Bias in random regret models due to formal and empirical comparison with random utility model measurement error

This study addresses the so-called uncertainty problem due to measurement error in random utility and random regret choice models. Based on formal analysis and empirical comparison, we provide new insights about the uncertainty problem in discrete choice modeling. First, we formally show how measurement error affects the random regret model differently from the random utility model. Then, random measurement error is introduced into level-of-service variables and the effect of measurement error is analyzed by comparing the estimated parameters of the concerned choice models, before and after introducing measurement error. We argue that although measurement error leads to biased estimation results in both types of models, uncertainty tends to accumulate in random regret models because this model involves a comparison of alternatives. Therefore, input uncertainty tends to lead to larger bias in random regret models. Moreover, since random regret models assume semi-compensatory decision processes, bias in random utility models is homogenous across individuals and alternatives, while bias in random regret models is heterogeneous. Several approaches are discussed to overcome this uncertainty problem in random regret models.