| scat {mgcv} | R Documentation |
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.
scat(theta = NULL, link = "identity",min.df=3)
theta |
the parameters to be estimated nu = b + exp(theta_1) (where ‘b’ is |
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. |
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.
An object of class extended.family.
Natalya Pya (nat.pya@gmail.com)
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
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)