Market Simulation Using a Probabilistic Ideal Vector Model for Conjoint Data

In commercial applications of conjoint analysis to product design and product pricing it has become quite popular to further evaluate the estimated individual part-worth functions by predicting shares of choices for alternatives in hypothetical market scenarios (Wittink, Vriens and Burhenne 1994 and Baier 1999 for surveys on commercial applications). Wide-spread software packages for conjoint analysis (Sawtooth Software’s 1994 ACA system) already include specific modules to handle this so-called market simulation situation for which, typically, a threefold input is required: (I) The (estimated) individual part-worth functions have to be provided. (II) A definition of a hypothetical market scenario is needed that allows to calculate individual utility values for each available alternative. (III) A so-called choice rule has to be selected, which relates individual utility values to expected individual choice probabilities and, consequently, to market shares for the alternatives. In this context, the determination of an adequate choice rule seems to be the most cumbersome task. Well-known traditional choice rules are, e.g., the 1ST CHOICE rule (where the individuals are assumed to always select the choice alternative with the highest utility value), the BTL (Bradley,Terry, Luce) rule (where individual choice probabilities are related to corresponding shares of utility values), and the LOGIT rule (where exponentiated utility values are used). Furthermore, in newer choice rules implemented by various software developers, the similarity of an alternative to other alternatives is taken into account as a corrective when choice probabilities are calculated (Sawtooth Software 1994).