Optimal Experimental Designs for Nonlinear Conjoint Analysis

Estimators of choice-based multi-attribute preference models have a covariance matrix that depends on both the design matrix as well as the unknown parameters to be estimated from the data. As a consequence, researchers cannot optimally design the experiment (minimizing the variance). Several approaches have been considered in the literature, but they require prior assumptions about the values of the parameters that often are not available. Furthermore, the resulting design is neither optimal nor robust when the assumed values are far from the true parameters. In this paper, we develop efficient worst-case designs for the choice-based conjoint analysis which accounts for customer heterogeneity. The contributions of this method are manifold. First, we account for the uncertainty associated with ALL of the unknown parameters of the mixed logit model (both the mean and the elements in covariance matrix of the heterogeneity distribution). Second, we allow for the unknown parameters to be correlated. Third, this method is also computationally efficient, which in practical applications is an advantage over e.g. fully Bayesian designs. We conduct multiple simulations to evaluate the performance of this method. The worst case designs computed for the logit and mixed logit models are indeed more robust than the local and Bayesian benchmarks, when the prior guess about the parameters is far from their true values.