Add simulation using simex

And there is a great potential for overestimating the true `Bxy`

irr/simex_sim.R

@@ -0,0 +1,56 @@
+##install.packages(c("purrr", "simex", "irr"))
+
+.emulate_coding <- function(ground_truth, Q = 1) {
+    if (runif(1) > Q) {
+        return(sample(c(0, 1), size = 1, replace = TRUE))
+    } else {
+        return(ground_truth)
+    }
+}
+
+distort_gt <- function(x, Q = NULL) {
+    return(purrr::map_dbl(x, .emulate_coding, Q = Q))
+}
+
+N <- c(1000, 3600, 14400)
+m <- c(75, 150, 300)
+
+B0 <- c(0, 0.1, 0.3)
+Bxy <- c(0.1, 0.2, 0.5)
+
+Q <- c(.6, .8, .9)
+
+conditions <- expand.grid(N, m, B0, Bxy, Q)
+
+logistic <- function(x) {1/(1+exp(-1*x))}
+
+.step <- function(Bxy, B0, Q, N, m) {
+    x <- rbinom(N, 1, 0.5)
+    y <-  Bxy * x + rnorm(N, 0, .5) + B0
+
+    dx <- as.numeric(distort_gt(x, Q = Q))
+
+    randomx <- sample(x, m)
+    coder1x <- distort_gt(randomx, Q = Q)
+    coder2x <- distort_gt(randomx, Q = Q)
+    coding_data <- matrix(c(as.numeric(coder1x), as.numeric(coder2x)), nrow = 2, byrow = TRUE)
+    alpha <- irr::kripp.alpha(coding_data, method = "nominal")
+    estimated_q <- alpha$value^(1/2)
+    estimated_q2 <- alpha$value
+
+    res <- data.frame(x = as.factor(x), y = y, dx = as.factor(dx))
+
+    naive_mod <- glm(y~dx, data = res, x = TRUE, y = TRUE)
+    real_mod <- glm(y~x, data = res, x = TRUE, y = TRUE)
+
+    px <- matrix(c(estimated_q, 1-estimated_q, 1-estimated_q, estimated_q), nrow = 2)
+    colnames(px) <- levels(res$dx)
+    corrected_mod <- simex::mcsimex(naive_mod, SIMEXvariable = "dx", mc.matrix = px, jackknife.estimation = FALSE, B = 300)
+    px2 <- matrix(c(estimated_q2, 1-estimated_q2, 1-estimated_q2, estimated_q2), nrow = 2)
+    colnames(px2) <- levels(res$dx)
+    corrected_mod2 <- simex::mcsimex(naive_mod, SIMEXvariable = "dx", mc.matrix = px2, jackknife.estimation = FALSE, B = 300)
+
+    return(tibble::tibble(N, m, Q, Bxy, B0, estimated_q, naive_Bxy = as.numeric(coef(naive_mod)[2]), real_Bxy = as.numeric(coef(real_mod)[2]), corrected_Bxy = coef(corrected_mod)[2], corrected_Bxy2 = coef(corrected_mod2)[2]))
+}
+
+## res <- .step(0.2, 0, 0.8, N = 1000, m = 100)