Last modified: 28 March 2017

#### Abstract

We show how to optimally design a discrete choice experiment (DCE) with a no-choice option for estimating a nested logit model when partial profiles are used to study a large number of attributes. As a motivating example, we describe a DCE to identify and quantify the determinants that influence the competitive position of the coach bus as transport mode for medium-distance travel by Belgians. We measured the attractiveness of different bus services for different destinations (Lille, Amsterdam, Cologne, Paris and Frankfurt) by having participants choose their preferred bus trip out of two bus trips, while still allowing them to also choose not to take the bus but any other transport mode comprised by the no-choice option. Each bus trip is a combination of levels of seven attributes: price, duration, and comfort attributes including wifi, leg space, catering, entertainment and individual power outlet. Varying the levels of all seven attributes of the bus trips in the choice sets would be cognitively too demanding for respondents. To ensure sensible and manageable choice tasks, we present and compare new and existing optimal design approaches for a no-choice partial profile setting in which the levels of only a subset of the attributes vary within every choice set.

The simplest approach to obtain an optimal partial profile design with a no-choice option is to use the integrated algorithm of Palhazi Cuervo, Kessels et al. (2016) for the generation of optimal partial profile designs without a no-choice option and to add the no-choice option to every choice set afterwards. The integrated algorithm generates Bayesian D-optimal partial profile designs to estimate a multinomial logit (MNL) model involving main effects. The label ‘integrated’ refers to the fact that the set of constant attributes and the levels of the varying attributes are optimized simultaneously. The levels of the constant attributes are chosen randomly as they do not impact the respondents’ choices and the quality of the design. This simple approach offers a possible pathway since it has been shown that, when using full profiles instead of partial profiles, designs for the MNL model where a no-choice option has been added to every choice set also perform well for analyzing the resulting data. However, our situation is one that involves partial profiles and where the no-choice nested logit (NCNL) model is the most appealing model to account for the no-choice option. In this model, the no-choice option is put in a different nest from the real-choice profiles so that it is not treated as ‘just another’ profile. This is realistic if respondents are not interested in the product category under study, e.g. medium-distance travel by bus.

To generate Bayesian optimal partial profile designs for the NCNL model, the integrated algorithm has been adapted to also vary the levels of the constant attributes since they impact the quality of the resulting designs in this new setting. This is because of the presence of the no-choice option. Compared to the MNL model, the NCNL model is characterized by an additional parameter, called the dissimilarity coefficient, which usually lies between zero and one and measures to what extent the profiles in the real-choice nest are different. For our bus trip DCE where the real-choice profiles all involve the bus as transport mode and the no-choice option concerns any other transport mode, the dissimilarity coefficient is expected to be small or close to zero. One can optimize a partial profile design to obtain precise information about all parameters, including the preference parameters as well as the dissimilarity coefficient, or one may be interested in obtaining precise information about the preference parameters only. In the former case, we use the Bayesian D-optimality criterion derived for the NCNL model, while in the latter, we use the Bayesian DS-optimality criterion, where the letter ‘S’ stands for a subset of parameters, referring to the preference parameters. Both Bayesian optimality criteria require the specification of prior values for the preference parameters as well as for the dissimilarity coefficient, where we assume these are independent from each other. We used a multivariate normal prior distribution for the preference parameters and each of the eleven discretized decimals in the unit interval, i.e. [0, 0.1, …, 1], as a point prior for the dissimilarity coefficient. For other design scenarios, we combined the preference priors with all eleven discretized values in the unit interval or with the first half of them containing the six smallest values. This last scenario implements the idea that in DCEs where the real-choice profiles describe the product category and the no-choice option reflects disinterest in them, the dissimilarity coefficient tends to be small.

We compared the Bayesian optimal MNL and NCNL partial profile design approaches with each other and the main results are as follows. First, to compare the MNL designs where we added a no-choice option to every choice set, with the NCNL designs, we evaluated 1000 MNL designs with 1000 random selections of levels for the constant attributes and computed their efficiencies in terms of the NCNL optimality criteria, using the prior specifications for the preference parameters and the dissimilarity coefficient mentioned above. Overall, the NCNL designs outperform the MNL designs with efficiency gains of up to 25% for D-efficiency and up to 15% for DS-efficiency, where these maxima are obtained for dissimilarity coefficients around 0.5. The closer the dissimilarity coefficient is to the boundaries of the unit interval, the smaller the gains. Second, an evaluation of the performance of the NCNL designs for dissimilarity coefficients for which they have not been optimized, reveals that the designs are close to optimal for other values as well, except for large values near 1. This is the situation where the NCNL model is equal to the MNL model.

Palhazi Cuervo D, Kessels R, Goos P, Sörensen K (2016). An integrated algorithm for the optimal design of stated choice experiments with partial profiles, Transportation Research Part B: Methodological, 93A, 648-669.