Description:
This paper discusses the well-covered subject of discrete choice and its principles, introducing some new principles, and hopefully shedding new light. Emphasis is on the properties of the resulting models, rather than the mathematical process by which they were derived. For this purpose, a conceptual axiomatic discrete choice model is defined first, together with the corresponding composite disutility function. From this, a set of necessary conditions are defined that specific models must honor. IID, IIA, MDPU and attribute correlation are also discussed.The logit model is analyzed first, and its properties compared against the necessary conditions, demonstrating that it violates most of them, in spite of its mathematical robustness.Two alternative models are explored next: the scaled-utilities logit and the powit models. The former scales expected utilities by a common factor within a standard logit formulation, thus becoming ratios. The latter model assumes that the error term is multiplicative, resulting in a power function. It is shown that both alternative models honor all the necessary conditions, and furthermore, produce extremely close results, showing that scaling the utilities is equivalent to assuming a multiplicative error term. Finally a simple algorithm is proposed to deal with attribute correlation, based on correlation penalties, that can be applied to any ratio-based model form. The conclusions argue that the multiplicative error term or disutility scaling approaches, together with the attribute correlation algorithm, are a promising way to go