R: GAM scaled t family for heavy tailed data

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)

### 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

    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 1.8-17 Index]