sigma_from_family: Compute sigma as a function of eta for a GLM family

In RBesT: R Bayesian Evidence Synthesis Tools

Compute sigma as a function of eta for a GLM family

Description

For a GLM family with variance function V(mu), link function g, and dispersion parameter phi, the sampling standard deviation of the MLE on the link scale is: sigma(eta) = sqrt(phi * V(mu)) / |dmu/deta| where mu = linkinv(eta + offset).

Usage

sigma_from_family(eta, family, offset = 0, phi = 1)

Arguments

eta	Numeric vector of values on the link scale (parameter of interest).
family	An R family object (e.g., binomial(), MASS::negative.binomial(0.5)).
offset	Numeric scalar. Shift applied before evaluating the variance function. For NB/Poisson with log link, this is log(exposure). Default 0.
phi	Numeric scalar. Dispersion parameter. For gaussian family this is sigma^2 (user-supplied). For binomial/NB/Poisson this is 1 (the default).

Value

Numeric vector of sigma values (same length as eta).

RBesT documentation built on Sept. 18, 2026, 5:06 p.m.