mgcv (version 1.8-17)

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.

References

Wood, S.N., N. Pya and B. Saefken (2016), Smoothing parameter and model selection for general smooth models. Journal of the American Statistical Association. http://arxiv.org/abs/1511.03864

Examples

# NOT RUN {
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)

# }