I'm confused about the difference between sigma and the cov-matrix when one fits a multivariate normal gam.
More precise, I used for example mvn(d=2) when fitting a two-dimensional normal GAM to model $Y_1$ and $Y_2$. The GAM fit is denoted by b in the following
From the documentation, I known that the covariance matrix of $Y_1$ and $Y_2$ can be obtained via
covMatrix <- solve(crossprod(b$family$data$R))
(code is taken from the documentation of the "Multivariate normal additive models").
What I was thinking is that $\operatorname{Var}(Y_1) =$ covMatrix [1,1] and $\operatorname{Var}(Y_2)=$ covMatrix[2,2] hold.
When bringing back everything introduced so far to the usual GAM formula, I would assume that $$Y_1 = \mu_1 + \operatorname{Var}(Y_1) \cdot \epsilon_1, \quad \epsilon_1 \sim N(0,1). \tag{*}$$
Is this so far correct, i.e. does $(*)$ hold?
And if so, what is b$sig2? I fitted various multivariate Normal GAMs and all yielded b$sig2=1 which seems a bit strange to me since the covariance matrices varied greatly.
