I've fitted a non-exponential family GLM regression model with the response distributed as a t-distribution with $\nu$ degrees of freedom, scale $\theta$ and mean $\mu = X\beta$.
We estimate $\beta,\nu,$ and $\theta$.
I get $\theta = 0.6$, $\nu = 4.9$, and also my $\beta$ values.
I want to check my distributional assumption in a qqplot. In order to do so, I need to compute normalized quantile residuals. Any idea how?
I tried the following, and got good results, but I would like you to check my approach:
- First, define $F_i(y; \mu, \theta)$ as the cumulative distribution function of a scaled t-distribution with degrees of freedom 4.9 and scale 0.6 and mean parameter equal to the $i$th fitted value from my model.
- Then, take the inverse standard normal cumulative distributional function on each $F_i$.
Is that the way to do it?