On the robustness of random regret minimization modelling outcomes towards omitted attributes

As discrete choice models may be misspecified, it is crucial for choice modellers to have knowledge on the robustness of their modelling outcomes towards misspecification. This study investigates the robustness of Random Regret Minimization (RRM) modelling outcomes towards one sort of model misspecification: the omission of relevant attributes. We explore the effect of omitted attributes (orthogonal and correlated) in the context of labelled and unlabeled data. In the context of labelled data, we show that - just as in RUM models - in RRM models Alternative Specific Constants (ASCs) can be used to capture the average effect of omitted attributes. However, in contrast to RUM models, ASCs in RRM models are choice set composition specific. This implies that in order to achieve consistent parameter estimates when the choice set composition varies across choice observations, different sets of ASCs need to be estimated for each unique choice set composition. In the context of unlabeled data, we show - using Monte Carlo simulations - that RRM models are fairly robust towards the presence of an orthogonal omitted attribute, though not as robust as the linear-additive RUM model. Specifically, we find that: (1) Aggregate Demand Elasticities (ADEs) implied by RRM models are less robust towards the presence of an orthogonal omitted attributes than those implied by linear-additive RUM models, and (2) Average Sample Effects (ASEs) implied by RRM models are - in the presence of an omitted orthogonal attribute - more sensitive towards misspecification in terms of the underlying decision rule than those implied by its linear-additive RUM counterpart.