Efficient Conjoint Choice Designs in the Presence of Respondent Heterogeneity

Random effects or mixed logit models are often used to model differences in consumer preferences. Data from choice experiments are needed to estimate the mean vector and the variances of the multivariate heterogeneity distribution involved. In this paper, an efficient algorithm is proposed to construct semi-Bayesian D-optimal mixed logit designs that take into account the uncertainty about the mean vector of the distribution. These designs are compared to locally D-optimal mixed logit designs, Bayesian and locally D-optimal designs for the multinomial logit model and to nearly orthogonal designs (Sawtooth (CBC)) for a wide range of parameter values. It is found that the semi-Bayesian mixed logit designs outperform the competing designs not only in terms of estimation efficiency but also in terms of prediction accuracy. In particular, it is shown that assuming large prior values for the variance parameters for constructing semi-Bayesian mixed logit designs is most robust against the misspecification of the prior mean vector. In addition, the semi-Bayesian mixed logit designs are compared to the fully Bayesian mixed logit designs, which take also into account the uncertainty about the variances in the heterogeneity distribution and which can be constructed only using prohibitively large computing power. The differences in estimation and prediction accuracy turn out to be rather small in most cases, which indicates that the semi-Bayesian approach is currently the most appropriate one if one needs to estimate mixed logit models.