Struct PenalizedLogisticFit 

pub struct PenalizedLogisticFit { /* private fields */ }

A fitted ridge-penalized logistic regression — a penalized GLM — and its shrinkage-aware diagnostics.

Maximizes the L2-penalized log-likelihood

ℓ(β) − ½λ‖β_pen‖²

(a detected intercept column is left unpenalized), fit by penalized IRLS: each Newton step solves (XᵀWX + λP) Δ = Xᵀ(y − p) − λPβ with W = diag(pᵢ(1 − pᵢ)) and P the penalty selector. The penalty is the GLM analogue of ridge — it tames separation and multicollinearity in logistic regression, at the cost of biased-but-lower-variance coefficients.

The diagnostic that changes: effective degrees of freedom

As in ridge OLS, the penalty means the model no longer spends p degrees of freedom. The effective df is the trace of the penalized hat matrix,

df = tr[ (XᵀWX + λP)⁻¹ XᵀWX ],

which falls from p toward the unpenalized/intercept count as λ grows. It replaces the raw parameter count in aic / bic, and the coefficient covariance is the sandwich (XᵀWX + λP)⁻¹ (XᵀWX) (XᵀWX + λP)⁻¹, not the naïve inverse information — so the reported standard errors account for the shrinkage.

Implementations

impl PenalizedLogisticFit

pub fn new(x: Array2<f64>, y: Array1<f64>, lambda: f64) -> Result<Self>

Fit ridge-penalized logistic regression of binary y on X with penalty lambda ≥ 0 (default: up to 100 IRLS iterations, tolerance 1e-10).

At lambda = 0 this reproduces the ordinary LogisticFit.

Errors

• RegressionError::EmptyInput / RegressionError::ShapeMismatch.
• RegressionError::InvalidParameter if lambda < 0.
• RegressionError::InvalidResponse if y is not 0/1 or is one class.
• RegressionError::RankDeficient if the penalized information is singular.
• RegressionError::NotConverged if IRLS fails to converge.

pub fn with_options( x: Array2<f64>, y: Array1<f64>, lambda: f64, max_iter: usize, tol: f64, ) -> Result<Self>

Like PenalizedLogisticFit::new with an explicit iteration cap and tolerance.

pub fn lambda(&self) -> f64

The penalty λ this model was fit with.

pub fn n_observations(&self) -> usize

Number of observations.

pub fn n_parameters(&self) -> usize

Number of coefficients (design columns, intercept included).

pub fn has_intercept(&self) -> bool

Whether an unpenalized intercept is present.

pub fn iterations(&self) -> usize

IRLS iterations taken to converge.

pub fn design_matrix(&self) -> ArrayView2<'_, f64>

The design matrix as fitted.

pub fn response(&self) -> ArrayView1<'_, f64>

The binary response.

pub fn coefficients(&self) -> ArrayView1<'_, f64>

Penalized coefficients (log-odds scale), aligned to the design columns.

pub fn fitted_probabilities(&self) -> ArrayView1<'_, f64>

Fitted probabilities pᵢ = P(yᵢ = 1).

pub fn covariance(&self) -> ArrayView2<'_, f64>

Sandwich coefficient covariance (XᵀWX + λP)⁻¹ (XᵀWX) (XᵀWX + λP)⁻¹.

pub fn log_likelihood(&self) -> f64

Unpenalized log-likelihood at the penalized estimate.

pub fn effective_df(&self) -> f64

Effective degrees of freedom tr[(XᵀWX + λP)⁻¹ XᵀWX] — falls from p toward the intercept count as λ grows.

pub fn coefficient_standard_errors(&self) -> Array1<f64>

Coefficient standard errors from the sandwich covariance.

pub fn residual_deviance(&self) -> f64

Residual deviance −2ℓ (unpenalized log-likelihood).

pub fn aic(&self) -> f64

AIC using the effective degrees of freedom, −2ℓ + 2·df.

pub fn bic(&self) -> f64

BIC using the effective degrees of freedom, −2ℓ + ln(n)·df.

Trait Implementations

impl Clone for PenalizedLogisticFit

fn clone(&self) -> PenalizedLogisticFit

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for PenalizedLogisticFit

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.