Error by omitted variables in regret-based choice models: formal and empirical comparison with utility-based models using orthogonal design data

Random regret minimization models have mostly relied on the assumption of identically and independently distributed error terms. Professionally designed stated choice experiments use various design and implementation principles to ensure that any errors meet this assumption. Based on the behavioral theory that individuals arrive at a decision by first processing the attribute values of a choice alternative according to an integration rule to derive the stochastic utility associated with the choice alternatives and then apply the deterministic utility maximizing rule, this assumption can be reasonable met for utility maximizing models. The question is whether this assumption is equally defendable for random regret minimization models in light of the difference in model specification, rooted in fundamental behavioral differences between the underlying decision theories. This study focuses on the effect of omitted variables which is one of main sources of error. Based on a formal analysis and empirical comparison, we argue and show that omitted variables cause correlation between unobserved regrets. Consequently, the independence assumption is difficult to defend because the omitted variables simultaneously affect the comparison of choice alternatives. To capture this effect, we propose an error components structure for regret-based choice models. Empirical results obtained for classic random regret-minimization models for two different data sets support our theoretical arguments. If these results can be generalized to other data sets, it is advisable to adopt an error components structure when estimating these classic random regret-minimization models unless one has reason to believe the effect of the omitted variables is small and therefore can be ignored.