GLM_binary: Inference for single regression coefficient in high... In SIHR: Statistical Inference in High Dimensional Regression

Description

Computes the bias corrected estimator of a single regression coefficient in the high dimensional binary outcome regression model and the corresponding standard error. It also constructs the confidence interval for the target regression coefficient and tests whether it is equal to a pre-specified value b0.

Usage

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 GLM_binary( X, y, index, model = "logistic1", intercept = TRUE, init.coef = NULL, lambda = NULL, mu = NULL, step = NULL, resol = 1.5, maxiter = 6, b0 = 0, alpha = 0.05, verbose = TRUE )

Arguments

 X Design matrix, of dimension n x p y Outcome vector, of length n index An integer between 1 and p indicating the index of the targeted regression coefficient. For example, index = 1 means that the first regression coefficient is our inference target model The fitted GLM, either logistic1 or logistic2 or probit or inverse t1 (default = logistic1) ; model="logistic1" uses SIHR::LF_logistic with weight=NULL; model="logistic2" uses SIHR::LF_logistic with weight=rep(1,n) intercept Should intercept be fitted for the initial estimator (default = TRUE) init.coef Initial estimator of the regression vector (default = NULL) lambda The tuning parameter used in the construction of init.coef (default = NULL) mu The dual tuning parameter used in the construction of the projection direction (default = NULL) step The step size used to compute mu; if set to NULL it is computed to be the number of steps (< maxiter) to obtain the smallest mu such that the dual optimization problem for constructing the projection direction converges (default = NULL) resol The factor by which mu is increased/decreased to obtain the smallest mu such that the dual optimization problem for constructing the projection direction converges (default = 1.5) maxiter Maximum number of steps along which mu is increased/decreased to obtain the smallest mu such that the dual optimization problem for constructing the projection direction converges (default = 6) b0 The null value to be tested against alpha Level of significance to test the null hypothesis that the target regression coefficient is equal to b0 (default = 0.05) verbose Should inetrmediate message(s) be printed (default = TRUE)

Value

 prop.est The bias corrected estimator of the target regression coefficient se The standard error of the bias-corrected estimator CI The confidence interval for the target regression coefficient decision decision=1 implies the target regression coefficient is not equal to b0 \newline decision=0 implies the target regression coefficient is equal to b0 proj The projection direction, of length p

\insertRef

glmSIHR

Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 sp = 20 n = 400 p = 800 f = function(x){ pnorm(x) } sig1 = toeplitz(seq(0.6, 0,length.out = p/10)) Sig = Matrix::bdiag(rep(list(sig1),10))+diag(rep(0.4,p)) X = MASS::mvrnorm(n, mu=rep(0,p), Sigma=Sig) b = rep(0,p) b[1:sp] = rep(c(0.4,-0.4), sp/2) prob = f(X %*% b) y = array(dim = 1) for(i in 1:n){ y[i] = rbinom(1,1,prob[i]) } Est = SIHR::GLM_binary(X = X, y = y, index = 1, model = "probit", intercept = FALSE)

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