I thought I’d post it here so that more people can benefit from Paul’s answer, which I’m sure will be worthwhile to read. Me, colleagues, and friends have one question:

What is the best references to understand better how the syntax for design formulas can be used?

I’ve been using Stan and Rethinking before, but recently switched to brms. One thing I stumble upon often is how to express my models in the lme4 syntax; especially for group effects (yes, I know about response | aterms ~ pterms + (gterms | group), but there’s more.

Table 2 in [https://arxiv.org/pdf/1406.5823.pdf](Fitting linear mixed-effects models using lme4) was close to what I needed but not complete. I’ve read lots of text now, and still, I can’t seem to see the difference between several variants, e.g.,

formula = tp ~ 1 + technique + category + (1 | subject)
subject is a group effect (random) w/ fixed mean

formula = tp ~ 1 + technique + (1 + category | subject)
?!?
formula = tp ~ 1 + technique + category + (1 + category | subject)
Same as previous but here we also look at category as population effect?

where technique is A and B, category is A and B, and subject is an individual (1…35) who has used the two techniques and is categorized according to a category (low and high experience). (Yes, learning bias was accounted for in the design.)

Any input, pointers, tips would be much appreciated!

formula = tp ~ 1 + technique + category + (1 | subject) assumes the intercept (1) to vary across subjects but the effect of technique and categegory to be constant across subjects.

formula = tp ~ 1 + technique + (1 + category | subject) makes no sense since category does not appear in the “pterms” part, but in the “gterms” part.

formula = tp ~ 1 + technique + category + (1 + category | subject) assumes both the intercept and the effect of category to vary across subjects, while technique is assumed to have a constant effect across subjects.

Hmm I see. Unfortunately, I don’t know of any better reference than the lme4 JSS paper at the moment. Maybe there are some nice blog post out there about this syntax but I am currently not aware of any.

I get it… (1 | subject) is varying intercepts, while (1 + category | subject) is varying intercept and slopes. A bit more shorthand to write it this way compared to what I’ve been getting used to ;)