Randomized Response Regression

Description

rrreg is used to conduct multivariate regression analyses of survey data using randomized response methods.

Usage

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rrreg(formula, p, p0, p1, q, design, data, start = NULL, 
h = NULL, group = NULL, matrixMethod = "efficient",
maxIter = 10000, verbose = FALSE, optim = FALSE, em.converge = 10^(-8), 
glmMaxIter = 10000, solve.tolerance = .Machine$double.eps)

Arguments

formula

An object of class "formula": a symbolic description of the model to be fitted.

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). For "mirrored" and "disguised" designs, p cannot equal .5.

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

One of the four standard designs: "forced-known", "mirrored", "disguised", or "unrelated-known".

data

A data frame containing the variables in the model.

start

Optional starting values of coefficient estimates for the Expectation-Maximization (EM) algorithm.

h

Auxiliary data functionality. Optional named numeric vector with length equal to number of groups. Names correspond to group labels and values correspond to auxiliary moments.

group

Auxiliary data functionality. Optional character vector of group labels with length equal to number of observations.

matrixMethod

Auxiliary data functionality. Procedure for estimating optimal weighting matrix for generalized method of moments. One of "efficient" for two-step feasible and "cue" for continuously updating. Default is "efficient". Only relevant if h and group are specified.

maxIter

Maximum number of iterations for the Expectation-Maximization algorithm. The default is 10000.

verbose

A logical value indicating whether model diagnostics counting the number of EM iterations are printed out. The default is FALSE.

optim

A logical value indicating whether to use the quasi-Newton "BFGS" method to calculate the variance-covariance matrix and standard errors. The default is FALSE.

em.converge

A value specifying the satisfactory degree of convergence under the EM algorithm. The default is 10^(-8).

glmMaxIter

A value specifying the maximum number of iterations to run the EM algorithm. The default is 10000.

solve.tolerance

When standard errors are calculated, this option specifies the tolerance of the matrix inversion operation solve.

Details

This function allows users to perform multivariate regression analysis on data from the randomized response technique. Four standard designs are accepted by this function: mirrored question, forced response, disguised response, and unrelated question. The method implemented by this function is the Maximum Likelihood (ML) estimation for the Expectation-Maximization (EM) algorithm.

Value

rrreg returns an object of class "rrreg". The function summary is used to obtain a table of the results. The object rrreg is a list that contains the following components (the inclusion of some components such as the design parameters are dependent upon the design used):

est

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

vcov

Variance-covariance matrix for the effects of covariates on the randomized response item.

se

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

data

The data argument.

coef.names

Variable names as defined in the data frame.

x

The model matrix of covariates.

y

The randomized response vector.

design

Call of standard design used: "forced-known", "mirrored", "disguised", or "unrelated-known".

p

The p argument.

p0

The p0 argument.

p1

The p1 argument.

q

The q argument.

call

The matched call.

References

Blair, Graeme, Kosuke Imai and Yang-Yang Zhou. (2014) "Design and Analysis of the Randomized Response Technique." Working Paper. Available at http://imai.princeton.edu/research/randresp.html.

See Also

predict.rrreg for predicted probabilities.

Examples

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data(nigeria)

set.seed(1)

## Define design parameters
p <- 2/3  # probability of answering honestly in Forced Response Design
p1 <- 1/6 # probability of forced 'yes'
p0 <- 1/6 # probability of forced 'no'

## Fit linear regression on the randomized response item of whether 
## citizen respondents had direct social contacts to armed groups

rr.q1.reg.obj <- rrreg(rr.q1 ~ cov.asset.index + cov.married + 
                    I(cov.age/10) + I((cov.age/10)^2) + cov.education + cov.female,   
                    data = nigeria, p = p, p1 = p1, p0 = p0, 
                    design = "forced-known")
  
summary(rr.q1.reg.obj)

## Replicates Table 3 in Blair, Imai, and Zhou (2014)