# Model between-subject condition as population effect or random intercept?

I have an experiment where participants were assigned to one of four conditions (between-subject), and I want to predict a binary outcome (is_correct). Each participant answered one question so no repeated measures. So far I have come up with two models written in lme4-style formula syntax:

# condition as population effect
is_correct ~ condition

# condition as random intercept
is_correct ~ 1 + (1 | condition)


Which formulation should I use if I want to compare those conditions and determine which condition helps participants get more answers correct? I plan to fit a Bayesian GLM in brms.

Note that in your first model:

is_correct ~ condition


..this is not a mixed model, you are fitting fixed effects for condition and there are no random effects.

is_correct ~ 1 + (1 | condition)

...this is a mixed model where you are controlling for clustering within condition. However, since you only have 4 conditions, it seems likely that the first model will be better.