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.

From the paper


Now, I might have a stupid 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!

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

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