Accounting for model uncertainty in individualized designs for discrete choice experiments

Abstract

We develop a method for finding optimal designs in discrete choice experiments (DCEs). More specifically, we deal with individualized designs, which are sequentially generated for each person undertaking a survey, using, at each stage, responses from previous choice sets in order to select the next best set. Currently, the optimal design for a DCE is predicated on a specific mixed logit model that represents the probability of choosing a specific alternative in a choice set through a linear predictor combining several attributes or factors deemed to be relevant in each choice. Using a unique model represents a major limitation, which we overcome by allowing for a collection of different models characterized by distinct linear predictors. Our approach is fully Bayesian and incorporates a prior distribution on the model space as well as a prior on the parameter space specific to each respondent. To perform our optimal design strategy for DCEs, we specify two distinct utility functions, one being targeted to model discrimination while the other aims at the dual purpose of model discrimination and parameter estimation. We implement our methodology using a sequential Monte Carlo algorithm suitably tailored to account for model uncertainty and individual-specific parameters. To evaluate our methodology, several simulation settings are considered in detail. Comparisons with alternative methods are also investigated.

Keywords:

• Bayesian sequential design
• model discrimination
• mutual information
• optimal design
• sequential Monte Carlo
• total entropy

Acknowledgments

We are indebted to the participants in the workshop on Model Oriented Design and Analysis (MODA 11) for useful comments on preliminary versions of this article. Moreover, we are grateful to the Editor and the referees whose comments and suggestions improved the article and to James McGree (QUT, Brisbane, Australia) for having made available his code to compute the total entropy utility function that we adapted to the DCEs framework. Partial funding was provided by Università Cattolica del Sacro Cuore (research project track D1).

Additional information

Notes on contributors

Guido Consonni

Guido Consonni is a Full Professor of Statistics in the Department of Statistical Sciences of Università Cattolica del Sacro Cuore, Largo Gemelli, 1; 20123 Milan, Italy. His email is [email protected].

Laura Deldossi

Laura Deldossi is an Associate Professor of Statistics in the Department of Statistical Sciences of Università Cattolica del Sacro Cuore, Largo Gemelli, 1; 20123 Milan, Italy. Her email is [email protected].

Eleonora Saggini

Eleonora Saggini is a Research Associate in the Department of Statistical Sciences of Università Cattolica del Sacro Cuore, Largo Gemelli, 1; 20123 Milan, Italy. Her email is [email protected].