rrreg.predictor is used to jointly model the randomized response item as both outcome and predictor for an additional outcome given a set of covariates.

rrreg.predictor(formula, p, p0, p1, q, design, data, rr.item,
model.outcome = "logistic", fit.sens = "bayesglm", fit.outcome = "bayesglm",
bstart = NULL, tstart = NULL, parstart = TRUE, maxIter = 10000, verbose =
FALSE, optim = FALSE, em.converge = 10^(-4), glmMaxIter = 20000, estconv =
TRUE, solve.tolerance = .Machine\$double.eps)

## Arguments

formula An object of class "formula": a symbolic description of the model to be fitted with the randomized response item as one of the covariates. 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). The probability of forced 'no' (Forced Response Design). The probability of forced 'yes' (Forced Response Design). The probability of answering 'yes' to the unrelated question, which is assumed to be independent of covariates (Unrelated Question Design). One of the four standard designs: "forced-known", "mirrored", "disguised", or "unrelated-known". A data frame containing the variables in the model. Observations with missingness are list-wise deleted. A string containing the name of the randomized response item variable in the data frame. Currently the function only allows for logistic regression, meaning the outcome variable must be binary. Indicator for whether to use Bayesian generalized linear modeling (bayesglm) in the Maximization step for the Expectation-Maximization (EM) algorithm to generate coefficients for the randomized response item as the outcome. Default is "bayesglm"; otherwise input "glm". Indicator for whether to use Bayesian generalized linear modeling (bayesglm) in the Maximization step for the EM algorithm to generate coefficients for the outcome variable given in the formula with the randomized response item as a covariate. Default is "bayesglm"; otherwise input "glm". Optional starting values of coefficient estimates for the randomized response item as outcome for the EM algorithm. Optional starting values of coefficient estimates for the outcome variable given in the formula for the EM algorithm. Option to use the function rrreg to generate starting values of coefficient estimates for the randomized response item as outcome for the EM algorithm. The default is TRUE, but if starting estimates are inputted by the user in bstart, this option is overidden. Maximum number of iterations for the Expectation-Maximization algorithm. The default is 10000. A logical value indicating whether model diagnostics counting the number of EM iterations are printed out. The default is FALSE. 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. A value specifying the satisfactory degree of convergence under the EM algorithm. The default is 10^(-4). A value specifying the maximum number of iterations to run the EM algorithm. The default is 20000 . Option to base convergence on the absolute value of the difference between subsequent coefficients generated through the EM algorithm rather than the subsequent log-likelihoods. The default is TRUE. When standard errors are calculated, this option specifies the tolerance of the matrix inversion operation solve.

## Value

rrreg.predictor returns an object of class "rrpredreg" associated with the randomized response item as predictor. The object rrpredreg 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.t

Point estimates for the effects of the randomized response item as predictor and other covariates on the separate outcome variable specified in the formula.

se.t

Standard errors for estimates of the effects of the randomized response item as predictor and other covariates on the separate outcome variable specified in formula.

est.b

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

vcov

Variance-covariance matrix for estimates of the effects of the randomized response item as predictor and other covariates on the separate outcome variable specified in formula as well as for estimates of the effects of covariates on the randomized response item.

se.b

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.

o

The separate outcome of interest 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.

## Details

This function allows users to perform multivariate regression analysis with the randomized response item as a predictor for a separate outcome of interest. It does so by jointly modeling the randomized response item as both outcome and predictor for an additional outcome given the same set of covariates. Four standard designs are accepted by this function: mirrored question, forced response, disguised response, and unrelated question.

## 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.

rrreg for multivariate regression.

## Examples


data(nigeria)

## Define design parameters

set.seed(44)

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 joint model of responses to an outcome regression of joining a civic
## group and the randomized response item of having a militant social connection# NOT RUN {
rr.q1.pred.obj <-
rrreg.predictor(civic ~ cov.asset.index + cov.married + I(cov.age/10) +
I((cov.age/10)^2) + cov.education + cov.female
+ rr.q1, rr.item = "rr.q1", parstart = FALSE, estconv = TRUE,
data = nigeria, verbose = FALSE, optim = TRUE,
p = p, p1 = p1, p0 = p0, design = "forced-known")

summary(rr.q1.pred.obj)
# }## Replicates Table 4 in Blair, Imai, and Zhou (2014)