Say that you are in the library of your department of statistics, and that you come across a book with the following picture in the front page.
You will probably think that this is a book about linear regression things.
What would be the picture that would make you think about linear mixed models?
For a talk, I’ve used the following picture which is based on the
sleepstudy dataset from the lme4 package. The idea was to illustrate the difference between independent regression fits from subject-specific data (gray) versus predictions from random-effects models, especially that (1) predicted values from random-effects model are shrinkage estimators and that (2) individuals trajectories share a common slope with a random-intercept only model (orange). The distributions of subject intercepts are shown as kernel density estimates on the y-axis (R code).
(The density curves extend beyond the range of observed values because there are relatively few observations.)