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Generalized linear models — Lodestar.Stats.Regression

One entry point, GeneralizedLinearModel.Fit: it fits a response through a link function instead of an identity one, by IRLS, and reports what a statsmodels GLM(...).fit() summary holds — the same inference table OrdinaryLeastSquares.Fit reports, fitted through a link instead of directly.

Four families, all closed. GlmFamily is Binomial (a {0, 1} response, through the logit link), Poisson (a non-negative count, through the log link), NegativeBinomial (an over-dispersed count, with a given α) or Gamma (a positive, skewed response, with an estimated scale) — no interface, no caller-supplied family. GlmLink chooses Gamma's link. IRLS cannot check that a caller-supplied family is internally consistent, and an incoherent one produces a plausible inference table rather than an error, so a family is chosen from a fixed set instead. Adding a member later is not a breaking change, which is how the negative binomial (#769) and Gamma (#770) joined.

Why this is not a second package

Decision 0003 measured this against the same three criteria decision 0003 gave Lodestar.Stats.Regression its own package on — dependency profile, audience, release cadence — and found none of them distinct from the OLS half already here. The IRLS loop reuses the least-squares core OrdinaryLeastSquares.Fit does, through Internal/LeastSquares.cs, so the two share code neither one exposes publicly: the Householder reflections on every iteration, where the OLS tries the normal equations first.

Types

Type	What it is
GeneralizedLinearModel	Fits the model by IRLS and builds the table.
GlmSummary	The fitted model, its errors, its p-values and its diagnostics.
GlmOptions	The intercept, the confidence level, the IRLS budget, the link and the negative binomial's α.
GlmFamily	The response distribution: Binomial, Poisson, NegativeBinomial or Gamma.
GlmLink	The link: each family's default, Log or Inverse.

See also

• Regression inference — reading the table (written for OLS; the same reading applies once a link function stands in for the identity one).
• statsmodels → .NET — what is delegated and what is not.
• Python → C# equivalence.