Package 'Styperidge.reg'

Full regression results using the S-type robust ridge regression estimators

Description

Full regression results using the S-type robust ridge regression estimators

Usage

regstyperidge(x, y)

Arguments

x	Explanatory variables (data.frame, matrix)
y	Dependent variables (data.frame, vector)

Value

A list of lists

Examples

library("mctest")
x <- Hald[,-1]
y <- Hald[,1]
regstyperidge(x,y)

library(isdals)
data(bodyfat)
x <- bodyfat[,-1]
y <- bodyfat[,1]
regstyperidge(x,y)

---

Weighted ridge regression

Description

Fits a ridge regression model with observation-specific weights. The weights can be supplied as a vector, data frame, or a square weight matrix. If a vector or data frame is supplied, it is internally converted to a diagonal weight matrix. In the example below, the weight vector W is generated from a Uniform(0, 1) distribution purely to illustrate how to call the function. In practice, users should provide weights that reflect the structure of their data.

Usage

Weightedridge.reg(x, y, W)

Arguments

x	Explanatory variables. A data.frame or matrix with observations in rows and predictors in columns.
y	Dependent variable. A numeric vector, data.frame, or matrix. For a univariate response, this should be a length-n vector or an n x 1 matrix.
W	Observation weights. Can be a numeric vector of length n, or a single-column data.frame of length n, or an n x n weight matrix. If W is a vector or data.frame, the function converts it to diag(W) internally.

Value

A list with the following components:

cc

Numeric scalar. The selected ridge parameter k.

beta

Numeric matrix (p x 1). Ridge regression coefficients on the standardized scale (no intercept).

betaor

Numeric matrix ((p+1) x 1). Coefficients on the original (unstandardized) scale, including the intercept in the first row.

e

Numeric matrix (n x 1). Residuals on the standardized scale (yr - yhat).

ew

Numeric matrix (n x 1). Weighted residuals (W^(1/2) %*% e).

yhat

Numeric matrix (n x 1). Fitted values on the standardized scale (xr %*% beta).

yhatw

Numeric matrix (n x 1). Fitted values in the weighted standardized space (xrw %*% beta).

yhator

Numeric matrix (n x 1). Fitted values on the original scale using betaor.

MSE

Numeric scalar. Mean squared error (MSE) computed from weighted residuals.

F

Numeric scalar. Overall model F statistic based on the weighted ANOVA decomposition.

sig

Numeric scalar. P-value associated with F.

varbeta

Numeric matrix (p x p). Estimated covariance matrix of beta on the standardized scale.

stdbeta

Numeric vector (length p). Standard errors of beta.

R2

Numeric scalar. Weighted coefficient of determination (R-squared).

R2adj

Numeric scalar. Adjusted weighted R-squared.

anovatable

A data.frame. ANOVA-style table with sums of squares, degrees of freedom, mean squares, F, and p-value.

confint

Numeric matrix (2 x p). Confidence intervals for beta; first row is lower, second row is upper.

Examples

## Example: Weighted ridge regression using the bodyfat data from isdals
library(isdals)
data(bodyfat)

## Explanatory variables (x) and response (y)
x <- bodyfat[ , -1]   # all columns except the first: predictors
y <- bodyfat[ ,  1]   # first column: response (body fat percentage)

## Generate observation weights uniformly on [0, 1]

n <- nrow(x)
W <- runif(n, min = 0, max = 1)

## Fit the weighted ridge regression model
fit <- Weightedridge.reg(x, y, W)

## Inspect some key outputs
fit$beta        # coefficients in the standardized scale
fit$betaor      # coefficients in the original scale (including intercept)
fit$R2          # R-squared
fit$R2adj       # Adjusted R-squared
fit$anovatable  # ANOVA table

---