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.

**Latex:**

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

Second layer: b0=\gamma_0+Ii

**Image:**

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

Thank you.