snazzieR (version 0.1.2)

ridge.regression: Ridge Regression with Automatic Lambda Selection

Description

Performs ridge regression with automatic selection of the optimal regularization parameter `lambda` by minimizing k-fold cross-validated mean squared error (CV-MSE) using Brent's method. Supports both formula and matrix interfaces.

Usage

ridge.regression(
  formula = NULL,
  data = NULL,
  x = NULL,
  y = NULL,
  lambda.range = c(1e-04, 100),
  folds = 5,
  ...
)

Value

A `ridge.model` object containing:

coefficients

Final ridge coefficients (no intercept)

std_errors

Standard errors of the coefficients

intercept

Intercept term (from y centering)

optimal.lambda

Best lambda minimizing CV-MSE

cv.ms

Minimum CV-MSE achieved

cv.results

Data frame with lambda and CV-MSE pairs

x.scale

Standardization info: mean and sd for each predictor

y.center

Centering constant for y

fitted.values

Final model predictions on training data

residuals

Training residuals (y - fitted)

call

Matched call (for debugging)

method

Always "ridge"

folds

Number of CV folds used

formula

Stored if formula interface used

terms

Stored if formula interface used

Arguments

formula

A model formula like `y ~ x1 + x2`. Mutually exclusive with `x`/`y`.

data

A data frame containing all variables used in the formula.

x

A numeric matrix of predictor variables (n × p). Used when formula is not provided.

y

A numeric vector of response variables (n × 1). Used when formula is not provided.

lambda.range

A numeric vector of length 2 specifying the interval for lambda optimization. Default: `c(1e-4, 100)`.

folds

An integer specifying the number of cross-validation folds. Default: `5`.

...

Additional arguments passed to internal methods.

Details

This function implements ridge regression with automatic hyperparameter tuning. The algorithm:

• Standardizes predictor variables (centers and scales)

• Centers the response variable

• Uses k-fold cross-validation to find the optimal lambda

• Fits the final model with the optimal lambda

• Returns a structured object for prediction and analysis

The ridge regression solution is computed using the closed-form formula: \(\hat{\beta} = (X^T X + \lambda I)^{-1} X^T y\)

References

Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.

See Also

predict.ridge.model

Examples

if (FALSE) {
# Formula interface
model1 <- ridge.regression(mpg ~ wt + hp + disp, data = mtcars)

# Matrix interface
X <- as.matrix(mtcars[, c("wt", "hp", "disp")])
y <- mtcars$mpg
model2 <- ridge.regression(x = X, y = y)

# Custom lambda range and folds
model3 <- ridge.regression(mpg ~ .,
    data = mtcars,
    lambda.range = c(0.1, 10), folds = 10
)
}