Accounting for variation in choice set size in Random Regret Minimization models

This paper derives a trick to account for variation in choice set size in Random Regret Minimization (RRM) models. In many choice situations the choice set size varies across choice observations. As in RRM models regret level differences increase with increasing choice set size, not accounting for variation in choice set size results in RRM models to predict relatively deterministic choice behaviour in observations where the choice set is large and relatively random choice behaviour in observations where the choice set is small. Such variation in choice consistency across observations is behaviourally unrealistic and leads to inferior performance of RRM models in the context of data sets with varying choice set sizes. The proposed trick resolves this in an econometrically pragmatic and behaviourally meaningful way by rescaling the regret levels as a function of the choice set size. The trick can be applied in the estimation phase when the choice set size varies across choice observations as well as in the forecasting phase when forecasts are made over choice sets of varying sizes.