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GlmSummary

What a generalized linear fit reports, at statsmodels parity.

public sealed class GlmSummary

Properties — the per-parameter lists are parallel and in the design's own order, intercept first when one was fitted: Coefficients, StandardErrors, ZStatistics, PValues, ConfidenceLower and ConfidenceUpper. Deviance and NullDeviance are twice the log-likelihood gap to a saturated fit, for the fitted model and for the intercept-only one. Dispersion is the scale: for Gamma it is estimated as Pearson's χ² over the residual degrees of freedom, as statsmodels estimates it, and it multiplies the covariance behind StandardErrors; the other three families have no free dispersion and report 1. LogLikelihood is the fitted log-likelihood and Akaike is 2k - 2 logL. ResidualDegreesOfFreedom is rows less parameters, and HasIntercept says whether a column of ones was fitted. Converged says whether IRLS reached the tolerance — read this first — Iterations is how many it took, and DevianceChange is the absolute deviance change at the last one, which is what stays large on a fit Converged reports false for.

Example — the whole-model half of the table, on the separable design that does not converge within its budget.

using Lodestar.Stats.Regression;

double[] design = [-2.0, -1.0, 1.0, 2.0];
double[] response = [0.0, 0.0, 1.0, 1.0];

GlmSummary fit = GeneralizedLinearModel.Fit(
    design, response, 1, GlmFamily.Binomial,
    new GlmOptions { MaximumIterations = 15, ThrowOnNonConvergence = false });

bool converged = fit.Converged;               // => False
int iterations = fit.Iterations;               // => 15
double stillMoving = fit.DevianceChange;       // => 1.8272381600430005E-06

Remarks — there is no public constructor. A summary is what GeneralizedLinearModel.Fit returns, and the arithmetic between the lists is the invariant that makes it one: ZStatistics[j] is Coefficients[j] / StandardErrors[j], and PValues[j] is the two-sided normal tail read off it through the chi-square(1) distribution z² follows.

A Converged of false does not mean the numbers are missing — it means they should not be trusted. The design above separates perfectly: every y = 1 sits above every y = 0, so the logit slope keeps growing without bound and IRLS exhausts its 15-iteration budget rather than reaching Tolerance. The standard errors on that fit are in the hundreds, which is the table telling you it is not usable, not a bug.

Applies to — net10.0, netstandard2.0.

See also — GeneralizedLinearModel, GlmOptions, GlmFamily.