inst/doc/misreport-vignette.R

In misreport: Statistical Analysis of Misreporting on Sensitive Survey Questions

params <-
structure(list(EVAL = TRUE), .Names = "EVAL")

## ----set-options, include = 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options(width = 10000)
knitr::opts_chunk$set(comment = "")
set.seed(121)

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n <- 10000
A <- data.frame(i = 1:n)

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A$age <- round(runif(n, 18, 90))
A$gender <- sample(c("Woman", "Man"), n, replace = TRUE, prob = c(0.52, 0.48))
A$education <- sample(c("Below high school",
                        "High school",
                        "College"),
                      n, replace = TRUE, prob = c(0.25, 0.35, 0.4))
A$education <- factor(A$education, levels = c("Below high school",
                                              "High school",
                                              "College"))

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# Display first 10 rows of the data
print(A[1:10, ], row.names = FALSE)

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A$treatment <- sample(c(rep(0, n/2), rep(1, n/2)), n)

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param_sensitive <- c("Intercept" = -0.5,
                     "gender (Woman)" = 0.25,
                     "age" = 0.01,
                     "education (High school)" = -0.3,
                     "education (College)" = -0.5)

lin_pred <- cbind(1,
                  A$gender == "Woman",
                  A$age,
                  A$education == "High school",
                  A$education == "College") %*% param_sensitive

# Simulate whether respondents hold sensitive belief
A$true_belief <- rbinom(n, 1, prob = plogis(lin_pred))

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prop.table(table(A$true_belief))

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param_misreport <- c("Intercept" = -0.5,
                     "gender (Woman)" = -0.3,
                     "age" = -0.01,
                     "education (High school)" = 0.3,
                     "education (College)" = 0.5,
                     "treatment" = 0)

lin_pred <- cbind(1,
                  A$gender == "Woman",
                  A$age,
                  A$education == "High school",
                  A$education == "College",
                  A$treatment) %*% param_misreport

A$misreport <- rbinom(n, 1, prob = plogis(lin_pred))

# By the monotonicity assumption, only those who hold the sensitive belief misreport it. Therefore, if true_belief = 0, then a respondent does not misreport.
A$misreport[A$true_belief == 0] <- 0

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J <- 4

param_control <- c("Intercept" = -0.25,
                   "gender (female)" = 0.25,
                   "age" = 0.01,
                   "education (high school)" = -0.25,
                   "education (college)" = -0.5,
                   "U" = 0,
                   "Z" = 0.25)

lin_pred <- cbind(1,
                  A$gender == "Woman",
                  A$age,
                  A$education == "High school",
                  A$education == "College",
                  A$misreport,
                  A$true_belief) %*% param_control

# Simulate responses to the control items
A$y_star <- rbinom(n, J, prob = plogis(lin_pred))

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# List experiment response
A$y <- A$y_star + A$true_belief * A$treatment

# Direct question response
A$direct <- ifelse(A$misreport == 1, 0, A$true_belief)

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# Display first 10 rows of the data
print(A[1:10, ], row.names = FALSE)

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library(misreport)

model.1 <- listExperiment(y ~ 1 + gender + age + education,
                          data = A, J = J,
                          treatment = "treatment",
                          direct = "direct",
                          sensitive.response = 1,
                          n.runs = 1,
                          control.constraint = "partial",
                          misreport.treatment = FALSE)

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#  library(misreport)
#  
#  model.1 <- listExperiment(y ~ 1 + gender + age + education,
#                            data = A, J = J,
#                            treatment = "treatment",
#                            direct = "direct",
#                            sensitive.response = 1,
#                            control.constraint = "partial",
#                            misreport.treatment = FALSE)

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#  # Show 3 significant digits
#  summary(model.1, digits = 3)

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# Show 3 significant digits
summary(model.1, digits = 3)

# Recalling the population parameters:
cat("# Recalling the population parameters for comparison:\nControl:  ",
    format(param_control[-6], nsmall = 2),
    "\nSensitive:",
    format(param_sensitive, nsmall = 2),
    "\nMisreport:",
    format(param_misreport[-6], nsmall = 2))

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# Predicted probabilities of misreporting (covariates held at their observed values)
pred.woman <- predict(model.1, newdata = data.frame(A[, names(A) != "gender"], gender = "Woman"))$u.hat

pred.man <- predict(model.1, newdata = data.frame(A[, names(A) != "gender"], gender = "Man"))$u.hat

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# Mean predicted probability of misreporting (gender set to "Woman")
mean(pred.woman)
# Mean predicted probability of misreporting (gender set to "Man")
mean(pred.man)
# Mean difference in predicted probabilities of misreporting between women and men
mean(pred.woman - pred.man)

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# Display first 10 rows of posterior predicted probabilities
model.1$w[1:10, ]

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weighted.mean(pred.woman - pred.man, rowSums(model.1$w[, 1:2]))

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n_sims <- 1000

# Simulate model parameters
coefs <- c(model.1$par.control, model.1$par.sens, model.1$par.misreport)
par_sim <- mvtnorm::rmvnorm(n_sims, coefs, model.1$vcov.mle)

# Get the matrix of parameters for the misreport submodel
# Note that the parameter estimates in par_sim are in the following order: control, sensitive, misreport
par_sim_misreport <- par_sim[, (length(coefs)-length(model.1$par.misreport)+1):length(coefs)]

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par_sim_misreport[1:10, ]

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pp_diff <- rep(NA, n_sims)

# For each row of parameters, calculate the mean difference in predicted probabilities
for(i in 1:n_sims) {

  pp_woman <- predict(model.1, newdata = data.frame(A[, names(A) != "gender"], gender = "Woman"), par.misreport = par_sim_misreport[i, ])$u.hat

  pp_man <- predict(model.1, newdata = data.frame(A[, names(A) != "gender"], gender = "Man"), par.misreport = par_sim_misreport[i, ])$u.hat

  pp_diff[i] <- mean(pp_woman - pp_man)

}

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mean(pp_diff)
quantile(pp_diff, c(0.05, 0.95)) # 90% interval