Last modified: 28 March 2017

#### Abstract

Discrete choice experiments (DCEs) are commonly used in health economics, marketing and transportation research, to collect and to understand respondent preferences for the attributes of products, services or policies. Typically, in a DCE, respondents make choices on a series of choice sets, each composed of two or more alternatives. These alternatives are defined as combinations of different attribute levels. The choices of respondent will reveal the partworths, which are the respondent's assessment of the different attribute levels. It is important to obtain informative and consistent choices in order to assess the true preference structure of respondents. The number of choice sets, alternatives and attributes, as well as the number of attribute levels and their range define the design dimensions of a DCE. All these dimensions, which are to be specified by the researcher, define the complexity of the choice task and vary across different studies.

Most of the literature in choice modelling assumes that respondents are perfectly capable of consistently processing information and that respondent’s choices are not influenced by the design dimensionality (Swait & Adamowicz, 2001). Consequently, classical choice models do not take into account the complexity of DCEs. In contrast, there are many studies in psychology and behavioral decision theory that have considered the limited ability of respondents to process complex information (Keller & Staelin, 1987; DeShazo & Fermo, 2002).

One might therefore expect a direct relationship between the complexity of a choice set and the choice consistency. Some authors have investigated this relationship. For instance Breffle and Rowe (2002) obtained larger error variances as the complexity of choice sets increased, however they found no significant effect of dimensional complexity on the parameter estimates. DeShazo and Fermo (2002) found a quadratic relationship between varying number of alternatives and the variance of the error term in utility function, by which variance initially decreases up to a certain number of alternatives and then it starts to increase. The initial decline in error variance results from a better match between true preferences and the provided alternatives; while the increase at the later stage is caused by a considerable increase in design complexity. Additionally, it was shown by Hensher (2006) that the number of choice sets significantly affects the parameter estimates. On the other hand, Carlsson and Martinsson (2008) tested the impact of the number of choice sets on willingness to pay and did not find a significant effect of the inclusion of relatively modest number of choice sets.

Of course, the efficiency of the parameter estimates depends also on the design. Most developments in the design of experiment ignore the effect of choice complexity while generating the designs. Danthurebandara, *et al*. (2011) showed that the designs that are generated while taking the complexity into account outperform the designs constructed ignoring the choice complexity in case the error variance can be modeled as a function of the complexity.

In most choice experiments, the number of alternatives and the number of choice sets are selected rather arbitrarily and are kept fixed throughout the experiment. In general the information in the experiment will increase with larger and with more choice sets. However, if one assumes that the error variance is related to the choice complexity, the relationship between the information in the experiment and the size of the choice sets and the number of choice sets becomes much more complicated. That raises many questions about the efficiency of discrete choice designs.

In this study, our aim is to investigate the effect of the task complexity on the efficiency of the design. We will consider different choice sets sizes in combination with different number of choice sets. Furthermore we will use these insights to generate efficient designs where we allow for varying number of alternatives in different choice sets.* * So the goal is to generate Bayesian *D*-optimal designs for the heteroscedastic conditional logit (HCL) model, which has previously been used for quantifying the individual’s choice inconsistency and parameterizes the scale factor as a function of the complexity of the choice set. The complexity is measured by the number of alternatives in the choice set, the number of attributes and by the following measures of complexity (Sándor and Franses, 2009): the number of trade-offs (a measure for the similarity of alternatives in terms of utility), the mean dispersion (a measure of the average variability of alternatives) and the standard deviation of these dispersions across alternatives. The proposed designs are compared with Bayesian *D*-optimal designs for similar design settings but constructed ignoring the choice complexity.

**Keywords:** Discrete Choice Model, Optimal Design, Choice Complexity, Heteroscedastic Conditional Logit Model, Choice Consistency

**References:**

Carlsson, F., & Martinsson, P. (2008). How much is too much? Environmental and Resource Economics, 40(2), 165-176.

Danthurebandara, V. M., Yu, J., & Vandebroek, M. (2011). Effect of choice complexity on design efficiency in conjoint choice experiments. Journal of Statistical Planning and Inference, 141(7), 2276-2286.

DeShazo, J. R., & Fermo, G. (2002). Designing choice sets for stated preference methods: the effects of complexity on choice consistency. Journal of Environmental Economics and management, 44(1), 123-143.

Hensher, D. A. (2006). Revealing differences in willingness to pay due to the dimensionality of stated choice designs: an initial assessment.Environmental and Resource Economics, 34(1), 7-44.

Keller, K. L., & Staelin, R. (1987). Effects of quality and quantity of information on decision effectiveness. Journal of consumer research, 14(2), 200-213.

Sándor, Z., & Franses, P. H. (2009). Consumer price evaluations through choice experiments. Journal of Applied Econometrics, 24(3), 517-535.

Swait, J., & Adamowicz, W. (2001). The influence of task complexity on consumer choice: a latent class model of decision strategy switching. Journal of Consumer Research, 28(1), 135-148.