ci {DDL}

Computing confidence intervals

Description

generic function

Usage

ci(x, alpha = 0.05, alternative = c("two.sided", "less", "greater"))

Arguments

x

An object of class

alpha

alpha Level of significance to construct confidence interval

alternative

indicates the alternative hypothesis to construct confidence interval and must be one of "two.sided" (default), "less", or "greater".

Examples

index = 1
n=100
p=200
s=5
q=3
sigmaE=2
sigma=2
pert=1

H = pert*matrix(rnorm(n*q,mean=0,sd=1),n,q,byrow = TRUE)
Gamma = matrix(rnorm(q*p,mean=0,sd=1),q,p,byrow = TRUE)
#value of X independent from H
E = matrix(rnorm(n*p,mean=0,sd=sigmaE),n,p,byrow = TRUE)

#defined in eq. (2), high-dimensional measured covariates
X = E + H %*% Gamma

delta = matrix(rnorm(q*1,mean=0,sd=1),q,1,byrow = TRUE)

#px1 matrix, creates beta with 1s in the first s entries and the remaining p-s as 0s
beta = matrix(rep(c(1,0),times = c(s,p-s)),p,1,byrow = TRUE)

#nx1 matrix with values of mean 0 and SD of sigma, error in Y independent of X
nu = matrix(rnorm(n*1,mean=0,sd=sigma),n,1,byrow = TRUE)

#eq. (1), the response of the Structural Equation Model
Y = X %*% beta + H %*% delta + nu

result = DDL(X, Y, index)
# default alpha is 0.05
ci(result, alpha = 0.05)
ci(result, alpha = 0.05, alternative = "less")
ci(result, alpha = 0.05, alternative = "greater")