Extracting the degrees of freedom of t distribution of a GAM I would have a rather easy question regarding the output when fitting a GAM using the mgvz package and assuming t distributed data.
Sample code is taken from https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/scat.html
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)

summary(b) yields the output “Family: Scaled t(5.376,2.088)”.
My question is whether I am right assuming that:
•   5.376 = degrees of freedom of the t distribution (nu)
•   2.088 = sigma

The documentation is a bit confusing, but the first is nu and the second is sigma as is explained in the docs for the argument 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.

you can check this by providing those values yourself
b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),
        family=scat(theta=c(10, 2), link="identity"),
        data=dat)
summary(b)

which now outputs Family: Scaled t(10,2) 
edit: See also Simpson's answer bellow
