Accounting for cognitive effort in random regret-only models:effect of attribute variation and choice set size

Behaviorally, regret-based choice models implicitly assume that individuals anticipate the amount of attribute-level regret by comparing the attribute levels of a considered choice alternative against the attribute levels of the best or all other choice alternatives. Arguing that the amount of effort depends on attribute variation and number of paired comparisons, we suggest a way of incorporating the effects of these factors into two regret-based choice models. The cognitive effort involved in anticipating the amount of regret in paired comparisons of choice alternatives is incorporated into the scale of the regret function of each alternative. Because more cognitive effort causes higher randomness in the assessment of the amount of regret (i.e. higher variance of error terms), the cognitive effort is expressed as a flexible heteroscedastic scale factor, which is a decreasing function of attribute variation and number of paired comparisons. The models are applied to two different data sets, and compared with a heteroscedastic multinomial logit model. Estimation results of the suggested flexible heteroscedastic random regret models show a significant improvement in predictive performance over their homoscedastic formulations. A similar but smaller improvement is obtained for multinomial logit models. These results imply that the conventional assumption of identically distributed error terms underlying random regret models may not sufficiently reflect the process of anticipating the amount of regret.