ITE_Logistic: Inference for difference of case probabilities in high...

Description Usage Arguments Value Examples

View source: R/LF_logistic.R

Description

Computes the bias corrected estimator of the difference between case probabilities or a linear combination of the difference between two regression vectors with respect to two high dimensional logistic regression models and the corresponding standard error. It also constructs the confidence interval for the difference of case probabilities or a linear combination of the difference between the regression vectors and test whether it is above zero or not. Here the case probability refers to the conditional probability of the binary response variable taking value 1 given the predictors are assigned to loading.

Usage

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ITE_Logistic(
  X1,
  y1,
  X2,
  y2,
  loading,
  weight = NULL,
  trans = TRUE,
  intercept = TRUE,
  intercept.loading = TRUE,
  init.coef1 = NULL,
  init.coef2 = NULL,
  lambda1 = NULL,
  lambda2 = NULL,
  mu1 = NULL,
  mu2 = NULL,
  step1 = NULL,
  step2 = NULL,
  resol = 1.5,
  maxiter = 6,
  alpha = 0.05,
  verbose = TRUE
)

Arguments

X1

Design matrix for the first sample, of dimension n_1 x p

y1

Outcome vector for the first sample, of length n_1

X2

Design matrix for the second sample, of dimension n_2 x p

y2

Outcome vector for the second sample, of length n_2

loading

Loading, of length p

weight

The weight vector used for bias correction, of length n; if set to NULL, the weight is the inverse of the first derivative of the logit function (default = NULL)

trans

Should results for the case probability (TRUE) or the linear combination (FALSE) be reported (default = TRUE)

intercept

Should intercept(s) be fitted for the initial estimators (default = TRUE)

intercept.loading

Should intercept be included for the loading (default = TRUE)

init.coef1

Initial estimator of the first regression vector (default = NULL)

init.coef2

Initial estimator of the second regression vector (default = NULL)

lambda1

The tuning parameter in the construction of init.coef1 (default = NULL)

lambda2

The tuning parameter in the construction of init.coef2 (default = NULL)

mu1

The dual tuning parameter used in the construction of the first projection direction (default = NULL)

mu2

The dual tuning parameter used in the construction of the second projection direction (default = NULL)

step1

The step size used to compute mu1; if set to NULL it is computed to be the number of steps (< maxiter) to obtain the smallest mu1 such that the dual optimization problem for constructing the projection direction converges (default = NULL)

step2

The step size used to compute mu2; if set to NULL it is computed to be the number of steps (< maxiter) to obtain the smallest mu2 such that the dual optimization problem for constructing the second projection direction converges (default = NULL)

resol

The factor by which mu1 (and mu2) is increased/decreased to obtain the smallest mu1 (and mu2) such that the dual optimization problem for constructing the first (and the second) projection direction converges (default = 1.5)

maxiter

Maximum number of steps along which mu1 (and mu2) is increased/decreased to obtain the smallest mu (and mu2) such that the dual optimization problem for constructing the first (and the second) projection direction converges (default = 6)

alpha

Level ofsignificance to test the null hypothesis which claims that the first case probability is not greater than the second case probability (default = 0.05)

verbose

Should inetrmediate message(s) be printed (default = TRUE)

Value

prop.est

The bias-corrected estimator for the difference between case probabilities or the linear combination of the difference between two regression vectors

se

The standard error for the bias-corrected estimator

CI

The confidence interval for the difference between case probabilities or the linear combination of the difference between two regression vectors

decision

decision=1 implies the first case probability or linear combination is greater than the second one\newline decision=0 implies the first case probability or linear combination is less than the second one

Examples

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A1gen <- function(rho,p){
A1 <- matrix(0,p,p)
for(i in 1:p){
  for(j in 1:p){
    A1[i,j] <- rho^(abs(i-j))
  }
}
A1
}
n1 <- 100
n2 <- 100
p <- 400
mu <- rep(0,p)
rho <- 0.5
Cov <- (A1gen(rho,p))/2
beta1 <- rep(0,p)
beta1[1:10] <- c(1:10)/5
beta2 <- rep(0,p)
beta2[1:5] <- c(1:5)/10
X1 <- MASS::mvrnorm(n1,mu,Cov)
X2 <- MASS::mvrnorm(n2,mu,Cov)
exp_val1 <- X1%*%beta1
exp_val2 <- X2%*%beta2
prob1 <- exp(exp_val1)/(1+exp(exp_val1))
prob2 <- exp(exp_val2)/(1+exp(exp_val2))
y1 <- rbinom(n1,1,prob1)
y2 <- rbinom(n2,1,prob2)
loading <- c(1,rep(0,(p-1)))
Est <- ITE_Logistic(X1 = X1, y1 = y1, X2 = X2, y2 = y2,loading = loading, trans = FALSE)

SIHR documentation built on Oct. 7, 2021, 9:08 a.m.