Optimal Design for Mixed Logit Models
C Cirillo, FUNDP, BE
This paper looks at the theory to formulate optimal designs; or in other words at the methods which help us to pick input optimally in our data collection methods
Experimental choice designs have been extensively applied in marketing and related fields. Conjoint choice experiments are designed to collect data from alternatives specified under hypothetical scenarios (i.e. Stated Preference experiments). They should provide as much information as possible on the parameters of the choice model calibrated using the collected data. The problem of design efficiency is not new but has seen very few applications in transportation. This is mainly due to the fact that transport data, from conjoint choice experiments, are often analyzed with standard logit models. The major difficulty in design for non-linear models (as those deriving from logit models) is that the optimal design depends on values of the parameters. The problem is even more complicate if one wants to develop optimal design for mixed logit models or other random effects models. The information matrix in this case does not have a closed form and should be evaluated by means of simulations over the distributions of the random coefficients.
Mixed logit models have received considerable interest from econometricians and transport modelers, mainly for they ability to recover heterogeneity in the coefficients across individuals. However, very little is known on the efficiency of design constructed for logit models and on the derived parameters estimated with mixed logit models.
The objective of this paper is to give a comprehensive overview of the problem and to point out the research directions that should be pursued in order to apply optimal designs to the construction of real Stated Choice experiments in transportation.
Association for European Transport