R/RRcor.models.R

In RRreg: Correlation and Regression Analyses for Randomized Response Data

get.x.est <- function(z, model, p, par2, group) {
  x.est <- z
  numGroups <- length(table(group))
  for (i in 1:numGroups) {
    # verschiedene x.est je nach gruppe
    pt <- p.truth(model, p = p, par2 = par2, group = i)
    y.mu <- y.mean(model, p = p, par2 = par2, group = i)
    sel <- group == i
    x.est[sel] <- (z[sel] - (1 - pt) * y.mu) / pt
  }
  x.est
}

## in coming call for selection: get.quotient(X[sel,i],models[i],p.list[[i]], par2, group=1)
# => response z within group 1 etc
get.quotient <- function(z, model, p, par2, group, pi, piVar) {
  
  pt <- p.truth(model, p, par2, group)
  # second, irrelevant distribution y
  y.mu <- y.mean(model, p, par2, group)
  y.var <- y.variance(y.mu, model, p, par2)

  # sensitive attribute x
  #   if (model =="FR"){
  #     x.est <- get.x.est (z,model,p,par2,rep(group,length(z)) )
  #     x.mu <- mean(x.est)
  #     x.var <- (var(z)-pt*(1-pt)*(x.mu-y.mu)^2 - (1-pt)*y.var)/pt
  #     print("in cor.models")
  #     print(x.mu)
  #     print(x.var)
  #   }else{
  # sensitive attribute x: take mean and variance from both groups!!!
  x.mu <- pi
  x.var <- piVar
  # NOT VARIANCE OF x.est !!!!! => VARIANCE OF TRUE VALUES NEEDED !!!
  #   }

  # noise (in paper u): mask.mu = 0
  # mask=noise term u (random error)
  mask.var <- (1 - pt) / pt * (x.var + y.var / pt + (x.mu - y.mu)^2)
  quotient <- mask.var / x.var
}

# probability of answering to sensitive question
p.truth <- function(model, p, par2, group) {
  switch(model,
    "direct" = pt <- 1,
    "Warner" = pt <- 2 * p - 1, # ifelse(2*p-1<0, 1-2*p,2*p-1),
    "Crosswise" = pt <- 2 * p - 1, # ifelse(2*p-1<0, 1-2*p,2*p-1),
    "Triangular" = pt <- 1 - p,
    "Mangat" = pt <- p,
    "Kuk" = pt <- p[1] - p[2],
    "FR" = pt <- 1 - sum(p),
    "UQTknown" = pt <- p[1],
    "SLD" = pt <- par2 - 1 + p[group],
    #          "CDM" = pt <- 1-p[group],
    "UQTunknown" = pt <- p[group],
    "mix.norm" = pt <- p[1],
    "mix.exp" = pt <- p[1],
    "mix.unknown" = pt <- p[group]
    #          "CDMsym" = {
    #            idx <- 2*group-1   # idx=1 für G1 ; idx=3 für G2
    #            pt <- 1- p[idx]-p[idx+1]  # 1-p1-p2 für gruppe 1
    #          }
  )
  pt
}

# mean of unrelated question
y.mean <- function(model, p, par2, group) {
  switch(model,
    "SLD" = y.mu <- (1 - p[group]) / (2 - par2 - p[group]),
    "UQTunknown" = y.mu <- par2,
    #          "CDM" = y.mu <- 1-par2,
    #          "CDMsym" = {
    #            idx <- 2*group-1   # idx=1 für G1 ; idx=3 für G2
    #            y.mu <- (p[idx]*(1-par2)) / (p[idx]+p[idx+1])
    #          },
    "direct" = y.mu <- 0,
    "Warner" = y.mu <- 1 / 2,
    "Crosswise" = y.mu <- 1 / 2,
    "Triangular" = y.mu <- 1,
    "Mangat" = y.mu <- 1,
    "Kuk" = y.mu <- p[2] / (1 - p[1] + p[2]),
    "FR" = y.mu <- ifelse(all(p == 0), 0, 1 / sum(p) * p %*% 0:(length(p) - 1)),
    "UQTknown" = y.mu <- p[2],
    "mix.norm" = y.mu <- p[2],
    "mix.exp" = y.mu <- p[2],
    "mix.unknown" = y.mu <- par2[1]
  )
  y.mu
}

# variance of unrelated question
y.variance <- function(y.mu, model, p, par2 = NULL) {
  if (model == "FR") {
    y.var <- ifelse(all(p == 0), 0, 1 / sum(p) * p %*% (0:(length(p) - 1))^2 -
      (1 / sum(p) * p %*% (0:(length(p) - 1)))^2)
  } else if (model == "mix.norm") {
    y.var <- p[3]^2
  } else if (model == "mix.exp") {
    y.var <- p[2]^2
  } else if (model == "mix.unknown") {
    y.var <- par2[2]
  } else {
    y.var <- y.mu * (1 - y.mu)
  }
  y.var
}

# reverse sign of correlation for certain combinatins of model and p
# if done for both variables, nothing happens
r.sign <- function(r, mod1, p1, mod2, p2) {
  reverse1 <- mod1 %in% c("Warner", "Crosswise") && p1 < .5
  reverse2 <- mod2 %in% c("Warner", "Crosswise") && p2 < .5
  r <- ifelse(reverse1 + reverse2 == 1, -r, r)
  return(r)
}