I possess a basic understanding of random vs. fixed effects, and how to code random effects models in SAS. However, I'm having trouble wrapping my head around the derivation of random effects terms, and how a random intercept model, for example, can describe the variation in $k$ intercepts with a single parameter ($\sigma^2$ for a normal dbn) rather than $k-1$ parameters, which can amount to a huge saving in degrees of freedom. Isn't that cheating? ;)
The old school technique would be to use the maximum likelihood method to solve for $k-1$ parameters for each category.
- How does a random intercept model avoid this by using a single parameter?
- Isn't the end result the same--both random and fixed effect models will estimate $k-1$ intercept terms?