Volumetric Conjoint Analysis!

The Volumetric Conjoint Analysis research case study article by co-authors Jaehwan Kim of The Leeds School of Business at The University of Colorado at Boulder; Greg M. Allenby of The Fisher College of Business at The Ohio State University; and Peter E. Rossi of The Graduate School of Business at The University of Chicago illustrates artistically that Conjoint Analysis by definition states that it is a statistical technique used in market research to determine how people value different features that make up an individual product or service. With this in mind, why cannot there be a Volumetric Conjoint Analysis? The quantity of any good demanded by consumers is dependent on the attributes and benefits of an offering, the rate at which marginal utility of the offering decreases, and the availability of substitutes.

Traditional conjoint models are designed to make market share predictions and are difficult to adapt to modeling volume data. Recently, a new demand model is proposed in which product attributes are related to satiation parameters, allowing for volume predictions and identification of product line configurations that maximize profits.

In order to estimate quantity demanded for various product configurations, rather than simply market shares, volumetric data are collected in some conjoint surveys. However, while (laten) linear models provide accurate estimates of marginal utility part-worths for ratings and choice data, their use with volumetric data is problematic. Volumetric data reflects the expected demand for the alternative product under investigation, often expressed in terms of multiple purchases.

For discussion purposes, consider, for example the consumption of soft drinks. Even though if a particular household is brand loyal, demand is often reported in terms of multiple container types and volumes for a specific time period (e.g. two liter bottles and three six-packs). On the contrary, another approach to modeling volume data collected in a conjoint survey would be to use a count regression model such as a Poisson regression. A separate Poisson regression could be fit to the quantity responses for each product configuration presented. The difficulty with this approach is that the linear Pisson regression function does not accomodate satiation effects and the assumption of independent Poisson regression limit substitution possibilities.

In summary, the eventual goal of a volumetric conjoint analysis is to make optimal policy recommendations which are difficult to justify using an ad hoc statistical specification.