Detecting dominance in stated choice data and accounting for dominance-based scale differences in logit models

- Strictly dominant alternatives in stated choice experiments should be avoided as they can bias parameter estimates in logit models.
- Strictly dominant alternatives can occur in all existing experimental design types.
- Zero minimum regret is an indicator for the presence of a strictly dominant alternative.
- Minimum regret can be used to adjust the scale parameter in a heteroscedastic logit model to account for dominance.

Stated choice surveys have been used for several decades to estimate preferences of agents using choice models, and are widely applied in the transportation domain. Different types of experimental designs that underlie such surveys have been used in practice. In unlabelled experiments, where all alternatives are described by the same generic utility function, such designs may suffer from choice tasks containing a dominant alternative. Also in labelled experiments with alternative specific attributes and constants such dominance may occur, but to a lesser extent. We show that dominant alternatives are problematic because they affect scale and may bias parameter estimates. We propose a new measure based on minimum regret to calculate dominance and automatically detect such choice tasks in an experimental design or existing dataset. This measure is then used to define a new experimental design type that removes dominance and ensures the making of trade-offs between attributes. Finally, we propose a new regret-scaled multinomial logit model that takes the level of dominance within a choice task into account. Results using simulated and empirical data show that the presence of dominant alternatives can bias model estimates, but by making scale a function of a smooth approximation of normalised minimum regret we can properly account for scale differences without the need to remove choice tasks with dominant alternatives from the dataset.