From answer of @Taylor and @Zhanxiong from this link In a GLM, is the log likelihood of the saturated model always zero?
Is it true that there are 2 ways to estimate the saturated model:
invert the design matrix $\mathbb{X}$ to calculate vector $\beta$ (answer of @Taylor)
using MLE method to calculate the $\theta$. (answer of @Zhanxiong)
I'm wondering if these 2 methods are equivalent and if they produce the same saturated model ? I believe they do but don't know why
(because in the 2nd way, I see that we don't have a vector of coefficients $\beta$, just the vector or parameter of the distribution $\theta$, I wonder how can we obtain the vector $\beta$ after estimating the $\theta$ ?)
Thank you very much!
