Extending Valuation to Controlled Value Functions and Non- Uniform Scaling with Generalised Unobserved Variances

Abstract

A common by-product of discrete choice models is the marginal rate of substitution between two attributes (one usually measured in monetary units). The typical output is a point estimate value. In reality there is a distribution of values around a mean which is the product of non-linearities in the role of each attribute in utility space, as well as covariate influences that condition the role of taste weights in dimensioning the relative importance of each attribute in a choice setting. This paper considers the broad issue of breaking away from valuation to valuation functions, the need to use appropriate experimental design procedures and mean centering or orthogonal codes in estimation with translation back to the real attribute levels in order to reveal the appropriate evaluation distributions. By relaxing the strict constant variance condition in practical discrete choice models, we are able further to absorb unobserved sources of behavioural variability which if not allowed for tend to produce an overvaluation. We illustrate the methods discussed above with a case study on choice of existing and potential commuter modes in six Australian capital cities.