louis_lr_saem: louis_lr_saem

In misaem: Linear Regression and Logistic Regression with Missing Covariates

Description

Used in main function miss.saem. Calculate the variance of estimated parameters for logistic regression model with missing data, using Monte Carlo version of Louis formula.

Usage

louis_lr_saem(
  beta,
  mu,
  Sigma,
  Y,
  X.obs,
  pos_var = 1:ncol(X.obs),
  rindic = as.matrix(is.na(X.obs)),
  whichcolXmissing = (1:ncol(rindic))[apply(rindic, 2, sum) > 0],
  mc.size = 2
)

Arguments

beta	Estimated parameter of logistic regression model.
mu	Estimated parameter μ.
Sigma	Estimated parameter Σ.
Y	Response vector N * 1
X.obs	Design matrix with missingness N * p
pos_var	Index of selected covariates.
rindic	Missing pattern of X.obs. If a component in X.obs is missing, the corresponding position in rindic is 1; else 0.
whichcolXmissing	The column index in covariate containing at least one missing observation.
mc.size	Monte Carlo sampling size.

Value

Variance of estimated β.

Examples

# Generate dataset
N <- 50  # number of subjects
p <- 3     # number of explanatory variables
mu.star <- rep(0,p)  # mean of the explanatory variables
Sigma.star <- diag(rep(1,p)) # covariance
beta.star <- c(1, 1,  0) # coefficients
beta0.star <- 0 # intercept
beta.true = c(beta0.star,beta.star)
X.complete <- matrix(rnorm(N*p), nrow=N)%*%chol(Sigma.star) +
              matrix(rep(mu.star,N), nrow=N, byrow = TRUE)
p1 <- 1/(1+exp(-X.complete%*%beta.star-beta0.star))
y <- as.numeric(runif(N)<p1)
# Generate missingness
p.miss <- 0.10
patterns <- runif(N*p)<p.miss #missing completely at random
X.obs <- X.complete
X.obs[patterns] <- NA

# Louis formula to obtain variance of estimates
V_obs = louis_lr_saem(beta.true,mu.star,Sigma.star,y,X.obs)

misaem documentation built on April 12, 2021, 9:06 a.m.