I have a fairly boring and probably straightforward question regarding the syntax for a non-crossed design in brms, so let me couch it in terms that make it a little less boring.
Consider an experiment in which a person is given different combinations of coloured balls to throw at statistics faculty at a prestigious university. The balls are stored in a small bag, which is given to the thrower. In different conditions of the experiment, the thrower is first given a bag containing either 4 red balls, 4 red and 2 blue balls, 6 red balls, or 6 red and 2 blue balls. The conditions are limited to this set for practical reasons. The thrower has to carry the bag some distance to the throwing destination (faculty lunch room, on the top floor of the ivory tower), potentially fatiguing their muscles. The balls have different weights, and thus can plausibly affect performance on the basis of (a) which colour ball is being thrown on a specific trial (call this variable “colour”), and (b) the overall composition of the bag they carried before commencing throwing (call this variable “composition”). The researcher running the experiment is interested in the effects of both of these variables, and so wants to obtain estimates of performance for all relevant composition*colour combinations. Naturally, for some levels of the composition factor, no blue balls are included in the bag, so the two variables are not fully-crossed. What would the appropriate syntax be for such a model in brms, to avoid the estimation of effects that are impossible in the design (e.g., the effect of colour when the composition is 4 red balls + 0 blue balls)? Would a model that produces estimates of these impossible effects be biased in its estimates of the genuine effects, given that there are no data in the non-existent design cells? (That is, is it a problem? My intuition is “no”, but I’m wary nonetheless.) How many times could the researcher run this experiment before being escorted off the premises?