

Description

Usage

Arguments

Value

References

See Also

Examples

cmreg_p

Description

Usage

Arguments

Value

References

See Also

Examples

Print and summarise crosswise regression fits

Description

Usage

Arguments

Value

Simulate Survey Data and Compute Bias-Corrected Estimates

Description

Usage

Arguments

Details

Value

References