24 Lecture 15 - 2019
24.1 Multilevel models
Most models forget things about the data as they move from one case to the other
Fixed effects: the model forgets everything between clusters. no information is passed between clusters.
Multilevel model: remember and pool information
Default should be multilevel modeling
- nearly every case is improved by multilevel modeling
- if not, it’s just as good
Why use multilevel modeling?
- deal with clustering in data (eg. classroom within schools, students within classrooms, …)
- handles imbalance in sampling
- handles pseudo replications
24.2 Varying intercepts
Example tadpole
Outcome: number surviving
Tadpoles in tanks at different densities
Model 1 index for each tank
Model 2 multilevel with varying intercepts
Untitled
Varying intercepts = random intercepts
“Random” and “varying” unclear
Distinction of varying intercepts is the prior learns from the data
Adaptive regularization
From the example, survival across tanks has some distribution. This distribution is the prior for each tank. And the distribution needs its own prior