PoSIAdjRSquared (version 0.1.0)

construct_adj_r_squared: Construct adjusted R squared

Description

This function computes the adjusted R squared and returns some useful matrices from this computation.

Usage

construct_adj_r_squared(X, k, y, n, intercept = c(TRUE, FALSE), sst)

Value

X_M_k

The design matrix of model k

P_M_k

The projection matrix of model k

R_M_k

The orthogonal projection matrix of model k

kappa_M_k

Adjustment factor for model complexity kappa of model k

adj_r_squared

The adjusted R squared value of model k

Arguments

X

Design matrix of type "matrix" and dimension nxp

k

Index set included in model k

y

Response vector of type "matrix" and dimension nx1

n

An integer for the sample size

intercept

Logical value: TRUE if fitted models should contain intercept, FALSE if not

sst

An integer for the total sum of squares

References

Pirenne, S. and Claeskens, G. (2024). Exact Post-Selection Inference for Adjusted R Squared.

Examples

# Generate data
n <- 100
k <- 1:10
Data <- datagen.norm(seed = 7, n, p = 10, rho = 0, beta_vec = c(1,0.5,0,0.5,0,0,0,0,0,0))
X <- Data$X
y <- Data$y
sst <- sum((y-mean(y))^2)

construct_adj_r_squared(X, k, y, n, intercept=FALSE, sst)