# ITE_Logistic: Inference for difference of case probabilities in high... In SIHR: Statistical Inference in High Dimensional Regression

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```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.