Linear Mixed Models (with random intercepts, but no random slopes): Transposing from R to Algebraic form

I’m working on a psychological experiment using Linear Mixed Models (LMM). In this model, I have a random intercept for each subject, but I do not have random slopes. With this model, I want to check the effect of the (1) group the participant was assigned (group) [categorical], (2) the passing of the time (time) [treated as categorical], and (3) the interaction of these both terms (group x time) on the results of depression (value)

I’m having some trouble transposing from the R language to form a valid math equation and I’ve based the following formula on this paper, but I would like to know if something is missing.


First layer: Yij=b0+b1X1ij+b2X2ij+b3(X1∗X2)+eij

Second layer: b0=\gamma_0+Ii


The results will be published in an upcoming article and I want to be sure the equations are adequate.
Thank you.

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