Exploring multiple-levels: Classrooms and schools

In the last exercise, you ignored the hierarchical structure of the data. But, students learn within classrooms and classrooms exist within schools. Aggregating student scores by classroom or school can account for this lack of independence. However, aggregation methods are important, especially for unequal group sizes.

In this exercise, you will use summary means (in pseudo-code: mean(mathgain) by school or mean(mathgain) by classroom). Another reasonable method would be to take 2 means (1st student by class, 2nd by class by school). Hierarchical models avoid aggregation by modeling this structure.

For this exercise, plot both datasets. Then, fit a linear model. How do the number of observations compare across models?

Plot housepov (x-axis) against mathgain (y-axis) using class-level data (classData). Use ggplot and add an lm smoothing line to the plot.
Repeat using the school-level data (schoolData), which has the same column names.

Take Hint (-10 XP)

Exercise

Exploring multiple-levels: Classrooms and schools

Instructions 1/3