Main-effects brand x price studies can reflect differential substitution patterns among brands when we estimate point estimates of utilities at the individual level via HB and build choice simulators that leverage those individual-level utilities. But, as the number of brands increases and the data become sparser, IIA plays a bigger role and differential substitution patterns may be smoothed. One approach that might help preserve brand substitution patterns is to build simulators using lower level draws (rather than point estimates). We compare results for multiple brand x price studies when simulating on lower-level draws vs. point estimates
