Bias caused by omitted variables in random regret choice models: Formal and empirical analysis of orthogonal design data

The aim of this study is to explore the bias caused by omitted variables in both random utility and random regret models. Since the behavioural underpinnings of these models differ, the bias is also expected to differ. We focus our analysis on stated choice data, based on orthogonal fractional factorial experimental designs, because the endogeneity, defined as a correlation between selected and omitted explanatory variables is a nonissue in such data. We will show that while the bias caused by omitted variables in the random utility model can be simply neutralised by using alternative specific constants, it still exists in the random regret model because the bias in this type of choice models depends on the attribute dominance structure in the data and thus is not constant.