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)/\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)
Arguments
theta |
the parameters to be estimated |
link |
The link function: one of |
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 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)