I am unsure how the correct mathematical notation of two mixed model I've estimated in R should look like. The data consists of test scores of students that were in different classes. Some of the students have repeated measures. So after taking a test for the first time, the students have tried different study methods and then again taken a test. Two models were estimated to see if test scores are on average different (1) and if the stuy methods had a significant effect on test score (2) The models look in R look like this:
Test_score ~ Study_method + FE1 + FE2 + FE3 + (1 | Classroom ID) Test_score ~ Study_method + FE1 + FE2 + FE3 + (1 | Classroom ID / Student_ID)
The data is structured as follows:
How is the mathematical notation of these two models? I'm especially unsure about the many subscripts and the repeated measures of some students.