An example of multilevel modeling :
Consider an educational study with data from students in many schools,predicting in each school the students’ grades y on a standardized test given their scores on a pre-test x and other information. Assume just one student-level predictor x (for example, a pre-test score) and one school-level predictor u (for example, average parents’ incomes).
We write the model in which the regressions have the same slope in each of the schools, and only the intercepts vary.
By varying intercept , I understood the deviation of jth school average score $(\bar y_j)$ from overall mean score $(\bar y)$ .
- What is meant by same slope in this example , that is , what is the interpretation of same slope in this example ? Will the interpretation include group level variable ?