# A simulation study of linear mixed model

I am reading this paper, a note on BIC in mixed effects models, and I was trying to repeat their simulation study. And I will paste part of the experiment settings here to clarify my question.

Now, I might have a rather basic question, but when we fitting the model, besides the observed time points and the response, what other variables are given? I was thinking since we are trying to figure out $$\beta$$, so definitely $$\beta$$ cannot be given. And we want to know whether $$\alpha_1$$ and $$\alpha_2$$ are zeros or not, i.e. $$c_i=1$$ or $$0$$, so $$C_i$$ is not given also. Then what is given? We cannot just regress $$y_{ij}$$ on the time points $$t_{ij}$$, right?

Which makes me really confused... Any help? Thanks!

• It looks like the the $c_i$ are the covariates that are to be selected. They are distributed as standard normal variates. – Robert Long Feb 1 '19 at 17:23