Weight-aware gamma location-scale family

A gamma location-scale family for distributional regression of a positive, right-skewed response, with a (log) mean and a log scale each modelled by its own linear predictor. It is a weight-aware, metadata-carrying adaptation of mgcv's gammals: unlike gammals it honours prior weights (needed for a weighted MLE and for EM mixtures), and it carries the circlss parameter metadata so circ_gam treats it as a first-class location-scale family.

Usage

gammalss(link = list("identity", "log"), b = -7)

Arguments

link: Two-element list of link names, following gammals: "identity" for the (log) mean and "log" for the log scale.
b: The log-scale link's offset, as in gammals.

Value

An object of class c("general.family", "extended.family", "family") for use with gam (or its front end circ_gam).

Details

This is the positive-response member of the circlss linear-circular (l~c) leg: a positive, skewed quantity that varies around a cycle – rainfall by season, a concentration or rate by time of day, a speed by direction – over a circular covariate fitted with a cyclic smooth. As for gausslss, circ_gam places the fitted mean on the "can".

The parameterization follows gammals: a (log) mean and a log scale. At unit weights the fit matches gammals; integer prior weights reproduce a row-replicated fit. Log-likelihood derivatives up to fourth order are implemented, so the family supports full Newton REML (method = "REML"); optimizer = "efs" also works.

This family adapts GPL-licensed code from mgcv; see the package's inst/COPYRIGHTS.

Examples

library(mgcv)
set.seed(1); n <- 300
phi <- runif(n, -pi, pi)                       # circular covariate (radians)
y <- rgamma(n, shape = 4, rate = 4 / exp(0.4 + 0.8 * sin(phi)))
b <- circ_gam(list(y ~ s(phi, bs = "cc"), ~ s(phi, bs = "cc")),
              data = data.frame(y, phi), family = gammalss())
head(predict(b, type = "response"))            # columns named mu, scale