Good morning, Ellie and all,
My log likelihood functions have sigma^2 and
s^2 in them respectively and I can't optimize them without some values
there. Are we supposed to do random draws for sigma and then run repeated
MLEs and average them?
No, I don't think so.
You can estimate sigma^2 in the same way as beta.
Include sigma^2 as well as beta in par of llik and start.
Kentaro