## Let’s rename “fixed” to “Population-level” and “Random” to “Varying”

I was reading this interesting preprint on ordinal regression using brms (which I recently praised in a tutorial on computing Bayes factors) by Paul Bürkner and Matt Vuorre. Now see this footnote about their vocabulary: Hallelujah and Eureka!! I think that these terms may help solve (some of) the long-standing confusion about the difference between “fixed” and “random” effects. TL;DR: The mathematical distinction is that Varying (previously “random”) parameters have an associated variance while Population-level (previously “fixed”) parameters do not. The major practical implication is that Varying parameters have shrinkage in a regression towards the mean-like way whereas the Population-level parameters do not. However, understanding which of …