scat {mgcv} R Documentation

## 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)/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",min.df=3)
```

### Arguments

 `theta` the parameters to be estimated nu = b + exp(theta_1) (where ‘b’ is `min.df`) and sig = exp(theta_2). If supplied and both 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"`. `min.df` minimum degrees of freedom. Should not be set to 2 or less as this implies infinite response variance.

### 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.

### Value

An object of class `extended.family`.

### Author(s)

Natalya Pya (nat.pya@gmail.com)

### 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 http://dx.doi.org/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