scat {mgcv}R Documentation

GAM scaled t family for heavy tailed data

Description

Family for use with gam, implementing regression for the heavy tailed response variables, y, using a scaled t model. The idea is that (y - mu)/sig ~ t_nu where mu is determined by a linear predictor, while sig and nu are parameters to be estimated alongside the smoothing parameters.

Usage

scat(theta = NULL, link = "identity")

Arguments

theta

the parameters to be estimated nu = 2 + exp(theta_1) and sig = exp(theta_2). If supplied and positive, then taken to be fixed values of nu and sig. If any negative, then absolute values taken as starting values.

link

The link function: one of "identity", "log" or "inverse".

Details

Useful in place of Gaussian, when data are heavy tailed.

Value

An object of class extended.family.

Author(s)

Natalya Pya (nyp20@bath.ac.uk)

Examples

library(mgcv)
## Simulate some t data...
set.seed(3);n<-400
dat <- gamSim(1,n=n)
dat$y <- dat$f + rt(n,df=3)*2

b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=scat(link="identity"),data=dat)

b
plot(b,pages=1)


[Package mgcv version 1.8-0 Index]