inferust 0.1.22

use nalgebra::{DMatrix, DVector};
use statrs::distribution::{ChiSquared, ContinuousCDF, Normal};

use crate::error::{InferustError, Result};
use crate::irls::irls_weighted_solve;

/// GLM residual vectors using common statsmodels-compatible definitions.
#[derive(Debug, Clone)]
pub struct GlmResiduals {
    pub response: Vec<f64>,
    pub pearson: Vec<f64>,
    pub deviance: Vec<f64>,
}

/// Binary classification metrics computed from fitted probabilities.
#[derive(Debug, Clone)]
pub struct BinaryClassificationMetrics {
    pub threshold: f64,
    pub true_positives: usize,
    pub false_positives: usize,
    pub true_negatives: usize,
    pub false_negatives: usize,
    pub accuracy: f64,
    pub precision: f64,
    pub recall: f64,
    pub f1_score: f64,
    pub log_loss: f64,
    pub brier_score: f64,
}

/// Likelihood-ratio test summary for nested likelihood models.
#[derive(Debug, Clone)]
pub struct LikelihoodRatioTest {
    pub statistic: f64,
    pub df: usize,
    pub p_value: f64,
}

/// Predicted mean with a Wald confidence interval on the response scale.
#[derive(Debug, Clone)]
pub struct PredictionInterval {
    pub mean: f64,
    pub lower: f64,
    pub upper: f64,
}

/// Average marginal effect summary for a logistic regression predictor.
#[derive(Debug, Clone)]
pub struct LogisticMarginalEffect {
    pub name: String,
    pub effect: f64,
    pub std_error: f64,
    pub z_statistic: f64,
    pub p_value: f64,
    pub confidence_interval: (f64, f64),
}

/// Binary logistic regression result.
#[derive(Debug, Clone)]
pub struct LogisticResult {
    pub coefficients: Vec<f64>,
    pub std_errors: Vec<f64>,
    pub z_statistics: Vec<f64>,
    pub p_values: Vec<f64>,
    pub covariance_matrix: Vec<Vec<f64>>,
    pub fitted_probabilities: Vec<f64>,
    pub log_likelihood: f64,
    pub null_log_likelihood: f64,
    pub pseudo_r_squared: f64,
    pub aic: f64,
    pub bic: f64,
    pub n: usize,
    pub k: usize,
    pub feature_names: Vec<String>,
    observed: Vec<f64>,
    design_matrix: Vec<Vec<f64>>,
    iterations: usize,
}

impl LogisticResult {
    /// Predict probabilities for raw X rows, without the intercept column.
    pub fn predict_proba(&self, x: &[Vec<f64>]) -> Vec<f64> {
        x.iter()
            .map(|row| {
                let mut eta = if self.feature_names[0] == "const" {
                    self.coefficients[0]
                } else {
                    0.0
                };
                let offset = if self.feature_names[0] == "const" {
                    1
                } else {
                    0
                };
                for (j, &value) in row.iter().enumerate() {
                    eta += self.coefficients[offset + j] * value;
                }
                sigmoid(eta)
            })
            .collect()
    }

    /// Wald confidence intervals for coefficients at the requested alpha level.
    pub fn confidence_intervals(&self, alpha: f64) -> Result<Vec<(f64, f64)>> {
        if !(0.0..1.0).contains(&alpha) {
            return Err(InferustError::InvalidInput(
                "alpha must be between 0 and 1".into(),
            ));
        }
        let normal = Normal::new(0.0, 1.0)
            .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
        let z = normal.inverse_cdf(1.0 - alpha / 2.0);
        Ok(self
            .coefficients
            .iter()
            .zip(self.std_errors.iter())
            .map(|(coef, se)| (coef - z * se, coef + z * se))
            .collect())
    }

    /// Exponentiated coefficients, matching statsmodels' common odds-ratio view.
    pub fn odds_ratios(&self) -> Vec<f64> {
        self.coefficients.iter().map(|coef| coef.exp()).collect()
    }

    /// Wald test of a linear restriction `R·β = q` on the logistic coefficients.
    ///
    /// Logistic regression is asymptotic, so the chi-square form is canonical;
    /// the F-statistic in the result is informational only.
    pub fn wald_test(
        &self,
        r: &[Vec<f64>],
        q: &[f64],
    ) -> Result<crate::hypothesis::WaldTestResult> {
        crate::hypothesis::wald_linear(&self.coefficients, &self.covariance_matrix, r, q, None)
    }

    /// Average marginal effects for each non-intercept predictor.
    pub fn average_marginal_effects(&self) -> Vec<(String, f64)> {
        let scale = self.average_probability_slope();
        let offset = self.intercept_offset();

        self.feature_names
            .iter()
            .skip(offset)
            .zip(self.coefficients.iter().skip(offset))
            .map(|(name, coef)| (name.clone(), coef * scale))
            .collect()
    }

    /// Delta-method average marginal effects with standard errors and Wald intervals.
    pub fn average_marginal_effects_summary(
        &self,
        alpha: f64,
    ) -> Result<Vec<LogisticMarginalEffect>> {
        if !(0.0..1.0).contains(&alpha) {
            return Err(InferustError::InvalidInput(
                "alpha must be between 0 and 1".into(),
            ));
        }
        let normal = Normal::new(0.0, 1.0)
            .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
        let critical = normal.inverse_cdf(1.0 - alpha / 2.0);
        let scale = self.average_probability_slope();
        let offset = self.intercept_offset();

        let mut effects = Vec::with_capacity(self.coefficients.len().saturating_sub(offset));
        for j in offset..self.coefficients.len() {
            let effect = self.coefficients[j] * scale;
            let gradient = self.average_marginal_effect_gradient(j, scale);
            let variance = quadratic_form(&gradient, &self.covariance_matrix).max(0.0);
            let std_error = variance.sqrt();
            let z_statistic = effect / std_error;
            let p_value = 2.0 * (1.0 - normal.cdf(z_statistic.abs()));
            effects.push(LogisticMarginalEffect {
                name: self.feature_names[j].clone(),
                effect,
                std_error,
                z_statistic,
                p_value,
                confidence_interval: (effect - critical * std_error, effect + critical * std_error),
            });
        }

        Ok(effects)
    }

    fn intercept_offset(&self) -> usize {
        usize::from(
            self.feature_names
                .first()
                .is_some_and(|name| name == "const"),
        )
    }

    fn average_probability_slope(&self) -> f64 {
        self.fitted_probabilities
            .iter()
            .map(|p| p * (1.0 - p))
            .sum::<f64>()
            / self.n as f64
    }

    fn average_marginal_effect_gradient(&self, coefficient_index: usize, scale: f64) -> Vec<f64> {
        let mut gradient = vec![0.0; self.coefficients.len()];
        for parameter_index in 0..self.coefficients.len() {
            let slope_derivative = self
                .fitted_probabilities
                .iter()
                .zip(self.design_matrix.iter())
                .map(|(p, row)| (1.0 - 2.0 * p) * p * (1.0 - p) * row[parameter_index])
                .sum::<f64>()
                / self.n as f64;
            gradient[parameter_index] = self.coefficients[coefficient_index] * slope_derivative;
        }
        gradient[coefficient_index] += scale;
        gradient
    }

    /// Linear predictor values for raw X rows, without the intercept column.
    pub fn predict_linear(&self, x: &[Vec<f64>]) -> Vec<f64> {
        x.iter()
            .map(|row| linear_predict(row, &self.coefficients, &self.feature_names))
            .collect()
    }

    /// Response, Pearson, and deviance residuals for the training data.
    pub fn residuals(&self) -> GlmResiduals {
        let response = self
            .observed
            .iter()
            .zip(self.fitted_probabilities.iter())
            .map(|(yi, pi)| yi - pi)
            .collect::<Vec<_>>();
        let pearson = self
            .observed
            .iter()
            .zip(self.fitted_probabilities.iter())
            .map(|(yi, pi)| (yi - pi) / (pi * (1.0 - pi)).max(1e-12).sqrt())
            .collect::<Vec<_>>();
        let deviance = self
            .observed
            .iter()
            .zip(self.fitted_probabilities.iter())
            .map(|(yi, pi)| binomial_deviance_residual(*yi, *pi))
            .collect::<Vec<_>>();

        GlmResiduals {
            response,
            pearson,
            deviance,
        }
    }

    /// Model deviance against a saturated Bernoulli model.
    pub fn deviance(&self) -> f64 {
        -2.0 * self.log_likelihood
    }

    /// Null model deviance against a saturated Bernoulli model.
    pub fn null_deviance(&self) -> f64 {
        -2.0 * self.null_log_likelihood
    }

    /// Likelihood-ratio test against the intercept-only model.
    pub fn likelihood_ratio_test(&self) -> Result<LikelihoodRatioTest> {
        likelihood_ratio_test(self.log_likelihood, self.null_log_likelihood, self.k)
    }

    /// Classification metrics at a probability threshold.
    pub fn classification_metrics(&self, threshold: f64) -> Result<BinaryClassificationMetrics> {
        if !(0.0..1.0).contains(&threshold) {
            return Err(InferustError::InvalidInput(
                "threshold must be between 0 and 1".into(),
            ));
        }

        let mut true_positives = 0;
        let mut false_positives = 0;
        let mut true_negatives = 0;
        let mut false_negatives = 0;
        for (yi, pi) in self.observed.iter().zip(self.fitted_probabilities.iter()) {
            match (*pi >= threshold, *yi == 1.0) {
                (true, true) => true_positives += 1,
                (true, false) => false_positives += 1,
                (false, false) => true_negatives += 1,
                (false, true) => false_negatives += 1,
            }
        }

        let accuracy = (true_positives + true_negatives) as f64 / self.n as f64;
        let precision = safe_ratio(
            true_positives as f64,
            (true_positives + false_positives) as f64,
        );
        let recall = safe_ratio(
            true_positives as f64,
            (true_positives + false_negatives) as f64,
        );
        let f1_score = safe_ratio(2.0 * precision * recall, precision + recall);
        let log_loss =
            -binary_log_likelihood(&self.observed, &self.fitted_probabilities) / self.n as f64;
        let brier_score = self
            .observed
            .iter()
            .zip(self.fitted_probabilities.iter())
            .map(|(yi, pi)| (yi - pi).powi(2))
            .sum::<f64>()
            / self.n as f64;

        Ok(BinaryClassificationMetrics {
            threshold,
            true_positives,
            false_positives,
            true_negatives,
            false_negatives,
            accuracy,
            precision,
            recall,
            f1_score,
            log_loss,
            brier_score,
        })
    }

    /// Number of Newton/IRLS iterations used to fit the model.
    pub fn iterations(&self) -> usize {
        self.iterations
    }
}

/// Binary logistic regression builder.
pub struct Logistic {
    feature_names: Vec<String>,
    add_intercept: bool,
    max_iter: usize,
    tolerance: f64,
}

impl Default for Logistic {
    fn default() -> Self {
        Self::new()
    }
}

impl Logistic {
    /// Create a new logistic regression builder. An intercept term is added by default.
    pub fn new() -> Self {
        Self {
            feature_names: Vec::new(),
            add_intercept: true,
            max_iter: 100,
            tolerance: 1e-8,
        }
    }

    /// Set human-readable names for predictor columns.
    pub fn with_feature_names(mut self, names: Vec<String>) -> Self {
        self.feature_names = names;
        self
    }

    /// Fit without an intercept.
    pub fn no_intercept(mut self) -> Self {
        self.add_intercept = false;
        self
    }

    /// Set maximum Newton iterations.
    pub fn max_iter(mut self, max_iter: usize) -> Self {
        self.max_iter = max_iter;
        self
    }

    /// Set convergence tolerance on the largest coefficient update.
    pub fn tolerance(mut self, tolerance: f64) -> Self {
        self.tolerance = tolerance;
        self
    }

    /// Fit a binary logistic regression model.
    pub fn fit(&self, x: &[Vec<f64>], y: &[f64]) -> Result<LogisticResult> {
        let n = y.len();
        if n < 2 {
            return Err(InferustError::InsufficientData { needed: 2, got: n });
        }
        if x.len() != n {
            return Err(InferustError::DimensionMismatch {
                x_rows: x.len(),
                y_len: n,
            });
        }
        if let Some(value) = y.iter().find(|value| **value != 0.0 && **value != 1.0) {
            return Err(InferustError::InvalidInput(format!(
                "logistic regression requires binary 0/1 y values, got {value}"
            )));
        }

        let p = x[0].len();
        let ncols = if self.add_intercept { p + 1 } else { p };
        if n <= ncols {
            return Err(InferustError::InsufficientData {
                needed: ncols + 1,
                got: n,
            });
        }

        let mut design = Vec::with_capacity(n * ncols);
        for row in x {
            if row.len() != p {
                return Err(InferustError::InvalidInput(
                    "all rows in X must have the same length".into(),
                ));
            }
            if self.add_intercept {
                design.push(1.0);
            }
            design.extend_from_slice(row);
        }

        let x_mat = DMatrix::from_row_slice(n, ncols, &design);
        let y_vec = DVector::from_column_slice(y);
        let mut beta = DVector::zeros(ncols);
        let mut hessian = DMatrix::zeros(ncols, ncols);
        let mut converged = false;
        let mut iterations = 0;

        for iter in 0..self.max_iter {
            iterations = iter + 1;
            let eta = &x_mat * &beta;
            let mu = eta.map(sigmoid);
            let gradient = x_mat.transpose() * (&y_vec - &mu);
            hessian.fill(0.0);
            for i in 0..n {
                let w = (mu[i] * (1.0 - mu[i])).max(1e-12);
                for j in 0..ncols {
                    for k in 0..ncols {
                        hessian[(j, k)] += w * x_mat[(i, j)] * x_mat[(i, k)];
                    }
                }
            }

            let delta = hessian
                .clone()
                .lu()
                .solve(&gradient)
                .ok_or(InferustError::SingularMatrix)?;
            let max_delta = delta.iter().map(|v| v.abs()).fold(0.0_f64, f64::max);
            beta += delta;
            if max_delta < self.tolerance {
                converged = true;
                break;
            }
        }

        if !converged {
            return Err(InferustError::InvalidInput(format!(
                "logistic regression failed to converge in {} iterations",
                self.max_iter
            )));
        }

        let eta = &x_mat * &beta;
        let probabilities = eta.map(sigmoid);
        hessian.fill(0.0);
        for i in 0..n {
            let w = (probabilities[i] * (1.0 - probabilities[i])).max(1e-12);
            for j in 0..ncols {
                for k in 0..ncols {
                    hessian[(j, k)] += w * x_mat[(i, j)] * x_mat[(i, k)];
                }
            }
        }

        let cov = hessian.try_inverse().ok_or(InferustError::SingularMatrix)?;
        let covariance_matrix: Vec<Vec<f64>> = (0..ncols)
            .map(|i| (0..ncols).map(|j| cov[(i, j)]).collect())
            .collect();
        let design_matrix: Vec<Vec<f64>> = (0..n)
            .map(|i| (0..ncols).map(|j| x_mat[(i, j)]).collect())
            .collect();
        let coefficients: Vec<f64> = beta.iter().cloned().collect();
        let std_errors: Vec<f64> = (0..ncols).map(|i| cov[(i, i)].sqrt()).collect();
        let z_statistics: Vec<f64> = coefficients
            .iter()
            .zip(std_errors.iter())
            .map(|(coef, se)| coef / se)
            .collect();
        let normal = Normal::new(0.0, 1.0)
            .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
        let p_values = z_statistics
            .iter()
            .map(|z| 2.0 * (1.0 - normal.cdf(z.abs())))
            .collect::<Vec<_>>();

        let log_likelihood = binary_log_likelihood(y, probabilities.as_slice());
        let y_mean = y.iter().sum::<f64>() / n as f64;
        let null_probs = vec![y_mean; n];
        let null_log_likelihood = binary_log_likelihood(y, &null_probs);
        let pseudo_r_squared = 1.0 - log_likelihood / null_log_likelihood;
        let n_params = ncols as f64;
        let aic = -2.0 * log_likelihood + 2.0 * n_params;
        let bic = -2.0 * log_likelihood + n_params * (n as f64).ln();

        let mut feature_names = Vec::with_capacity(ncols);
        if self.add_intercept {
            feature_names.push("const".to_string());
        }
        if self.feature_names.is_empty() {
            for i in 0..(ncols - usize::from(self.add_intercept)) {
                feature_names.push(format!("x{}", i + 1));
            }
        } else {
            feature_names.extend(self.feature_names.iter().cloned());
        }

        Ok(LogisticResult {
            coefficients,
            std_errors,
            z_statistics,
            p_values,
            covariance_matrix,
            fitted_probabilities: probabilities.iter().cloned().collect(),
            log_likelihood,
            null_log_likelihood,
            pseudo_r_squared,
            aic,
            bic,
            n,
            k: ncols - usize::from(self.add_intercept),
            feature_names,
            observed: y.to_vec(),
            design_matrix,
            iterations,
        })
    }
}

/// Poisson regression result for count outcomes with a log link.
#[derive(Debug, Clone)]
pub struct PoissonResult {
    pub coefficients: Vec<f64>,
    pub std_errors: Vec<f64>,
    pub z_statistics: Vec<f64>,
    pub p_values: Vec<f64>,
    pub covariance_matrix: Vec<Vec<f64>>,
    pub fitted_values: Vec<f64>,
    pub log_likelihood: f64,
    pub null_log_likelihood: f64,
    pub pseudo_r_squared: f64,
    pub deviance: f64,
    pub pearson_chi_squared: f64,
    pub aic: f64,
    pub bic: f64,
    pub n: usize,
    pub k: usize,
    pub feature_names: Vec<String>,
    observed: Vec<f64>,
    design_matrix: Vec<Vec<f64>>,
    iterations: usize,
}

impl PoissonResult {
    /// Predict expected counts for raw X rows, without the intercept column.
    pub fn predict(&self, x: &[Vec<f64>]) -> Vec<f64> {
        x.iter()
            .map(|row| {
                let mut eta = if self.feature_names[0] == "const" {
                    self.coefficients[0]
                } else {
                    0.0
                };
                let offset = if self.feature_names[0] == "const" {
                    1
                } else {
                    0
                };
                for (j, &value) in row.iter().enumerate() {
                    eta += self.coefficients[offset + j] * value;
                }
                eta.exp()
            })
            .collect()
    }

    /// Wald confidence intervals for coefficients at the requested alpha level.
    pub fn confidence_intervals(&self, alpha: f64) -> Result<Vec<(f64, f64)>> {
        if !(0.0..1.0).contains(&alpha) {
            return Err(InferustError::InvalidInput(
                "alpha must be between 0 and 1".into(),
            ));
        }
        let normal = Normal::new(0.0, 1.0)
            .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
        let z = normal.inverse_cdf(1.0 - alpha / 2.0);
        Ok(self
            .coefficients
            .iter()
            .zip(self.std_errors.iter())
            .map(|(coef, se)| (coef - z * se, coef + z * se))
            .collect())
    }

    /// Incidence-rate ratios, i.e. exponentiated coefficients.
    pub fn incidence_rate_ratios(&self) -> Vec<f64> {
        self.coefficients.iter().map(|coef| coef.exp()).collect()
    }

    /// Wald test of a linear restriction `R·β = q` on the Poisson coefficients.
    ///
    /// Poisson regression is asymptotic; the chi-square form is canonical.
    pub fn wald_test(
        &self,
        r: &[Vec<f64>],
        q: &[f64],
    ) -> Result<crate::hypothesis::WaldTestResult> {
        crate::hypothesis::wald_linear(&self.coefficients, &self.covariance_matrix, r, q, None)
    }

    /// Linear predictor values for raw X rows, without the intercept column.
    pub fn predict_linear(&self, x: &[Vec<f64>]) -> Vec<f64> {
        x.iter()
            .map(|row| linear_predict(row, &self.coefficients, &self.feature_names))
            .collect()
    }

    /// Response, Pearson, and deviance residuals for the training data.
    pub fn residuals(&self) -> GlmResiduals {
        let response = self
            .observed
            .iter()
            .zip(self.fitted_values.iter())
            .map(|(yi, mui)| yi - mui)
            .collect::<Vec<_>>();
        let pearson = self
            .observed
            .iter()
            .zip(self.fitted_values.iter())
            .map(|(yi, mui)| (yi - mui) / mui.max(1e-12).sqrt())
            .collect::<Vec<_>>();
        let deviance = self
            .observed
            .iter()
            .zip(self.fitted_values.iter())
            .map(|(yi, mui)| poisson_deviance_residual(*yi, *mui))
            .collect::<Vec<_>>();

        GlmResiduals {
            response,
            pearson,
            deviance,
        }
    }

    /// Null model deviance against a saturated Poisson model.
    pub fn null_deviance(&self) -> f64 {
        let mean = self.observed.iter().sum::<f64>() / self.n as f64;
        poisson_deviance(&self.observed, &vec![mean; self.n])
    }

    /// Likelihood-ratio test against the intercept-only model.
    pub fn likelihood_ratio_test(&self) -> Result<LikelihoodRatioTest> {
        likelihood_ratio_test(self.log_likelihood, self.null_log_likelihood, self.k)
    }

    /// Fitted mean confidence intervals for the training rows.
    pub fn fitted_mean_intervals(&self, alpha: f64) -> Result<Vec<PredictionInterval>> {
        prediction_intervals(
            &self.design_matrix,
            &self.coefficients,
            &self.covariance_matrix,
            alpha,
        )
    }

    /// Mean confidence intervals for raw X rows, without the intercept column.
    pub fn predict_mean_intervals(
        &self,
        x: &[Vec<f64>],
        alpha: f64,
    ) -> Result<Vec<PredictionInterval>> {
        let design = build_prediction_design(x, &self.feature_names);
        prediction_intervals(&design, &self.coefficients, &self.covariance_matrix, alpha)
    }

    /// Number of Newton/IRLS iterations used to fit the model.
    pub fn iterations(&self) -> usize {
        self.iterations
    }
}

/// Poisson regression builder for non-negative count outcomes.
pub struct Poisson {
    feature_names: Vec<String>,
    add_intercept: bool,
    max_iter: usize,
    tolerance: f64,
    offset: Option<Vec<f64>>,
    exposure: Option<Vec<f64>>,
}

impl Default for Poisson {
    fn default() -> Self {
        Self::new()
    }
}

impl Poisson {
    /// Create a new Poisson regression builder. An intercept term is added by default.
    pub fn new() -> Self {
        Self {
            feature_names: Vec::new(),
            add_intercept: true,
            max_iter: 100,
            tolerance: 1e-8,
            offset: None,
            exposure: None,
        }
    }

    /// Set human-readable names for predictor columns.
    pub fn with_feature_names(mut self, names: Vec<String>) -> Self {
        self.feature_names = names;
        self
    }

    /// Fit without an intercept.
    pub fn no_intercept(mut self) -> Self {
        self.add_intercept = false;
        self
    }

    /// Set maximum Newton iterations.
    pub fn max_iter(mut self, max_iter: usize) -> Self {
        self.max_iter = max_iter;
        self
    }

    /// Set convergence tolerance on the largest coefficient update.
    pub fn tolerance(mut self, tolerance: f64) -> Self {
        self.tolerance = tolerance;
        self
    }

    /// Add an offset term to the linear predictor.
    pub fn with_offset(mut self, offset: Vec<f64>) -> Self {
        self.offset = Some(offset);
        self
    }

    /// Add exposure values; the log exposure is used as an offset.
    pub fn with_exposure(mut self, exposure: Vec<f64>) -> Self {
        self.exposure = Some(exposure);
        self
    }

    /// Fit a Poisson regression model using Newton/IRLS updates.
    pub fn fit(&self, x: &[Vec<f64>], y: &[f64]) -> Result<PoissonResult> {
        let n = y.len();
        if n < 2 {
            return Err(InferustError::InsufficientData { needed: 2, got: n });
        }
        if x.len() != n {
            return Err(InferustError::DimensionMismatch {
                x_rows: x.len(),
                y_len: n,
            });
        }
        if let Some(value) = y.iter().find(|value| **value < 0.0 || !value.is_finite()) {
            return Err(InferustError::InvalidInput(format!(
                "poisson regression requires finite non-negative y values, got {value}"
            )));
        }
        let offset = combine_offset_exposure(n, self.offset.as_deref(), self.exposure.as_deref())?;

        let p = x[0].len();
        let ncols = if self.add_intercept { p + 1 } else { p };
        if n <= ncols {
            return Err(InferustError::InsufficientData {
                needed: ncols + 1,
                got: n,
            });
        }

        let mut design = Vec::with_capacity(n * ncols);
        for row in x {
            if row.len() != p {
                return Err(InferustError::InvalidInput(
                    "all rows in X must have the same length".into(),
                ));
            }
            if self.add_intercept {
                design.push(1.0);
            }
            design.extend_from_slice(row);
        }

        let x_mat = DMatrix::from_row_slice(n, ncols, &design);
        let y_vec = DVector::from_column_slice(y);
        let mean = (y.iter().sum::<f64>() / n as f64).max(1e-12);
        let mut beta = DVector::zeros(ncols);
        if self.add_intercept {
            beta[0] = mean.ln();
        }
        let mut hessian = DMatrix::zeros(ncols, ncols);
        let mut converged = false;
        let mut iterations = 0;

        for iter in 0..self.max_iter {
            iterations = iter + 1;
            let eta = &x_mat * &beta + DVector::from_column_slice(&offset);
            let mu = eta.map(|value| value.clamp(-700.0, 700.0).exp());
            let gradient = x_mat.transpose() * (&y_vec - &mu);
            hessian.fill(0.0);
            for i in 0..n {
                for j in 0..ncols {
                    for k in 0..ncols {
                        hessian[(j, k)] += mu[i].max(1e-12) * x_mat[(i, j)] * x_mat[(i, k)];
                    }
                }
            }

            let delta = hessian
                .clone()
                .lu()
                .solve(&gradient)
                .ok_or(InferustError::SingularMatrix)?;
            let max_delta = delta.iter().map(|v| v.abs()).fold(0.0_f64, f64::max);
            beta += delta;
            if max_delta < self.tolerance {
                converged = true;
                break;
            }
        }

        if !converged {
            return Err(InferustError::InvalidInput(format!(
                "poisson regression failed to converge in {} iterations",
                self.max_iter
            )));
        }

        let eta = &x_mat * &beta + DVector::from_column_slice(&offset);
        let fitted = eta.map(|value| value.clamp(-700.0, 700.0).exp());
        hessian.fill(0.0);
        for i in 0..n {
            for j in 0..ncols {
                for k in 0..ncols {
                    hessian[(j, k)] += fitted[i].max(1e-12) * x_mat[(i, j)] * x_mat[(i, k)];
                }
            }
        }

        let cov = hessian.try_inverse().ok_or(InferustError::SingularMatrix)?;
        let covariance_matrix: Vec<Vec<f64>> = (0..ncols)
            .map(|i| (0..ncols).map(|j| cov[(i, j)]).collect())
            .collect();
        let design_matrix: Vec<Vec<f64>> = (0..n)
            .map(|i| (0..ncols).map(|j| x_mat[(i, j)]).collect())
            .collect();
        let coefficients: Vec<f64> = beta.iter().cloned().collect();
        let std_errors: Vec<f64> = (0..ncols).map(|i| cov[(i, i)].sqrt()).collect();
        let z_statistics: Vec<f64> = coefficients
            .iter()
            .zip(std_errors.iter())
            .map(|(coef, se)| coef / se)
            .collect();
        let normal = Normal::new(0.0, 1.0)
            .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
        let p_values = z_statistics
            .iter()
            .map(|z| 2.0 * (1.0 - normal.cdf(z.abs())))
            .collect::<Vec<_>>();

        let fitted_values = fitted.iter().cloned().collect::<Vec<_>>();
        let log_likelihood = poisson_log_likelihood(y, &fitted_values);
        let null_fitted = vec![mean; n];
        let null_log_likelihood = poisson_log_likelihood(y, &null_fitted);
        let pseudo_r_squared = 1.0 - log_likelihood / null_log_likelihood;
        let deviance = poisson_deviance(y, &fitted_values);
        let pearson_chi_squared = y
            .iter()
            .zip(fitted_values.iter())
            .map(|(yi, mui)| (yi - mui).powi(2) / mui.max(1e-12))
            .sum();
        let n_params = ncols as f64;
        let aic = -2.0 * log_likelihood + 2.0 * n_params;
        let bic = -2.0 * log_likelihood + n_params * (n as f64).ln();

        let mut feature_names = Vec::with_capacity(ncols);
        if self.add_intercept {
            feature_names.push("const".to_string());
        }
        if self.feature_names.is_empty() {
            for i in 0..(ncols - usize::from(self.add_intercept)) {
                feature_names.push(format!("x{}", i + 1));
            }
        } else {
            feature_names.extend(self.feature_names.iter().cloned());
        }

        Ok(PoissonResult {
            coefficients,
            std_errors,
            z_statistics,
            p_values,
            covariance_matrix,
            fitted_values,
            log_likelihood,
            null_log_likelihood,
            pseudo_r_squared,
            deviance,
            pearson_chi_squared,
            aic,
            bic,
            n,
            k: ncols - usize::from(self.add_intercept),
            feature_names,
            observed: y.to_vec(),
            design_matrix,
            iterations,
        })
    }
}

/// Link function for [`Gamma`] regression.
///
/// `InversePower` (`g(mu) = 1/mu`) is the canonical link for the Gamma
/// family and is the default here, matching
/// `statsmodels.genmod.families.Gamma()`'s default link. `Log`
/// (`g(mu) = ln(mu)`) is the most common choice in applied work (e.g. cost,
/// claim-size, or duration models) because it keeps the mean strictly
/// positive for any linear predictor. `Identity` (`g(mu) = mu`) is supported
/// for completeness but offers no positivity guarantee and can be
/// numerically fragile far from convergence.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum GammaLink {
    Log,
    Identity,
    InversePower,
}

impl GammaLink {
    fn linkfun(&self, mu: f64) -> f64 {
        match self {
            GammaLink::Log => mu.ln(),
            GammaLink::Identity => mu,
            GammaLink::InversePower => 1.0 / mu,
        }
    }

    fn linkinv(&self, eta: f64) -> f64 {
        match self {
            GammaLink::Log => eta.clamp(-700.0, 700.0).exp(),
            GammaLink::Identity => eta,
            GammaLink::InversePower => 1.0 / eta,
        }
    }

    /// Returns `(mu, dmu/deta)` at the given linear predictor. `mu` is
    /// floored away from zero/negative values for numerical stability
    /// during IRLS before convergence; the derivative is recomputed from
    /// the floored `mu` so the two stay consistent.
    fn mu_and_derivative(&self, eta: f64) -> (f64, f64) {
        match self {
            GammaLink::Log => {
                let mu = eta.clamp(-700.0, 700.0).exp().max(1e-8);
                (mu, mu)
            }
            GammaLink::Identity => (eta.max(1e-8), 1.0),
            GammaLink::InversePower => {
                let mu = (1.0 / eta).max(1e-8);
                (mu, -mu * mu)
            }
        }
    }
}

/// Gamma regression result for positive, right-skewed continuous outcomes
/// (e.g. costs, durations, claim sizes).
#[derive(Debug, Clone)]
pub struct GammaResult {
    pub coefficients: Vec<f64>,
    pub std_errors: Vec<f64>,
    pub z_statistics: Vec<f64>,
    pub p_values: Vec<f64>,
    pub covariance_matrix: Vec<Vec<f64>>,
    pub fitted_values: Vec<f64>,
    pub log_likelihood: f64,
    pub null_log_likelihood: f64,
    pub pseudo_r_squared: f64,
    pub deviance: f64,
    pub pearson_chi_squared: f64,
    /// Moment (Pearson chi-squared / df_resid) estimate of the Gamma
    /// dispersion parameter; matches statsmodels' default `scale`.
    pub dispersion: f64,
    pub aic: f64,
    pub bic: f64,
    pub n: usize,
    pub k: usize,
    pub feature_names: Vec<String>,
    link: GammaLink,
    observed: Vec<f64>,
    design_matrix: Vec<Vec<f64>>,
    iterations: usize,
}

impl GammaResult {
    /// Predict the mean response for raw X rows, without the intercept column.
    pub fn predict(&self, x: &[Vec<f64>]) -> Vec<f64> {
        x.iter()
            .map(|row| {
                let eta = linear_predict(row, &self.coefficients, &self.feature_names);
                self.link.linkinv(eta)
            })
            .collect()
    }

    /// Wald confidence intervals for coefficients at the requested alpha level.
    pub fn confidence_intervals(&self, alpha: f64) -> Result<Vec<(f64, f64)>> {
        if !(0.0..1.0).contains(&alpha) {
            return Err(InferustError::InvalidInput(
                "alpha must be between 0 and 1".into(),
            ));
        }
        let normal = Normal::new(0.0, 1.0)
            .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
        let z = normal.inverse_cdf(1.0 - alpha / 2.0);
        Ok(self
            .coefficients
            .iter()
            .zip(self.std_errors.iter())
            .map(|(coef, se)| (coef - z * se, coef + z * se))
            .collect())
    }

    /// Wald test of a linear restriction `R·β = q` on the Gamma coefficients.
    ///
    /// Gamma regression is asymptotic; the chi-square form is canonical.
    pub fn wald_test(
        &self,
        r: &[Vec<f64>],
        q: &[f64],
    ) -> Result<crate::hypothesis::WaldTestResult> {
        crate::hypothesis::wald_linear(&self.coefficients, &self.covariance_matrix, r, q, None)
    }

    /// Linear predictor values for raw X rows, without the intercept column.
    pub fn predict_linear(&self, x: &[Vec<f64>]) -> Vec<f64> {
        x.iter()
            .map(|row| linear_predict(row, &self.coefficients, &self.feature_names))
            .collect()
    }

    /// Response, Pearson, and deviance residuals for the training data.
    pub fn residuals(&self) -> GlmResiduals {
        let response = self
            .observed
            .iter()
            .zip(self.fitted_values.iter())
            .map(|(yi, mui)| yi - mui)
            .collect::<Vec<_>>();
        let pearson = self
            .observed
            .iter()
            .zip(self.fitted_values.iter())
            .map(|(yi, mui)| (yi - mui) / mui.max(1e-12))
            .collect::<Vec<_>>();
        let deviance = self
            .observed
            .iter()
            .zip(self.fitted_values.iter())
            .map(|(yi, mui)| gamma_deviance_residual(*yi, *mui))
            .collect::<Vec<_>>();

        GlmResiduals {
            response,
            pearson,
            deviance,
        }
    }

    /// Null model deviance against a saturated Gamma model.
    pub fn null_deviance(&self) -> f64 {
        let mean = self.observed.iter().sum::<f64>() / self.n as f64;
        gamma_deviance(&self.observed, &vec![mean; self.n])
    }

    /// Likelihood-ratio test against the intercept-only model.
    pub fn likelihood_ratio_test(&self) -> Result<LikelihoodRatioTest> {
        likelihood_ratio_test(self.log_likelihood, self.null_log_likelihood, self.k)
    }

    /// Fitted mean confidence intervals for the training rows.
    pub fn fitted_mean_intervals(&self, alpha: f64) -> Result<Vec<PredictionInterval>> {
        gamma_prediction_intervals(
            &self.design_matrix,
            &self.coefficients,
            &self.covariance_matrix,
            alpha,
            self.link,
        )
    }

    /// Mean confidence intervals for raw X rows, without the intercept column.
    pub fn predict_mean_intervals(
        &self,
        x: &[Vec<f64>],
        alpha: f64,
    ) -> Result<Vec<PredictionInterval>> {
        let design = build_prediction_design(x, &self.feature_names);
        gamma_prediction_intervals(
            &design,
            &self.coefficients,
            &self.covariance_matrix,
            alpha,
            self.link,
        )
    }

    /// Number of IRLS iterations used to fit the model.
    pub fn iterations(&self) -> usize {
        self.iterations
    }

    /// Link function used to fit the model.
    pub fn link(&self) -> GammaLink {
        self.link
    }
}

/// Gamma regression builder for positive, right-skewed continuous outcomes.
pub struct Gamma {
    feature_names: Vec<String>,
    add_intercept: bool,
    max_iter: usize,
    tolerance: f64,
    link: GammaLink,
}

impl Default for Gamma {
    fn default() -> Self {
        Self::new()
    }
}

impl Gamma {
    /// Create a new Gamma regression builder. An intercept term is added by
    /// default, and the link defaults to [`GammaLink::InversePower`] (the
    /// canonical link, matching `statsmodels.genmod.families.Gamma()`'s
    /// default). Use [`Gamma::with_link`] to switch to `Log` (the most
    /// common choice in practice) or `Identity`.
    pub fn new() -> Self {
        Self {
            feature_names: Vec::new(),
            add_intercept: true,
            max_iter: 100,
            tolerance: 1e-8,
            link: GammaLink::InversePower,
        }
    }

    /// Set human-readable names for predictor columns.
    pub fn with_feature_names(mut self, names: Vec<String>) -> Self {
        self.feature_names = names;
        self
    }

    /// Fit without an intercept.
    pub fn no_intercept(mut self) -> Self {
        self.add_intercept = false;
        self
    }

    /// Set maximum IRLS iterations.
    pub fn max_iter(mut self, max_iter: usize) -> Self {
        self.max_iter = max_iter;
        self
    }

    /// Set convergence tolerance on the largest coefficient update.
    pub fn tolerance(mut self, tolerance: f64) -> Self {
        self.tolerance = tolerance;
        self
    }

    /// Set the link function. Defaults to [`GammaLink::InversePower`].
    pub fn with_link(mut self, link: GammaLink) -> Self {
        self.link = link;
        self
    }

    /// Fit a Gamma regression model using IRLS (Fisher scoring), matching
    /// `statsmodels.GLM(y, X, family=sm.families.Gamma(link=...)).fit()`.
    pub fn fit(&self, x: &[Vec<f64>], y: &[f64]) -> Result<GammaResult> {
        let n = y.len();
        if n < 2 {
            return Err(InferustError::InsufficientData { needed: 2, got: n });
        }
        if x.len() != n {
            return Err(InferustError::DimensionMismatch {
                x_rows: x.len(),
                y_len: n,
            });
        }
        if let Some(value) = y.iter().find(|value| **value <= 0.0 || !value.is_finite()) {
            return Err(InferustError::InvalidInput(format!(
                "gamma regression requires finite, strictly positive y values, got {value}"
            )));
        }

        let p = x[0].len();
        let ncols = if self.add_intercept { p + 1 } else { p };
        if n <= ncols {
            return Err(InferustError::InsufficientData {
                needed: ncols + 1,
                got: n,
            });
        }

        let mut design = Vec::with_capacity(n * ncols);
        for row in x {
            if row.len() != p {
                return Err(InferustError::InvalidInput(
                    "all rows in X must have the same length".into(),
                ));
            }
            if self.add_intercept {
                design.push(1.0);
            }
            design.extend_from_slice(row);
        }

        let x_mat = DMatrix::from_row_slice(n, ncols, &design);
        let y_mean = y.iter().sum::<f64>() / n as f64;

        let mut eta: Vec<f64> = y
            .iter()
            .map(|&yi| self.link.linkfun(((yi + y_mean) / 2.0).max(1e-8)))
            .collect();
        let mut beta = DVector::zeros(ncols);
        let mut converged = false;
        let mut iterations = 0;

        for iter in 0..self.max_iter {
            iterations = iter + 1;
            let mut w = vec![0.0; n];
            let mut z = vec![0.0; n];
            for i in 0..n {
                let (mu_i, dmu_deta_i) = self.link.mu_and_derivative(eta[i]);
                let safe_slope = if dmu_deta_i.abs() < 1e-12 {
                    dmu_deta_i.signum() * 1e-12
                } else {
                    dmu_deta_i
                };
                w[i] = (safe_slope * safe_slope) / (mu_i * mu_i);
                z[i] = eta[i] + (y[i] - mu_i) / safe_slope;
            }

            let new_beta = irls_weighted_solve(&x_mat, &w, &z)?;
            let max_delta = (&new_beta - &beta)
                .iter()
                .map(|v| v.abs())
                .fold(0.0_f64, f64::max);
            beta = new_beta;
            let eta_vec = &x_mat * &beta;
            eta = eta_vec
                .iter()
                .map(|&v| {
                    if matches!(self.link, GammaLink::Identity) {
                        v.max(1e-8)
                    } else {
                        v
                    }
                })
                .collect();
            if max_delta < self.tolerance {
                converged = true;
                break;
            }
        }

        if !converged {
            return Err(InferustError::InvalidInput(format!(
                "gamma regression failed to converge in {} iterations",
                self.max_iter
            )));
        }

        let fitted_values: Vec<f64> = eta
            .iter()
            .map(|&e| self.link.linkinv(e).max(1e-12))
            .collect();

        let mut w_final = vec![0.0; n];
        for i in 0..n {
            let (mu_i, dmu_deta_i) = self.link.mu_and_derivative(eta[i]);
            let safe_slope = if dmu_deta_i.abs() < 1e-12 {
                dmu_deta_i.signum() * 1e-12
            } else {
                dmu_deta_i
            };
            w_final[i] = (safe_slope * safe_slope) / (mu_i * mu_i);
        }
        let w_diag = DMatrix::from_diagonal(&DVector::from_vec(w_final));
        let xtwx = x_mat.transpose() * &w_diag * &x_mat;

        let pearson_chi_squared: f64 = y
            .iter()
            .zip(fitted_values.iter())
            .map(|(yi, mui)| (yi - mui).powi(2) / (mui * mui).max(1e-24))
            .sum();
        let df_resid = (n - ncols) as f64;
        let dispersion = pearson_chi_squared / df_resid;

        let cov_unscaled = xtwx.try_inverse().ok_or(InferustError::SingularMatrix)?;
        let covariance_matrix: Vec<Vec<f64>> = (0..ncols)
            .map(|i| {
                (0..ncols)
                    .map(|j| cov_unscaled[(i, j)] * dispersion)
                    .collect()
            })
            .collect();
        let design_matrix: Vec<Vec<f64>> = (0..n)
            .map(|i| (0..ncols).map(|j| x_mat[(i, j)]).collect())
            .collect();
        let coefficients: Vec<f64> = beta.iter().cloned().collect();
        let std_errors: Vec<f64> = (0..ncols).map(|i| covariance_matrix[i][i].sqrt()).collect();
        let z_statistics: Vec<f64> = coefficients
            .iter()
            .zip(std_errors.iter())
            .map(|(coef, se)| coef / se)
            .collect();
        let normal = Normal::new(0.0, 1.0)
            .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
        let p_values = z_statistics
            .iter()
            .map(|z| 2.0 * (1.0 - normal.cdf(z.abs())))
            .collect::<Vec<_>>();

        let log_likelihood = gamma_log_likelihood(y, &fitted_values, dispersion);
        let null_fitted = vec![y_mean; n];
        // Use the full model's dispersion for the null LL — standard GLM practice
        // (statsmodels also uses the full-model scale in GLMResults.llnull).
        let null_log_likelihood = gamma_log_likelihood(y, &null_fitted, dispersion);
        let pseudo_r_squared = 1.0 - log_likelihood / null_log_likelihood;
        let deviance = gamma_deviance(y, &fitted_values);
        let n_params = ncols as f64;
        let aic = -2.0 * log_likelihood + 2.0 * n_params;
        let bic = -2.0 * log_likelihood + n_params * (n as f64).ln();

        let mut feature_names = Vec::with_capacity(ncols);
        if self.add_intercept {
            feature_names.push("const".to_string());
        }
        if self.feature_names.is_empty() {
            for i in 0..(ncols - usize::from(self.add_intercept)) {
                feature_names.push(format!("x{}", i + 1));
            }
        } else {
            feature_names.extend(self.feature_names.iter().cloned());
        }

        Ok(GammaResult {
            coefficients,
            std_errors,
            z_statistics,
            p_values,
            covariance_matrix,
            fitted_values,
            log_likelihood,
            null_log_likelihood,
            pseudo_r_squared,
            deviance,
            pearson_chi_squared,
            dispersion,
            aic,
            bic,
            n,
            k: ncols - usize::from(self.add_intercept),
            feature_names,
            link: self.link,
            observed: y.to_vec(),
            design_matrix,
            iterations,
        })
    }
}

/// Likelihood-ratio test for nested likelihood models.
pub fn likelihood_ratio_test(
    full_log_likelihood: f64,
    restricted_log_likelihood: f64,
    df: usize,
) -> Result<LikelihoodRatioTest> {
    if df == 0 {
        return Err(InferustError::InvalidInput(
            "likelihood-ratio test degrees of freedom must be positive".into(),
        ));
    }
    let statistic = 2.0 * (full_log_likelihood - restricted_log_likelihood);
    let chi_squared = ChiSquared::new(df as f64)
        .map_err(|_| InferustError::InvalidInput("invalid chi-squared distribution".into()))?;
    Ok(LikelihoodRatioTest {
        statistic,
        df,
        p_value: 1.0 - chi_squared.cdf(statistic.max(0.0)),
    })
}

fn linear_predict(row: &[f64], coefficients: &[f64], feature_names: &[String]) -> f64 {
    let offset = usize::from(feature_names.first().is_some_and(|name| name == "const"));
    let mut eta = if offset == 1 { coefficients[0] } else { 0.0 };
    for (j, &value) in row.iter().enumerate() {
        eta += coefficients[offset + j] * value;
    }
    eta
}

fn build_prediction_design(x: &[Vec<f64>], feature_names: &[String]) -> Vec<Vec<f64>> {
    let has_intercept = feature_names.first().is_some_and(|name| name == "const");
    x.iter()
        .map(|row| {
            let mut design_row = Vec::with_capacity(row.len() + usize::from(has_intercept));
            if has_intercept {
                design_row.push(1.0);
            }
            design_row.extend_from_slice(row);
            design_row
        })
        .collect()
}

fn prediction_intervals(
    design: &[Vec<f64>],
    coefficients: &[f64],
    covariance_matrix: &[Vec<f64>],
    alpha: f64,
) -> Result<Vec<PredictionInterval>> {
    if !(0.0..1.0).contains(&alpha) {
        return Err(InferustError::InvalidInput(
            "alpha must be between 0 and 1".into(),
        ));
    }
    let normal = Normal::new(0.0, 1.0)
        .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
    let critical = normal.inverse_cdf(1.0 - alpha / 2.0);
    Ok(design
        .iter()
        .map(|row| {
            let eta = row
                .iter()
                .zip(coefficients.iter())
                .map(|(xij, coef)| xij * coef)
                .sum::<f64>();
            let se_eta = quadratic_form(row, covariance_matrix).max(0.0).sqrt();
            PredictionInterval {
                mean: eta.exp(),
                lower: (eta - critical * se_eta).exp(),
                upper: (eta + critical * se_eta).exp(),
            }
        })
        .collect())
}

/// Like [`prediction_intervals`], but applies a [`GammaLink`]-aware inverse
/// transform instead of a hardcoded `.exp()`. The two raw Wald bounds on the
/// linear-predictor scale are min/max-ordered after the inverse-link
/// transform, since `InversePower` is a decreasing link and would otherwise
/// report a "lower" bound above the "upper" bound.
fn gamma_prediction_intervals(
    design: &[Vec<f64>],
    coefficients: &[f64],
    covariance_matrix: &[Vec<f64>],
    alpha: f64,
    link: GammaLink,
) -> Result<Vec<PredictionInterval>> {
    if !(0.0..1.0).contains(&alpha) {
        return Err(InferustError::InvalidInput(
            "alpha must be between 0 and 1".into(),
        ));
    }
    let normal = Normal::new(0.0, 1.0)
        .map_err(|_| InferustError::InvalidInput("invalid normal distribution".into()))?;
    let critical = normal.inverse_cdf(1.0 - alpha / 2.0);
    Ok(design
        .iter()
        .map(|row| {
            let eta = row
                .iter()
                .zip(coefficients.iter())
                .map(|(xij, coef)| xij * coef)
                .sum::<f64>();
            let se_eta = quadratic_form(row, covariance_matrix).max(0.0).sqrt();
            let raw_low = link.linkinv(eta - critical * se_eta);
            let raw_high = link.linkinv(eta + critical * se_eta);
            PredictionInterval {
                mean: link.linkinv(eta),
                lower: raw_low.min(raw_high),
                upper: raw_low.max(raw_high),
            }
        })
        .collect())
}

fn safe_ratio(numerator: f64, denominator: f64) -> f64 {
    if denominator == 0.0 {
        0.0
    } else {
        numerator / denominator
    }
}

fn combine_offset_exposure(
    n: usize,
    offset: Option<&[f64]>,
    exposure: Option<&[f64]>,
) -> Result<Vec<f64>> {
    let mut combined = vec![0.0; n];
    if let Some(values) = offset {
        if values.len() != n {
            return Err(InferustError::DimensionMismatch {
                x_rows: values.len(),
                y_len: n,
            });
        }
        combined.copy_from_slice(values);
    }
    if let Some(values) = exposure {
        if values.len() != n {
            return Err(InferustError::DimensionMismatch {
                x_rows: values.len(),
                y_len: n,
            });
        }
        for (target, value) in combined.iter_mut().zip(values.iter()) {
            if *value <= 0.0 || !value.is_finite() {
                return Err(InferustError::InvalidInput(
                    "exposure values must be finite and positive".into(),
                ));
            }
            *target += value.ln();
        }
    }
    Ok(combined)
}

fn sigmoid(value: f64) -> f64 {
    if value >= 0.0 {
        1.0 / (1.0 + (-value).exp())
    } else {
        let exp_value = value.exp();
        exp_value / (1.0 + exp_value)
    }
}

fn binomial_deviance_residual(y: f64, probability: f64) -> f64 {
    let p = probability.clamp(1e-12, 1.0 - 1e-12);
    let contribution = if y == 0.0 {
        -2.0 * (1.0 - p).ln()
    } else {
        -2.0 * p.ln()
    };
    (y - p).signum() * contribution.sqrt()
}

fn poisson_deviance_residual(y: f64, fitted: f64) -> f64 {
    let mu = fitted.max(1e-12);
    let contribution = if y == 0.0 {
        2.0 * mu
    } else {
        2.0 * (y * (y / mu).ln() - (y - mu))
    };
    (y - mu).signum() * contribution.sqrt()
}

fn poisson_log_likelihood(y: &[f64], fitted: &[f64]) -> f64 {
    y.iter()
        .zip(fitted.iter())
        .map(|(yi, mui)| {
            let mu = mui.max(1e-12);
            if *yi == 0.0 {
                -mu
            } else {
                yi * mu.ln() - mu - statrs::function::gamma::ln_gamma(yi + 1.0)
            }
        })
        .sum()
}

fn poisson_deviance(y: &[f64], fitted: &[f64]) -> f64 {
    2.0 * y
        .iter()
        .zip(fitted.iter())
        .map(|(yi, mui)| {
            let mu = mui.max(1e-12);
            if *yi == 0.0 {
                mu
            } else {
                yi * (yi / mu).ln() - (yi - mu)
            }
        })
        .sum::<f64>()
}

fn gamma_deviance_residual(y: f64, mu: f64) -> f64 {
    let m = mu.max(1e-12);
    let contribution = 2.0 * ((y - m) / m - (y / m).ln());
    (y - m).signum() * contribution.max(0.0).sqrt()
}

fn gamma_log_likelihood(y: &[f64], fitted: &[f64], dispersion: f64) -> f64 {
    let scale = dispersion.max(1e-12);
    let shape = 1.0 / scale;
    y.iter()
        .zip(fitted.iter())
        .map(|(yi, mui)| {
            let mu = mui.max(1e-12);
            let theta = scale * mu;
            (shape - 1.0) * yi.ln()
                - yi / theta
                - shape * theta.ln()
                - statrs::function::gamma::ln_gamma(shape)
        })
        .sum()
}

fn gamma_deviance(y: &[f64], fitted: &[f64]) -> f64 {
    2.0 * y
        .iter()
        .zip(fitted.iter())
        .map(|(yi, mui)| {
            let mu = mui.max(1e-12);
            (yi - mu) / mu - (yi / mu).ln()
        })
        .sum::<f64>()
}

fn quadratic_form(vector: &[f64], matrix: &[Vec<f64>]) -> f64 {
    vector
        .iter()
        .enumerate()
        .map(|(i, left)| {
            vector
                .iter()
                .enumerate()
                .map(|(j, right)| left * matrix[i][j] * right)
                .sum::<f64>()
        })
        .sum()
}

fn binary_log_likelihood(y: &[f64], probabilities: &[f64]) -> f64 {
    y.iter()
        .zip(probabilities.iter())
        .map(|(yi, pi)| {
            let p = pi.clamp(1e-12, 1.0 - 1e-12);
            yi * p.ln() + (1.0 - yi) * (1.0 - p).ln()
        })
        .sum()
}

#[cfg(test)]
mod tests {
    use super::{Gamma, GammaLink, Logistic};

    fn assert_close(actual: f64, expected: f64, tolerance: f64) {
        assert!(
            (actual - expected).abs() <= tolerance,
            "actual {actual} differed from expected {expected} by more than {tolerance}"
        );
    }

    fn fixture() -> (Vec<Vec<f64>>, Vec<f64>) {
        (
            vec![
                vec![0.2, 1.0],
                vec![1.1, 0.9],
                vec![1.8, 1.5],
                vec![2.4, 1.9],
                vec![3.0, 2.5],
                vec![3.7, 2.9],
                vec![4.1, 3.4],
                vec![4.8, 3.8],
                vec![5.2, 4.2],
                vec![5.9, 4.8],
                vec![2.2, 3.6],
                vec![4.6, 1.2],
            ],
            vec![0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0],
        )
    }

    #[test]
    fn logistic_matches_statsmodels_reference_values() {
        let (x, y) = fixture();
        let result = Logistic::new().fit(&x, &y).unwrap();

        let expected_coefficients = [-1.7689272112231273, 5.075491023368961, -5.333429371506223];
        let expected_std_errors = [2.0497905638092466, 9.672670992764024, 12.013832575525887];
        let expected_z = [
            -0.8629794879803845,
            0.5247248693939718,
            -0.44394071067473323,
        ];
        let expected_p = [0.38814874483671213, 0.5997744663371969, 0.6570854500881999];
        let expected_covariance = [
            [4.20164135548143, 2.328115175935611, -4.294521008650565],
            [2.3281151759356806, 93.56056413425858, -115.97606208303982],
            [-4.294521008650698, -115.97606208303978, 144.33217315276696],
        ];
        let expected_ci = [
            (-5.786442892139302, 2.248588469693047),
            (-13.882595756753815, 24.033577803491738),
            (-28.88010853583104, 18.213249792818594),
        ];
        let expected_odds = [
            0.17051581819526604,
            160.05076135215282,
            0.004827486348599407,
        ];
        let expected_ame = [0.6368929483098553, -0.6692600856510365];
        let expected_ame_se = [1.1662712154590942, 1.4683077393598531];
        let expected_ame_z = [0.5460933442133759, -0.45580368999676985];
        let expected_ame_p = [0.5850017747015581, 0.6485311504206718];
        let expected_ame_ci = [
            (-1.6489566301957226, 2.9227425268154335),
            (-3.5470903730177734, 2.2085702017157005),
        ];
        let expected_linear = [
            -6.087258378055558,
            -0.9859735198728705,
            -0.6331874264183313,
            0.2787354390005561,
            0.12397243011819903,
            1.5434443978739871,
            0.9069261214684587,
            2.3263980892242415,
            2.223222749969338,
            2.576008843423878,
            -9.803192697233815,
            15.17821625046663,
        ];
        let expected_response_residuals = [
            -0.0022664797317858963,
            -0.27170811607160383,
            0.6532118497285212,
            -0.5692361727365304,
            0.46904652640209454,
            0.1760351184308543,
            -0.7123707405174255,
            0.088960152720438,
            0.09768437569027344,
            0.07069850190439753,
            -5.5271786442116135e-05,
            2.559672049873285e-07,
        ];
        let expected_pred = [
            0.0022664797317858963,
            0.27170811607160383,
            0.3467881502714788,
            0.5692361727365304,
            0.5309534735979055,
            0.8239648815691457,
            0.7123707405174255,
            0.911039847279562,
            0.9023156243097266,
            0.9293014980956025,
            5.5271786442116135e-05,
            0.999999744032795,
        ];

        for (actual, expected) in result.coefficients.iter().zip(expected_coefficients) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.std_errors.iter().zip(expected_std_errors) {
            assert_close(*actual, expected, 1e-7);
        }
        for (actual, expected) in result.z_statistics.iter().zip(expected_z) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.p_values.iter().zip(expected_p) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual_row, expected_row) in result.covariance_matrix.iter().zip(expected_covariance) {
            for (actual, expected) in actual_row.iter().zip(expected_row) {
                assert_close(*actual, expected, 1e-7);
            }
        }
        let intervals = result.confidence_intervals(0.05).unwrap();
        for ((actual_low, actual_high), (expected_low, expected_high)) in
            intervals.iter().zip(expected_ci)
        {
            assert_close(*actual_low, expected_low, 1e-7);
            assert_close(*actual_high, expected_high, 1e-7);
        }
        for (actual, expected) in result.odds_ratios().iter().zip(expected_odds) {
            assert_close(*actual, expected, 1e-7);
        }
        let marginal_effects = result.average_marginal_effects();
        for ((_, actual), expected) in marginal_effects.iter().zip(expected_ame) {
            assert_close(*actual, expected, 1e-8);
        }
        let marginal_effect_summaries = result.average_marginal_effects_summary(0.05).unwrap();
        for (i, summary) in marginal_effect_summaries.iter().enumerate() {
            assert_close(summary.effect, expected_ame[i], 1e-8);
            assert_close(summary.std_error, expected_ame_se[i], 1e-7);
            assert_close(summary.z_statistic, expected_ame_z[i], 1e-8);
            assert_close(summary.p_value, expected_ame_p[i], 1e-8);
            assert_close(summary.confidence_interval.0, expected_ame_ci[i].0, 1e-7);
            assert_close(summary.confidence_interval.1, expected_ame_ci[i].1, 1e-7);
        }
        for (actual, expected) in result.predict_linear(&x).iter().zip(expected_linear) {
            assert_close(*actual, expected, 1e-8);
        }
        let residuals = result.residuals();
        for (actual, expected) in residuals.response.iter().zip(expected_response_residuals) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.predict_proba(&x).iter().zip(expected_pred) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.fitted_probabilities.iter().zip(expected_pred) {
            assert_close(*actual, expected, 1e-8);
        }

        assert_close(result.log_likelihood, -4.562687231980299, 1e-8);
        assert_close(result.null_log_likelihood, -8.150319193022398, 1e-8);
        assert_close(result.pseudo_r_squared, 0.4401830009447385, 1e-8);
        let lr = result.likelihood_ratio_test().unwrap();
        assert_close(lr.statistic, 7.175263922084197, 1e-8);
        assert_close(lr.p_value, 0.027663761786296846, 1e-8);
        let metrics = result.classification_metrics(0.5).unwrap();
        assert_eq!(metrics.true_positives, 6);
        assert_eq!(metrics.false_positives, 2);
        assert_eq!(metrics.true_negatives, 3);
        assert_eq!(metrics.false_negatives, 1);
        assert_close(metrics.accuracy, 0.75, 1e-12);
        assert_close(metrics.precision, 0.75, 1e-12);
        assert_close(metrics.recall, 0.8571428571428571, 1e-12);
        assert_close(metrics.f1_score, 0.8, 1e-12);
        assert_close(metrics.log_loss, 0.3802239359983583, 1e-8);
        assert_close(metrics.brier_score, 0.13378879035798572, 1e-8);
        assert_close(result.deviance(), 9.125374463960599, 1e-8);
        assert_close(result.null_deviance(), 16.300638386044795, 1e-8);
        assert_close(result.aic, 15.125374463960599, 1e-8);
        assert_close(result.bic, 16.580094413324602, 1e-8);
    }

    #[test]
    fn poisson_matches_statsmodels_reference_values() {
        let x = vec![
            vec![0.2, 1.0],
            vec![0.8, 1.4],
            vec![1.2, 1.1],
            vec![1.9, 1.7],
            vec![2.4, 2.2],
            vec![2.9, 2.0],
            vec![3.4, 2.8],
            vec![3.9, 3.1],
            vec![4.5, 3.5],
            vec![5.0, 3.8],
            vec![5.5, 4.0],
            vec![6.0, 4.4],
        ];
        let y = vec![
            1.0, 2.0, 1.0, 3.0, 4.0, 3.0, 6.0, 7.0, 8.0, 11.0, 12.0, 15.0,
        ];
        let result = super::Poisson::new().fit(&x, &y).unwrap();

        let expected_coefficients = [
            -0.2951503394477173,
            -0.03616781469762084,
            0.7449321063132242,
        ];
        let expected_std_errors = [0.6980807376733295, 0.5907644630566597, 0.9402699551201388];
        let expected_z = [
            -0.4228025835971919,
            -0.06122205542033766,
            0.7922534398305259,
        ];
        let expected_p = [0.6724393025092453, 0.951182364991655, 0.42821291425600383];
        let expected_covariance = [
            [0.4873167163105398, 0.32659752549853693, -0.5651175404455193],
            [
                0.32659752549853693,
                0.34900265081062354,
                -0.5508529831108175,
            ],
            [-0.5651175404455193, -0.5508529831108175, 0.8841075885016277],
        ];
        let expected_linear = [
            0.4425482039259827,
            0.7188203576326999,
            0.48087359985968436,
            0.902515393359284,
            1.256897539167086,
            1.0898272105556306,
            1.6676889882573995,
            1.873084712802556,
            2.1493568665092733,
            2.35475259105443,
            2.4856551049682647,
            2.7655440401447446,
        ];
        let expected_response_residuals = [
            -0.5566688785565874,
            -0.05201114305546595,
            -0.6174868214186802,
            0.5342022317773867,
            0.4854990456962174,
            0.0262398062036433,
            0.7000945103509153,
            0.4916581684379562,
            -0.5793389622864833,
            0.4644780431553919,
            -0.00898482411281698,
            -0.8876811761915047,
        ];
        let expected_pearson_residuals = [
            -0.4461684129371736,
            -0.03630835232263843,
            -0.48552021604909407,
            0.34019425128753666,
            0.25897422840882695,
            0.015216250570567455,
            0.30410433403511294,
            0.19272057444436014,
            -0.1977906800668425,
            0.14309918507623465,
            -0.002592724859328783,
            -0.22270335129661484,
        ];
        let expected_deviance_residuals = [
            -0.4777461138106821,
            -0.036463376419548,
            -0.5227106686475718,
            0.32890258177487897,
            0.25333078026564637,
            0.015193954968615907,
            0.2977528353282894,
            0.19036746219532374,
            -0.2000818015261937,
            0.14206657613918533,
            -0.002593048262055297,
            -0.22482700261973126,
        ];
        let expected_mean_intervals = [
            (1.5566688785565874, 0.7014041924113672, 3.454809685604827),
            (2.052011143055466, 0.9609052431530584, 4.382065517102281),
            (1.6174868214186802, 0.7649370758304063, 3.420233768408888),
            (2.4657977682226133, 1.5050447932288815, 4.039852276241836),
            (3.5145009543037826, 2.365579136396782, 5.221434687074627),
            (2.9737601937963567, 1.230323142905119, 7.187745545716136),
            (5.299905489649085, 3.98531735487219, 7.0481208139855465),
            (6.508341831562044, 5.078173204356604, 8.341289611807781),
            (8.579338962286483, 6.6635219182387155, 11.04596907355292),
            (10.535521956844608, 8.125372043959194, 13.660571147099128),
            (12.008984824112817, 8.838022127500595, 16.317646010075826),
            (15.887681176191505, 11.389976627471619, 22.16145137185786),
        ];
        let expected_pred = [
            1.5566688785565874,
            2.052011143055466,
            1.6174868214186802,
            2.4657977682226133,
            3.5145009543037826,
            2.9737601937963567,
            5.299905489649085,
            6.508341831562044,
            8.579338962286483,
            10.535521956844608,
            12.008984824112817,
            15.887681176191505,
        ];

        for (actual, expected) in result.coefficients.iter().zip(expected_coefficients) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.std_errors.iter().zip(expected_std_errors) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.z_statistics.iter().zip(expected_z) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.p_values.iter().zip(expected_p) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual_row, expected_row) in result.covariance_matrix.iter().zip(expected_covariance) {
            for (actual, expected) in actual_row.iter().zip(expected_row) {
                assert_close(*actual, expected, 1e-8);
            }
        }
        for (actual, expected) in result.predict_linear(&x).iter().zip(expected_linear) {
            assert_close(*actual, expected, 1e-8);
        }
        let residuals = result.residuals();
        for (actual, expected) in residuals.response.iter().zip(expected_response_residuals) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in residuals.pearson.iter().zip(expected_pearson_residuals) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in residuals.deviance.iter().zip(expected_deviance_residuals) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.predict(&x).iter().zip(expected_pred) {
            assert_close(*actual, expected, 1e-8);
        }
        for (actual, expected) in result.fitted_values.iter().zip(expected_pred) {
            assert_close(*actual, expected, 1e-8);
        }

        assert_close(result.log_likelihood, -20.660966448471754, 1e-8);
        assert_close(result.null_log_likelihood, -39.7471753812529, 1e-8);
        assert_close(result.pseudo_r_squared, 0.48019032169474163, 1e-8);
        let mean_intervals = result.fitted_mean_intervals(0.05).unwrap();
        for (actual, expected) in mean_intervals.iter().zip(expected_mean_intervals) {
            assert_close(actual.mean, expected.0, 1e-8);
            assert_close(actual.lower, expected.1, 1e-8);
            assert_close(actual.upper, expected.2, 1e-8);
        }
        let lr = result.likelihood_ratio_test().unwrap();
        assert_close(lr.statistic, 38.172417865562295, 1e-8);
        assert_close(lr.p_value, 5.140019658986294e-09, 1e-14);
        assert_close(result.deviance, 0.9110476849677485, 1e-8);
        assert_close(result.null_deviance(), 39.08346555053005, 1e-8);
        assert_close(result.pearson_chi_squared, 0.8579684437989112, 1e-8);
        assert_close(result.aic, 47.32193289694351, 1e-8);
        assert_close(result.bic, 48.77665284630751, 1e-8);
    }

    fn gamma_fixture() -> (Vec<Vec<f64>>, Vec<f64>) {
        (
            vec![
                vec![1.0, 0.5],
                vec![1.5, 0.8],
                vec![2.0, 1.2],
                vec![2.5, 0.6],
                vec![3.0, 1.5],
                vec![3.5, 2.0],
                vec![4.0, 1.1],
                vec![4.5, 2.4],
                vec![5.0, 1.8],
                vec![5.5, 2.7],
                vec![6.0, 2.1],
                vec![6.5, 3.0],
                vec![7.0, 2.5],
                vec![7.5, 3.3],
                vec![8.0, 2.9],
            ],
            vec![
                2.1, 3.4, 3.9, 4.5, 6.0, 8.1, 6.5, 10.2, 8.8, 12.5, 10.1, 14.8, 12.0, 16.5, 14.1,
            ],
        )
    }

    #[test]
    fn gamma_inverse_power_link_matches_statsmodels_reference_values() {
        let (x, y) = gamma_fixture();
        // Default link is InversePower (canonical), matching
        // `statsmodels.genmod.families.Gamma()`'s default.
        let result = Gamma::new().fit(&x, &y).unwrap();
        assert_eq!(result.link(), GammaLink::InversePower);

        let expected_coefficients = [
            0.27071028532791985,
            -0.009524975806982212,
            -0.04584071004624713,
        ];
        let expected_std_errors = [
            0.02457540732893319,
            0.007274298836052154,
            0.018165634336352685,
        ];
        let expected_z = [11.015495356986674, -1.3094012250054228, -2.5234852357735544];
        let expected_p = [
            3.2176180916993663e-28,
            0.19039847674504373,
            0.011619793983778806,
        ];
        let expected_covariance = [
            [
                0.0006039506453829831,
                -2.8015988801935685e-05,
                -0.00014569634712167863,
            ],
            [
                -2.8015988801935685e-05,
                5.2915423556189725e-05,
                -0.00011559287061448562,
            ],
            [
                -0.00014569634712167863,
                -0.00011559287061448562,
                0.0003299902708420756,
            ],
        ];
        let expected_ci = [
            (0.2225433720578091, 0.3188771985980306),
            (-0.023782339538426067, 0.0047323879244616455),
            (-0.08144469910182256, -0.010236720990671702),
        ];
        let expected_linear = [
            0.2382649544978141,
            0.21975025358044886,
            0.19665148165845886,
            0.21939341978271604,
            0.17337429283760253,
            0.14569144991098787,
            0.18218560104911918,
            0.11783019008550678,
            0.14057212820976395,
            0.09455300126465044,
            0.1172949393889076,
            0.07127581244379408,
            0.08943367956342656,
            0.04799862362293773,
            0.061572419737945486,
        ];
        let expected_fitted = [
            4.197008335143867,
            4.550620459848106,
            5.085138395940408,
            4.558021844913968,
            5.767867794198804,
            6.863820770614633,
            5.488907983075947,
            8.486789330258416,
            7.1137857321743345,
            10.57607888300696,
            8.525517001925902,
            14.030004930334107,
            11.181469943778819,
            20.833930736341298,
            16.24103785844437,
        ];
        let expected_response_residuals = [
            -2.0970083351438666,
            -1.1506204598481058,
            -1.1851383959404083,
            -0.058021844913968224,
            0.23213220580119565,
            1.2361792293853666,
            1.011092016924053,
            1.7132106697415832,
            1.6862142678256662,
            1.9239211169930392,
            1.5744829980740978,
            0.7699950696658941,
            0.8185300562211815,
            -4.333930736341298,
            -2.141037858444369,
        ];
        let expected_pearson_residuals = [
            -0.4996435955545903,
            -0.2528491378264739,
            -0.23305922153201053,
            -0.012729610977777877,
            0.04024575702561511,
            0.18010074427900172,
            0.18420640681927478,
            0.20186793887216914,
            0.23703472824592278,
            0.18191251580813053,
            0.18467888782796685,
            0.054882024168152424,
            0.07320415476111866,
            -0.20802271022152735,
            -0.1318288816949686,
        ];
        let expected_deviance_residuals = [
            -0.6209525425378858,
            -0.2779892768407318,
            -0.2541120657111918,
            -0.012784029983197194,
            0.039718181116480705,
            0.1702993419726945,
            0.1739744548336747,
            0.189689096270078,
            0.22053371922391035,
            0.17192215251140958,
            0.17439685030802043,
            0.053908977472835455,
            0.07149047241292979,
            -0.2244987834240372,
            -0.13811271593969068,
        ];
        let expected_mean_intervals = [
            (4.197008335143867, 3.5902799663252694, 5.050502547621352),
            (4.550620459848106, 3.908235338413849, 5.4457168918590915),
            (5.085138395940408, 4.364762802763695, 6.090303154154011),
            (4.558021844913968, 3.873153341369027, 5.537120563766771),
            (5.767867794198804, 5.013518311231344, 6.789425817328888),
            (6.863820770614633, 5.827029935479827, 8.349413936197664),
            (5.488907983075947, 4.641495860726754, 6.714860672593247),
            (8.486789330258416, 7.142886961412085, 10.453584741209449),
            (7.1137857321743345, 6.20383695145881, 8.336550634734538),
            (10.57607888300696, 8.902676916644284, 13.024184857803403),
            (8.525517001925902, 7.288807911537129, 10.267653851988971),
            (14.030004930334107, 11.515898182957502, 17.948439423457174),
            (11.181469943778819, 9.232460417669897, 14.173566926484623),
            (20.833930736341298, 15.51871537879328, 31.686758528502992),
            (16.24103785844437, 12.19058053569271, 24.32244264826881),
        ];

        for (actual, expected) in result.coefficients.iter().zip(expected_coefficients) {
            assert_close(*actual, expected, 1e-6);
        }
        for (actual, expected) in result.std_errors.iter().zip(expected_std_errors) {
            assert_close(*actual, expected, 1e-6);
        }
        for (actual, expected) in result.z_statistics.iter().zip(expected_z) {
            assert_close(*actual, expected, 1e-5);
        }
        for (actual, expected) in result.p_values.iter().zip(expected_p) {
            assert_close(*actual, expected, 1e-5);
        }
        for (actual_row, expected_row) in result.covariance_matrix.iter().zip(expected_covariance) {
            for (actual, expected) in actual_row.iter().zip(expected_row) {
                assert_close(*actual, expected, 1e-6);
            }
        }
        let intervals = result.confidence_intervals(0.05).unwrap();
        for ((actual_low, actual_high), (expected_low, expected_high)) in
            intervals.iter().zip(expected_ci)
        {
            assert_close(*actual_low, expected_low, 1e-6);
            assert_close(*actual_high, expected_high, 1e-6);
        }
        for (actual, expected) in result.predict_linear(&x).iter().zip(expected_linear) {
            assert_close(*actual, expected, 1e-6);
        }
        for (actual, expected) in result.predict(&x).iter().zip(expected_fitted) {
            assert_close(*actual, expected, 1e-6);
        }
        for (actual, expected) in result.fitted_values.iter().zip(expected_fitted) {
            assert_close(*actual, expected, 1e-6);
        }
        let residuals = result.residuals();
        for (actual, expected) in residuals.response.iter().zip(expected_response_residuals) {
            assert_close(*actual, expected, 1e-6);
        }
        for (actual, expected) in residuals.pearson.iter().zip(expected_pearson_residuals) {
            assert_close(*actual, expected, 1e-6);
        }
        for (actual, expected) in residuals.deviance.iter().zip(expected_deviance_residuals) {
            assert_close(*actual, expected, 1e-6);
        }
        let mean_intervals = result.fitted_mean_intervals(0.05).unwrap();
        for (actual, expected) in mean_intervals.iter().zip(expected_mean_intervals) {
            assert_close(actual.mean, expected.0, 1e-5);
            assert_close(actual.lower, expected.1, 1e-5);
            assert_close(actual.upper, expected.2, 1e-5);
        }

        assert_close(result.log_likelihood, -30.02219819989074, 1e-5);
        assert_close(result.null_log_likelihood, -62.92429434743555, 1e-5);
        assert_close(result.pseudo_r_squared, 0.5228838318929152, 1e-5);
        assert_close(result.deviance, 0.8105234362486319, 1e-6);
        assert_close(result.null_deviance(), 4.480208396442844, 1e-6);
        assert_close(result.pearson_chi_squared, 0.6692008212008194, 1e-6);
        assert_close(result.dispersion, 0.05576673510006824, 1e-6);
        assert_close(result.aic, 66.04439639978148, 1e-5);
        assert_close(result.bic, 68.16854700308811, 1e-5);
        let lr = result.likelihood_ratio_test().unwrap();
        assert_close(lr.statistic, 65.80419229508962, 1e-4);
        assert_close(lr.p_value, 5.10702591327572e-15, 1e-12);
    }

    #[test]
    fn gamma_log_link_matches_statsmodels_reference_values() {
        let (x, y) = gamma_fixture();
        let result = Gamma::new().with_link(GammaLink::Log).fit(&x, &y).unwrap();
        assert_eq!(result.link(), GammaLink::Log);

        let expected_coefficients = [0.8279544833007723, 0.12756958824671266, 0.3406066677268939];
        let expected_std_errors = [
            0.09433281030458336,
            0.04352065619887482,
            0.10677437685161423,
        ];
        let expected_fitted = [
            3.0827664916543105,
            3.6393103516014667,
            4.445185769769005,
            3.8622211851875705,
            5.593321236422364,
            7.068592486930868,
            5.545019684701075,
            9.20248570562508,
            7.9956242752252695,
            11.5793717948082,
            10.060793265653698,
            14.570177607604567,
            13.097983281057228,
            18.333470872083517,
            17.052051612722178,
        ];

        for (actual, expected) in result.coefficients.iter().zip(expected_coefficients) {
            assert_close(*actual, expected, 1e-6);
        }
        for (actual, expected) in result.std_errors.iter().zip(expected_std_errors) {
            assert_close(*actual, expected, 1e-6);
        }
        for (actual, expected) in result.fitted_values.iter().zip(expected_fitted) {
            assert_close(*actual, expected, 1e-6);
        }
        assert_close(result.log_likelihood, -22.72952575327173, 1e-5);
        assert_close(result.null_log_likelihood, -112.19784334734219, 1e-4);
        assert_close(result.pseudo_r_squared, 0.797415662590718, 1e-5);
        assert_close(result.deviance, 0.30565773351695225, 1e-6);
        assert_close(result.null_deviance(), 4.480208396442844, 1e-6);
        assert_close(result.pearson_chi_squared, 0.2799572480081527, 1e-6);
        assert_close(result.dispersion, 0.023329770667346067, 1e-6);
        assert_close(result.aic, 51.45905150654346, 1e-5);
        assert_close(result.bic, 53.58320210985009, 1e-5);
    }

    #[test]
    fn gamma_identity_link_converges_on_well_behaved_data() {
        let (x, y) = gamma_fixture();
        let result = Gamma::new()
            .with_link(GammaLink::Identity)
            .fit(&x, &y)
            .unwrap();
        assert_eq!(result.link(), GammaLink::Identity);
        // All fitted means should stay strictly positive, since the
        // underlying data is comfortably away from zero.
        assert!(result.fitted_values.iter().all(|&mu| mu > 0.0));
        assert!(result.dispersion > 0.0);
    }

    #[test]
    fn gamma_rejects_non_positive_y() {
        let (x, mut y) = gamma_fixture();
        y[0] = 0.0;
        assert!(Gamma::new().fit(&x, &y).is_err());
    }

    #[test]
    fn gamma_rejects_dimension_mismatch() {
        let (x, y) = gamma_fixture();
        assert!(Gamma::new().fit(&x[..x.len() - 1], &y).is_err());
    }
}