Families and links

Response families define the variance function and the weight semantics; links map the linear predictor to the mean. estimate_theta() and estimate_p() estimate the extra parameter those families carry and return the profile results listed here.

superglm.families	Convenience constructors for distribution families.
superglm.Poisson	Poisson distribution.
superglm.Gaussian	Gaussian distribution.
superglm.Gamma	Gamma distribution.
superglm.Binomial	Binomial (Bernoulli) distribution.
superglm.NegativeBinomial	Negative binomial (NB2) family with overdispersion controlled by theta.
superglm.Tweedie	Tweedie distribution.
superglm.LogLink	Log link: eta = log(mu), mu = exp(eta).
superglm.LogitLink	Logit link: eta = log(mu / (1-mu)), mu = expit(eta).
superglm.IdentityLink	Identity link: eta = mu, mu = eta.
superglm.ProbitLink	Probit link: eta = Phi^{-1}(mu), mu = Phi(eta).
superglm.CloglogLink	Complementary log-log link: eta = log(-log(1 - mu)).
superglm.CauchitLink	Cauchit link: eta = tan(pi*(mu - 0.5)), mu = 0.5 + arctan(eta)/pi.
superglm.InverseLink	Inverse (reciprocal) link: eta = 1/mu, mu = 1/eta.
superglm.InverseSquaredLink	Inverse-squared link: eta = 1/mu^2, mu = 1/sqrt(eta).
superglm.SqrtLink	Square-root link: eta = sqrt(mu), mu = eta^2.
superglm.PowerLink	Power link: eta = mu^p, mu = eta^(1/p).
superglm.NegativeBinomialLink	Negative binomial link: eta = log(mu / (mu + theta)).
superglm.NBProfileResult	Profile-likelihood estimate of the NB2 shape theta.
superglm.TweedieProfileResult	Profile-likelihood estimate of the Tweedie power p and dispersion phi.
superglm.tweedie_logpdf	Row log densities of Tweedie(mu, phi / w, p), 1 < p < 2 (Dunn & Smyth 2005).
superglm.generate_tweedie_cpg	Simulate Tweedie(mu, phi, p) as compound Poisson-gamma: N ~ Poisson, Y | N ~ Gamma.