Error distributions assumptions in random regret choice models: Towards error components frechit specifications

Recently introduced regret-based choice models in transportation research have invariably and uncritically adopted the assumption of independently and identically distributed error terms. The central argument underlying this paper is that this assumption is difficult to defend considering the fundamental nature of the concept of regret, which states that regret is generated through the comparison of choice alternatives on an attribute-by-attribute basis. The support this stance, we theoretically and empirically identify and diagnose specification errors in classic regret-based choice models, and provide a solution to remedy the problem. First, we formalize how different sources of error affect the formation of errors. Then, we provide theoretical and empirical evidence that the process of regret generation is irreconcilable with the commonly used assumption of IID Gumbel distributed error terms. Results of formal and empirical analysis comparing classic regret minimizing and linear additive utility maximizing models indicate that measurement error causes identical errors in utility-maximizing models but non-identical errors in regret-minimizing models. Omitted variables cause alternative specific and independent errors in utility-maximizing models, but pairs of alternatives specific and non-independent errors in regret-minimizing models. Finally, accounting for these findings, we suggest a general expression for the error terms of regret-based choice models as a solution for the stipulated problem.