Enum LikelihoodScaleMetadata 

pub enum LikelihoodScaleMetadata {
    ProfiledGaussian,
    FixedDispersion {
        phi: f64,
    },
    FixedGammaShape {
        shape: f64,
    },
    EstimatedGammaShape {
        shape: f64,
    },
    EstimatedBetaPhi {
        phi: f64,
    },
    FixedBetaPhi {
        phi: f64,
    },
    EstimatedTweediePhi {
        phi: f64,
    },
    EstimatedNegBinTheta {
        theta: f64,
    },
    FixedNegBinTheta {
        theta: f64,
    },
    Unspecified,
}

How a likelihood’s scale parameter is handled by the fit/result contract.

Variants

ProfiledGaussian

Gaussian identity fits profile sigma outside the fixed-scale GLM machinery.

FixedDispersion

Fixed exponential-dispersion parameter phi.

Fields

phi: f64

FixedGammaShape

Fixed Gamma shape k, equivalent to phi = 1 / k.

Fields

shape: f64

EstimatedGammaShape

Gamma shape k estimated jointly with the mean model.

Fields

shape: f64

EstimatedBetaPhi

Beta-regression precision phi estimated jointly with the mean model. Var(y) = mu(1-mu)/(1+phi); larger phi means less noise. Estimated from the working residuals after each mean fit and refreshed across outer iterations, exactly like the Gamma shape (issue #567).

Fields

phi: f64

FixedBetaPhi

Beta-regression precision phi held FIXED for the duration of the smoothing-parameter (λ) search (#2369). Identical role to EstimatedBetaPhi in every weight / variance / covariance expression (Var(y) = mu(1-mu)/(1+phi), the digamma mean score reads phi through the same Beta { phi } family variant), but the inner solver’s per-solve Pearson refresh is gated off (its guard is beta_phi_is_estimated(), which FixedBetaPhi does not satisfy). The fixed/estimated split mirrors FixedGammaShape vs EstimatedGammaShape and FixedNegBinTheta vs EstimatedNegBinTheta. This is a transient λ-search form produced only by with_beta_phi_frozen_for_search; the single final reported fit Pearson-refreshes phi at the converged η and records EstimatedBetaPhi.

Fields

phi: f64

EstimatedTweediePhi

Tweedie exponential-dispersion phi estimated jointly with the mean model. Var(y) = phi · mu^p with phi a genuine free parameter (unlike Binomial/Poisson, where phi ≡ 1). Estimated by the Pearson moment estimator phî = Σ wᵢ (yᵢ − μᵢ)² / μᵢ^p / Σ wᵢ at the converged η and refreshed across outer iterations, exactly like the Gamma shape and the Beta precision. phi enters the IRLS working weight prior·μ^{2−p}/phi, so the coefficient covariance Vb = H⁻¹ already scales as phi and the reported SEs track √phi (issue #771).

Fields

phi: f64

EstimatedNegBinTheta

Negative-Binomial overdispersion theta estimated jointly with the mean model. Var(y) = mu + mu^2 / theta; larger theta means less overdispersion (the Poisson limit is theta → ∞). Estimated by the maximum-likelihood theta score Σ wᵢ[ψ(yᵢ+θ) − ψ(θ) + lnθ + 1 − ln(θ+μᵢ) − (yᵢ+θ)/(μᵢ+θ)] = 0 at the converged η (MASS glm.nb’s theta.ml) and refreshed across outer iterations, exactly like the Gamma shape / Beta precision / Tweedie φ. Unlike those, theta is not a dispersion scale phi: it enters only the IRLS working weight W = μθ/(θ+μ) (the full NB2 Fisher information), so the stored penalized Hessian is already the true one and the coefficient covariance Vb = H⁻¹ takes no post-hoc multiply — phi ≡ 1 for NB, the overdispersion lives in the variance function. The theta carried here mirrors ResponseFamily::NegativeBinomial { theta } (the canonical store every weight/deviance expression reads), kept in sync by with_negbin_theta, exactly as EstimatedBetaPhi mirrors Beta { phi } (issue #802).

Fields

theta: f64

FixedNegBinTheta

Negative-Binomial overdispersion theta held fixed at a user-supplied value (--negative-binomial-theta, issue #983). Identical role to EstimatedNegBinTheta in every weight / variance / covariance expression (W = μθ/(θ+μ), Var(y) = μ + μ²/θ, phi ≡ 1), but the inner solver’s ML refresh is gated off: the recorded theta is the user’s, by construction. The fixed/estimated split mirrors FixedGammaShape vs EstimatedGammaShape.

Fields

theta: f64

Unspecified

The engine does not expose fixed-scale semantics for this family. Family has no scalar GLM scale by model definition (currently only Royston-Parmar). This is not a missing-value fallback.

Implementations

impl LikelihoodScaleMetadata

pub const fn fixed_phi(self) -> Option<f64>

pub const fn negbin_theta(self) -> Option<f64>

The Negative-Binomial theta carried in the scale metadata (estimated or user-fixed), or None for non-NB families.

pub const fn beta_phi_is_estimated(self) -> bool

Whether the Beta-regression precision phi is estimated from data.

pub const fn tweedie_phi_is_estimated(self) -> bool

Whether the Tweedie exponential-dispersion phi is estimated from data.

pub const fn gamma_shape(self) -> Option<f64>

pub const fn gamma_shape_is_estimated(self) -> bool

pub const fn wald_scale_is_estimated(self) -> bool

Whether the dispersion φ that multiplies the coefficient covariance Vb = φ·H⁻¹ was estimated from THIS fit’s own residuals.

This is the predicate that selects a Wald/parametric reference distribution: an estimated φ̂ carries its own sampling variability, so the reference must spend n − edf denominator degrees of freedom on it (Student-t for a parametric coefficient, F_{ref_df, residual_df} for the Wood smooth test). A φ the user supplied carries none, and the reference is the known-scale normal / χ². Getting this backwards is anti-conservative in one direction and needlessly wide in the other.

It is stated here, on the metadata, and matched EXHAUSTIVELY on purpose. The two summary surfaces each wrote their own matches! and they had drifted apart (issue #2470): the in-process CLI summary keyed on this metadata, while the persisted-model summary the Python summary() reads keyed on the family name (ResponseFamily::{Gaussian, Gamma}) — so a Gamma fit with a user-pinned shape got a χ² reference from one surface and an F reference from the other for the same fitted model. A family name cannot answer this question, because FixedGammaShape and EstimatedGammaShape are the same family. Only the scale metadata can.

The exhaustive match (no wildcard arm) is the durable half of the fix: a new scale variant cannot be added without an author deciding whether its φ is estimated, which is exactly the decision both call sites were silently making by omission.

Trait Implementations

impl Clone for LikelihoodScaleMetadata

fn clone(&self) -> LikelihoodScaleMetadata

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for LikelihoodScaleMetadata

impl Debug for LikelihoodScaleMetadata

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for LikelihoodScaleMetadata

fn deserialize<__D>( __deserializer: __D, ) -> Result<LikelihoodScaleMetadata, <__D as Deserializer<'de>>::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl PartialEq for LikelihoodScaleMetadata

fn eq(&self, other: &LikelihoodScaleMetadata) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl Serialize for LikelihoodScaleMetadata

fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for LikelihoodScaleMetadata