Crate regression_diagnostics 

regression-diagnostics

Statistical diagnostics for ordinary least squares regression models in Rust — the surface R’s car/lmtest and Python’s statsmodels expose, in a dependency-light crate. It fills the specific ecosystem gap that no maintained Rust crate offers Variance Inflation Factor, adjusted R², or residual diagnostics (autocorrelation, heteroskedasticity, normality, influence).

Everything operates on a single fitted-model type, OlsFit, computed once and reused by every diagnostic.

Scope

The core is OLS diagnostics, whose closed-form structure (a well-defined hat matrix and Gaussian residuals) is what makes them well-defined. Two further model families each get their own module, because their diagnostics are genuinely different — not reskinned OLS formulas:

• regularized — ridge and lasso, where the hat matrix changes (H_λ = X(XᵀX + λI)⁻¹Xᵀ) or does not exist in closed form; diagnostics are built on effective degrees of freedom and the active set.
• logistic — binary logistic regression, a non-Gaussian likelihood with deviance/Pearson residuals, pseudo-R², and the Hosmer–Lemeshow test.

Linear algebra

Internals use nalgebra (pure-Rust QR/SVD, no system BLAS — chosen for portability); the public API speaks ndarray. That boundary and its tradeoff are documented in the README.

Layout

• OlsFit — the fitted model; constructed with OlsFit::new or OlsFit::with_intercept. Read its intercept convention before use.
• multicollinearity — vif, condition_number.
• fit_statistics — R²/adjusted R², F-statistic, AIC/BIC, log-likelihood.
• residuals — Durbin-Watson, Breusch-Pagan, White, Jarque-Bera, the scaled residual forms, and QQ-plot data.
• influence — leverage, Cook’s distance, DFFITS.
• coefficients — standardized (beta) coefficients.
• Summary via OlsFit::summary — the one-call statsmodels-style report.
• regularized — RidgeFit and LassoFit with their shrinkage-aware diagnostics.
• logistic — LogisticFit with deviance/Pearson residuals, goodness-of-fit, Hosmer–Lemeshow, and logistic influence.

Quick start

use ndarray::array;
use regression_diagnostics::OlsFit;
use regression_diagnostics::multicollinearity::vif;

// Caller supplies the intercept column (first column of ones).
let x = array![
    [1.0, 1.0, 2.0],
    [1.0, 2.0, 4.1],
    [1.0, 3.0, 5.9],
    [1.0, 4.0, 8.0],
    [1.0, 5.0, 10.1],
];
let y = array![2.0, 4.1, 6.1, 8.0, 10.2];
let fit = OlsFit::new(x, y).unwrap();

println!("{}", fit.summary());     // full statsmodels-style report
let v = vif(&fit);                 // per-predictor VIF (NaN for intercept)
assert!(v[1].is_finite());

Re-exports

pub use error::RegressionError;

pub use error::Result;

Modules

coefficients

Coefficient-level utilities.

error

Error type shared across every diagnostic in the crate.

fit_statistics

Summary-level fit statistics: r_squared, adjusted_r_squared, f_statistic, and the likelihood-based aic / bic / log_likelihood.

influence

Influence diagnostics: which individual observations disproportionately move the fit.

logistic

Diagnostics for binary logistic regression — a different statistical framework from OLS, not an extension of it, and provided here as its own self-contained set of types.

multicollinearity

Multicollinearity diagnostics: vif and condition_number.

regularized

Diagnostics for regularized linear regression — the family the OLS diagnostics deliberately excluded, now provided as first-class types.

residuals

Residual diagnostics: the scaled residual forms plus the classic assumption-checking tests.

Structs

CoefficientRow

One row of the coefficient table.

OlsFit

A fitted ordinary-least-squares model: the shared representation every diagnostic in this crate is computed from.

Summary

A structured snapshot of every diagnostic in the crate for one fit.