mgcv (version 1.9-5)

scat: GAM scaled t family for heavy tailed data

Description

Family for use with gam or bam, 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",min.df=3)

Value

An object of class extended.family.

Details

Useful in place of Gaussian, when data are heavy tailed. min.df can be modified, but lower values can occasionally lead to convergence problems in smoothing parameter estimation. In any case min.df should be >2, since only then does a t random variable have finite variance.

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 111, 1548-1575 tools:::Rd_expr_doi("10.1080/01621459.2016.1180986")

Examples

library(mgcv)
## Simulate some t data...
set.seed(3);n<-400
dat <- gamSim(1,n=n)
dat$y <- dat$f + rt(n,df=4)*2

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

b
plot(b,pages=1)