Struct GlmFit 

pub struct GlmFit<F: Family> { /* private fields */ }

A generalized linear model fit by iteratively reweighted least squares (Fisher scoring) for an exponential-dispersion Family.

One solver serves every family. Each IRLS step forms the working response z = η + (y − μ)/(dμ/dη) and working weights w = (dμ/dη)² / V(μ), then solves the weighted normal equations (XᵀWX) β = XᵀWz. At convergence the score equations Xᵀ(y − μ) · (dμ/dη)/V = 0 hold and φ·(XᵀWX)⁻¹ is the coefficient covariance, with φ = 1 for the fixed-dispersion families (Poisson, negative binomial) and the Pearson estimate φ̂ = χ²/(n − p) for Gamma.

See the module docs for the response conventions and the link choice.

Implementations

impl<F: Family> GlmFit<F>

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

Fit y ~ X under family (default: up to 100 IRLS iterations, tolerance 1e-10 on the maximum coefficient step).

The caller owns the design matrix, including any intercept column, exactly as with OlsFit and LogisticFit.

Errors

• RegressionError::EmptyInput / RegressionError::ShapeMismatch.
• RegressionError::InvalidResponse if y is outside the family’s support (negative counts, non-positive Gamma responses).
• RegressionError::RankDeficient if the weighted design is singular.
• RegressionError::NotConverged if IRLS fails to converge.

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

Like GlmFit::new with an explicit iteration cap and step tolerance.

pub fn family(&self) -> &F

The family this model was fit under.

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 a constant (intercept) column was detected in the design.

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 response.

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

Estimated coefficients (link scale), aligned to the design columns.

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

Linear predictor η = Xβ.

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

Fitted means μᵢ = g⁻¹(ηᵢ).

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

IRLS working weights wᵢ = (dμ/dη)² / V(μ) at the MLE.

pub fn dispersion(&self) -> f64

Estimated dispersion φ: 1 for Poisson/negative binomial, the Pearson estimate χ²/(n − p) for Gamma.

pub fn log_likelihood(&self) -> f64

Maximized log-likelihood (evaluated at the estimated dispersion for Gamma).

pub fn covariance(&self) -> Array2<f64>

Coefficient covariance φ · (XᵀWX)⁻¹.

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

Coefficient standard errors √diag(φ · (XᵀWX)⁻¹).

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

Wald statistics βⱼ / seⱼ.

The reference distribution is the standard normal when the dispersion is known (Poisson, negative binomial) and Student’s t with n − p degrees of freedom when it is estimated (Gamma) — see GlmFit::p_values.

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

Two-sided Wald p-values.

Uses the standard normal for fixed-dispersion families and Student’s t with n − p degrees of freedom when the dispersion is estimated (the R glm() convention).

pub fn predict_mean(&self, x: ArrayView2<'_, f64>) -> Array1<f64>

Predicted means for a new design matrix x (same column layout as the training design): μ = g⁻¹(xβ).

impl<F: Family> GlmFit<F>

pub fn goodness_of_fit(&self) -> GoodnessOfFit

Overall goodness-of-fit summary: null/residual deviance, dispersion, McFadden’s pseudo-R², and AIC/BIC.

The residual deviance is the sum of per-observation unit deviances (equivalently the sum of squared deviance residuals). The null model is the mean-only fit, whose MLE mean is the sample mean ȳ for all log-link families here, so the null deviance is computed directly without a second IRLS solve.

The information criteria count k = p parameters when the dispersion is fixed (Poisson, negative binomial) and k = p + 1 when it is estimated (Gamma), charging the extra degree of freedom for φ̂. McFadden’s pseudo-R² compares the fitted log-likelihood to the mean-only model at the same dispersion.

Trait Implementations

impl<F: Clone + Family> Clone for GlmFit<F>

fn clone(&self) -> GlmFit<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Debug + Family> Debug for GlmFit<F>

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

Formats the value using the given formatter.