Hierarchical linear modeling

Okay kiddo, hierarchal linear modeling is a way to understand how different bits of information are related to each other.

Imagine we're trying to understand why some kids do better on a test than others. One thing that might affect this is which school they go to. But schools are made up of different classrooms, so we might also want to know if certain classrooms have better test scores than others. And then, of course, there are individual differences between kids themselves that could play a role.

So, hierarchical linear modeling is a way to take all of these factors into account at once. It's like we're stacking them up in a tower, with the biggest factors at the bottom and the smallest ones at the top. Each level affects the level above it.

At the bottom of the tower, we have individual test scores. Then we move up to classrooms, which affect the individual scores within them. And finally, at the top of the tower, we have schools, which affect the classroom scores within them.

By using this kind of model, we can see how much of the variance in test scores is due to individual differences, classroom differences, and school differences, all at the same time. It's like we're putting together a puzzle made up of lots of smaller puzzles.