lmreg (version 1.2)

hypsplit: Testable and untestable hypotheses in linear model

Description

Reduces a general hypothesis in a linear model into a pair of completely testable and completely untestable hypotheses.

Usage

hypsplit(X, A, xi, tol=sqrt(.Machine$double.eps))

Arguments

X

Design/model matrix or matrix containing values of explanatory variables (generally including intercept).

A

Coefficient matrix (A.beta = xi is the null hypothesis to be split).

xi

A vector (A.beta = xi is the null hypothesis to be tested).

tol

A relative tolerance to detect zero singular values while computing generalized inverse, in case X is rank deficient (default = sqrt(.Machine$double.eps)).

Value

A list of two objects:

testable

Coefficient matrix and constant vector for testable part of hypotheses.

untestable

Coefficient matrix and constant vector for untestable part of hypotheses.

References

Sengupta and Jammalamadaka (2019), Linear Models and Regression with R: An Integrated Approach.

Examples

# NOT RUN {
data(denim)
attach(denim)
X <- cbind(1, binaries(Denim), binaries(Laundry))
A <- rbind(c(0,1,0,0,0,0,0), c(0,0,1,0,0,0,0), c(0,0,0,1,0,0,0))
xi <- c(0,0,0)
hypotheses <- hypsplit(X, A, xi, tol=1e-13)
hypotheses[[1]]  # testable
hypotheses[[2]]  # untestable
detach(denim)
# }