mgcv (version 1.8-5)

scat: 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 $(y-\mu)/\sigma \sim t_\nu$ where $mu$ is determined by a linear predictor, while $\sigma$ 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 $\sigma = \exp(\theta_2)$. If supplied and positive, then taken to be fixed values of $\nu$ and $\sigma$. If any negative, then absolute values taken as starting values.

link

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

Value

• An object of class extended.family.

Details

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

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)