mathematical formula of mixed models for repeated measures

[Sule Yaylaci]

Dear Statalist users,
I have a question about the mathematical formula of linear mixed models when we have pre-/-post test data.
The data I work with come from a randomized controlled trial, where subjects were assigned to a control and treatment group and took had pre and post-test surveys. To analyze the effect of the treatment on the dependent variable (Y), I used the command 'mixed' on long-shaped data.

 mixed Y Time##Treatment covariates || id:

Now I am trying to convert it into a formula, yet I am not sure if the formula below captures the random effect. Unfortunately, it is in linear format; I could not figure out how to paste the subscripted version:

Y_(ij= ) β_0 + β_1 G_i + β_2 T_j + β_3 G_i T_j + γX_i + ε_ij

where
Y_ij denotes the response variable scores for subject i at time j ;
β₀ is the mean response ;
Gi refers to Group—Control (0) Treatment (1) ;
Tj refers to time (pre-test (0) or post-test (1) ;
X_i is the vector of control variables all measured in time 0 (pre-test survey).


Thanks much in advance.
Regards,
Sule

[Clyde Schechter]

Your equation is missing the term for the random intercept at the id level, and should read:

Y_(ij) =  β_0 + β_1 G_i + β_2 T_j + β_3 G_i T_j + γX_i + u_i + ε_ij