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GlmFamily

The response distribution a GeneralizedLinearModel fits, with the link statsmodels defaults it to.

public enum GlmFamily

Members — Binomial is a response in {0, 1}, through the logit link. Poisson is a non-negative count, through the log link. NegativeBinomial is a non-negative count whose variance μ + αμ² grows faster than its mean, through the log link, with α given by GlmOptions.NegativeBinomialAlpha; the log link is statsmodels' default for it rather than its canonical one. Gamma is a positive continuous response with variance φμ², through the inverse link by default or the log link through GlmOptions.Link, and the one family whose dispersion φ is estimated.

Example — the same design, read through each family's own link.

using Lodestar.Stats.Regression;

double[] design = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0];
double[] binomialResponse = [0.0, 0.0, 1.0, 0.0, 1.0, 1.0];

GlmSummary logit = GeneralizedLinearModel.Fit(design, binomialResponse, 1, GlmFamily.Binomial);

double onLogitScale = logit.Coefficients[1];  // => 1.2140275858506062

Example — over-dispersed counts: the negative binomial keeps a slope close to Poisson's and reports how much less sure of it the extra variance leaves the fit.

using Lodestar.Stats.Regression;

double[] x = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0];
double[] counts = [1.0, 0.0, 2.0, 3.0, 4.0, 3.0, 7.0, 6.0, 9.0, 11.0];

GlmSummary poisson = GeneralizedLinearModel.Fit(x, counts, 1, GlmFamily.Poisson);
GlmSummary negativeBinomial = GeneralizedLinearModel.Fit(
    x, counts, 1, GlmFamily.NegativeBinomial, new GlmOptions { NegativeBinomialAlpha = 0.5 });

double poissonError = Math.Round(poisson.StandardErrors[1], 4);            // => 0.0607
double widerError = Math.Round(negativeBinomial.StandardErrors[1], 4);     // => 0.1054

Remarks — closed on purpose. 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 this set rather than described by an interface (#616). Adding a member is not a breaking change, which is how NegativeBinomial (#769) and Gamma (#770) joined.

Applies to — net10.0, netstandard2.0.

See also — GeneralizedLinearModel.Fit, GlmSummary.