This is a good example where you want to include main effects in the model, however, because the lack of observed main effect is surely coincidental

To that point, if I were doing ML, I might do full range optiminzation on log variance in my target function to avoid minimization to negative values. Why not?

I dont mean to sound like “Bayes is better, you suck” kind of guy. I see this as a constrained optimization problem and I am not sure why negative variances are allowed in optimization. It is assuredly my lack of understanding. But maybe u Bluesky’ers can help? Why not constrain solutions?

I am a Bayesian, we dont have these issues. I suspect ppl encounter this a lot and it affects what they do and conclude. This effect is kind of weird to me; why dont the programs just use properly constrained optimization?

Computer modern latex font. It's the best because it shows you use latex.

Nice find.

I cant tell you how disconcerting hallucination on a Google search is. By 2008, we had witnessed the end of bullshit. Whenever someone was just bullshitting, we had smart phones and could call them out. Now, the smart phones are full of bullshit.