Likelihood estimation of consumer preferences in choice-based conjoint analysis

• An estimation method is proposed for value functions in choice based conjoint analysis.
• The method employs a likelihood function based on three sources of uncertainty.
• For individual choices we adopt multinomial logit with heterogeneous scale parameters.
• Interdependence of preferences is modeled using a multivariate normal distribution.
• The method exceeds average prediction performance of HB in 12 field data sets.

In marketing research the measurement of individual preferences and assessment of utility functions have long traditions. Conjoint analysis, and particularly choice-based conjoint analysis (CBC), is frequently employed for such measurement. The world today appears increasingly customer or user oriented wherefore research intensity in conjoint analysis is rapidly increasing in various fields, OR/MS being no exception. Although several optimization based approaches have been suggested since the introduction of the Hierarchical Bayes (HB) method for estimating CBC utility functions, recent comparisons indicate that challenging HB is hard. Based on likelihood maximization we propose a method called LM and compare its performance with HB using twelve field data sets. Performance comparisons are based on holdout validation, i.e. predictive performance. Average performance of LM indicates an improvement over HB and the difference is statistically significant. We also use simulation based data sets to compare the performance for parameter recovery. In terms of both predictive performance and RMSE a smaller number of questions in CBC appears to favor LM over HB.