Logistic Regression

Here we present how to perform the simulation studies in Zhang et al. (2022) for the logistic regression, with and without misclassification. We warn the readers that the code presented here may take time to run on a personal computer. Indeed, for the paper, the computations were performed on the “Baobab” and “Yggdrasil” HPC clusters provided by the University of Geneva.

Setting

We use the following setting for the logistic regression, with and without misclassification.

# packages
library(IBpaper)
library(ib)

# simulation specifics
MC <- 1000 # number of simulations
n <- 2000 # sample size
p <- 200 # number of coefficients
# Non-zero coefficients:
# intercept is 1
beta_nz <- c(1,rep(3,5),rep(-5,5),rep(7,5))
# Coefficients:
beta <- c(beta_nz,rep(0,p-15))

# seeds for random number generator
set.seed(895724)
seed <- vector("list",3)
seed$process <- sample.int(1e7,MC) # for the response
seed$design <- sample.int(1e7,MC) # for the design
seed$ib <- sample.int(1e7,MC) # for the iterative bootstrap

# IB specifics
H <- 200 # number of simulated estimators
bbc_control <- ibControl(H=H, maxit=1L) # control for bootstrap bias correction (BBC)
ib_control <- ibControl(H=H, maxit=50L) # control for iterative bootstrap (IB)

Logistic regression without misclassification

Here is the code for the simulation of the logistic regression computed on the actual responses without misclassification.

# For saving the results
res <- list(mle = matrix(ncol=p+1,nrow=MC),
            bbc = matrix(ncol=p+1,nrow=MC),
            jini = matrix(ncol=p+1,nrow=MC))

for(m in 1:MC){
  ##------- simulate the process ---------
  set.seed(seed$process[m]) # set the seed
  x <- matrix(rnorm(n*p,sd=p^(-.5)), nrow = n) # simulate the design
  logistic_object <- make_logistic(x, beta) # see ?make_logistic
  # simulate logistic responses
  y <- simulation(logistic_object, 
                  control = list(seed=seed$process[m])) 
  
  ##------ MLE estimation ----------------
  # Note: here the MLE is the initial estimator
  fit_mle <- glm(y ~ x, family=binomial(link="logit"), control = glm.control(maxit=200))
  res$mle[m,] <- coef(fit_mle)
  
  ##------ Bootstrap bias correction -----
  bbc_control$seed <- seed$ib[m] # update the seed
  fit_bbc <- ib(fit_mle, control = bbc_control) # compute BBC
  res$bbc[m,] <- getEst(fit_bbc) # retrieve estimator
  
  ##------ IB bias correction ------------
  ib_control$seed <- seed$ib[m] # update the seed
  fit_jini <- ib(fit_mle, control = ib_control) # compute IB
  res$jini[m,] <- getEst(fit_jini) # retrieve estimator
  # getIteration(fit_jini), if one wants to retrieve the number of iterations

  # print the iteration
  cat(m,"\n")
}

Logistic regression with misclassified responses

We first need to specify the misclassification mechanism, i.e. how the responses are misclassified.

# Random misclassification:
# False Positive (FP) follows rbeta(1.5,50)
# False Negative (FN) follows rbeta(1.1,10)
fp <- 1.5 / 51.5 # mean FP
fn <- 1.1 / 21.1 # mean FN

# Function to simulate responses with random misclassification
# see ?ib::simulation and ?ib::control for more details 
random_misclassification <- function(object, control, extra){
  ftd <- fitted(object)
  n <- length(ftd)
  N <- n * control$H
  u1 <- rbeta(N, shape1 = 1.5, shape2 = 50)
  u2 <- rbeta(N, shape1 = 1.1, shape2 = 20)
  mu_star <- u1 * (1 - rep(ftd,control$H)) + (1 - u2) * rep(ftd,control$H)
  matrix(ifelse(runif(N) > mu_star,0,1), ncol=control$H)
}

ib_control <- ibControl(H = H, maxit = 50L, sim = random_misclassification) # control for iterative bootstrap (IB)

Here is the code for the simulation of the logistic regression computed on the misclassified responses.

# For saving the results
res <- list(mle = matrix(ncol=p+1,nrow=MC),
            initial = matrix(ncol=p+1,nrow=MC),
            jini = matrix(ncol=p+1,nrow=MC))

for(m in 1:MC){
  ##------- simulate the process ---------
  set.seed(seed$process[m]) # set the seed
  x <- matrix(rnorm(n*p,sd=p^(-.5)), nr=n) # simulate the design
  logistic_object <- make_logistic(x, beta) # see ?make_logistic
  # simulate logistic with misclassified responses
  y <- simulation(logistic_object, 
                  control = list(seed=seed$process[m], sim=random_misclassification)) 
  
  ##------ MLE estimation ----------------
  fit_mle <- logistic_misclassification_mle(x,y,fp,fn) # see ?logistic_misclassification_mle
  res$mle[m,] <- fit_mle
  
  ##------ Initial estimator (inconsistent) ----------------
  fit_initial <- glm(y ~ x, family=binomial(link="logit"), control = glm.control(maxit=200))
  res$initial[m,] <- coef(fit_mle)
  
  ##------ IB bias correction ------------
  ib_control$seed <- seed$ib[m] # update the seed
  fit_jini <- ib(fit_initial, control = ib_control) # compute IB, see ? ib::ib for more details
  res$jini[m,] <- getEst(fit_jini) # retrieve estimator
  # getIteration(fit_jini), if one wants to retrieve the number of iterations

  # print the iteration
  cat(m,"\n")
}

References

Zhang, Yuming, Yanyuan Ma, Samuel Orso, Mucyo Karemera, Maria-Pia Victoria-Feser, and Stéphane Guerrier. 2022. “A Flexible Bias Correction Method Based on Inconsistent Estimators.” https://arxiv.org/pdf/2204.07907.pdf.

2022-04-29

Setting

Logistic regression without misclassification

Logistic regression with misclassified responses

References