CATE: Inference for difference of linear combinations of the...

In SIHR: Statistical Inference in High Dimensional Regression

Inference for difference of linear combinations of the regression vectors in high dimensional generalized linear regressions

Description

Computes the bias-corrected estimator of the difference of linear combinations of the regression vectors for the high dimensional generalized linear regressions and the corresponding standard error.

Usage

CATE(
  X1,
  y1,
  X2,
  y2,
  loading.mat,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  intercept.loading = FALSE,
  beta.init1 = NULL,
  beta.init2 = NULL,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  alpha = 0.05,
  verbose = FALSE
)

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_1
loading.mat	Loading matrix, nrow=p, each column corresponds to a loading of interest
model	The high dimensional regression model, either "linear" or "logistic" or "logistic_alter"
intercept	Should intercept(s) be fitted for the initial estimators (default = TRUE)
intercept.loading	Should intercept term be included for the loading (default = FALSE)
beta.init1	The initial estimator of the regression vector for the 1st data (default = NULL)
beta.init2	The initial estimator of the regression vector for the 2nd data (default = NULL)
lambda	The tuning parameter in fitting initial model. If NULL, it will be picked by cross-validation. (default = NULL)
mu	The dual tuning parameter used in the construction of the projection direction. If NULL it will be searched automatically. (default = NULL)
prob.filter	The threshold of estimated probabilities for filtering observations in logistic regression. (default = 0.05)
rescale	The factor to enlarge the standard error to account for the finite sample bias. (default = 1.1)
alpha	Level of significance to construct two-sided confidence interval (default = 0.05)
verbose	Should intermediate message(s) be printed (default = FALSE)

Value

A list consists of plugin estimators, debiased estimators, and confidence intervals. For logistic regression, it also returns those items after probability transformation.

est.plugin.vec	The vector of plugin(biased) estimators for the linear combination of regression coefficients, length of ncol(loading.mat); corresponding to different column in loading.mat
est.debias.vec	The vector of bias-corrected estimators for the linear combination of regression coefficients, length of ncol(loading.mat); corresponding to different column in loading.mat
se.vec	The vector of standard errors of the bias-corrected estimators, length of ncol(loading.mat); corresponding to different column in loading.mat
ci.mat	The matrix of two.sided confidence interval for the linear combination, dimension of ncol(loading.mat) x 2; the row corresponding to different column in loading.mat
prob.debias.vec	The vector of bias-corrected estimators after probability transformation, length of ncol(loading.mat); corresponding to different column in loading.mat.
prob.se.vec	The vector of standard errors of the bias-corrected estimators after probability transformation, length of ncol(loading.mat); corresponding to different column in loading.mat.
prob.ci.mat	The matrix of two.sided confidence interval of the bias-corrected estimators after probability transformation, dimension of ncol(loading.mat) x 2; the row corresponding to different column in loading.mat.

Examples

X1 = matrix(rnorm(100*5), nrow=100, ncol=5)
y1 = -0.5 + X1[,1] * 0.5 + X1[,2] * 1 + rnorm(100)
X2 = matrix(rnorm(90*5), nrow=90, ncol=5)
y2 = -0.4 + X2[,1] * 0.48 + X2[,2] * 1.1 + rnorm(90)
loading1 = c(1, 1, rep(0,3))
loading2 = c(-0.5, -1, rep(0,3))
loading.mat = cbind(loading1, loading2)
Est = CATE(X1, y1, X2, y2, loading.mat, model="linear")

## compute confidence intervals
ci(Est, alpha=0.05, alternative="two.sided")

## summary statistics
summary(Est)

SIHR documentation built on April 9, 2023, 5:08 p.m.