What’s the difference between fixed and random effects?

I was a tad confused by these “fixed” and “random” terms that get bandied about. Luckily Gelman (2005, p. 21) came to the rescue.

We prefer to sidestep the overloaded terms “fixed” and “random” with a cleaner distinction […]. We define effects (or coefficients) in a multilevel model as constant if they are identical for all groups in a population and varying if they are allowed to differ from group to group.

Gelman A. (2005). Analysis of variance—why it is more important than ever. Annals of Statistics, 33(1), 1–53

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