The generation of experimental designs specifically for the purpose of stated choice (SC) surveys has attracted much attention of late. Recently, researchers have suggested that from a statistical perspective, experimental designs underlying SC tasks should impart the maximum amount of information about the parameters of the attributes relevant to each specific choice task (e.g., Sandor and Wedel 2001). Generation of statistically efficient designs has been addressed by several authors (e.g., Ibinez et al. 2007; Sandor and Wedel 2001, 2002). Often, the premise behind the construction of statistically efficient designs is given as the need to reduce the number of choice sets shown to any one individual respondent, so as to reduce the cognitive effort and possible fatigue effects that each respondent may experience over the entire experiment. This represents a clear trade-off for choice modellers, given that the more choice observations obtained by the analyst, the more information that may potentially be used to estimate the parameters underlying the preferences within the sampled population.

The design approach necessities construction of the asymptotic variance-covariance (AVCM) that is likely to be obtained from models estimated from data collected using the generated design. The AVCM of a design is the inverse of the second derivatives of the log-likelihood function of the model that will be estimated post data collection. To obtain the AVCM of a design, the analyst is therefore required to make two strong assumptions, violations of which may result in a loss of statistical efficiency. Firstly, the analyst is required to assume, a priori, the parameter estimates that will result from the study. Information on the likely parameter estimates may be used to calculate the expected utilities for each of the alternatives present within the design, which in turn may be used to calculate the likely choice probabilities. The choice probabilities are then used to calculate the AVCM for the design. A number of different researchers have addressed the requirement of parameter priors.

The second assumption required in the construction of statistically efficient SC experiments is the final model form that will be estimated. Unfortunately, the log-likelihood functions of different discrete choice models are likely to be different and hence so to the AVCMs obtained for a given design as applied to different models. As such, a design optimized based on the AVCM for an MNL model is therefore unlikely to optimal for say a MMNL model. In this paper, we propose the use of a model averaging approach to solve the problem. This solution involves calculating the AVCM for all possible models that might be estimating post data collection and minimising a weighted average measure of efficiency across these possible models. This approach has the advantage of not requiring precise knowledge of exact econometric model to be estimated whilst allowing for statistical efficiency across a broad spectrum of possible model types. This approach does come at a cost however, with the generated design unlikely to be as efficient a design that is specific generated for a particular model type.

References

Ibinez, J.N., Daly, A.J. and Toner,J.P. (2007) Optimality and efficiency requirements for the design of stated choice experiments, Proceedings of the European Transport Conference. PTRC, London.

Sandor, Z. and Wedel, M. (2001) Designing Conjoint Choice Experiments Using Managers’ Prior Beliefs. Journal of Marketing Research, 38 (November), 430-444.

Sándor, Z. and Wedel, M. (2002), Profile Construction in Experimental Choice Designs for Mixed Logit Models, Marketing Science, 21(4), 455-475.