Quick and easy choice sets: Constructing optimal and nearly optimal stated choice experiments

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Abstract

In this paper we compare a number of common strategies for constructing discrete choice experiments. Two of the strategies, including one based on theoretical constructions for optimal discrete choice experiments, produce designs that are better than those that come about from random grouping and from using the LMA construction. A simple account of this theoretical construction is given.

Section snippets

Introduction and motivation

A discrete choice experiment (DCE) consists of several choice sets, each containing two or more options (sometimes called alternatives). Participants are shown the choice sets in turn and are asked which option they prefer. Each option is described by a set of attributes and each attribute can take one of several levels. DCEs are used in marketing to estimate the effect of the attributes on the “attractiveness” of the product under consideration. How well a DCE does this depends in part on

Strategy 1

The first design strategy is to take one orthogonal main effects design for five 4-level attributes and randomly pair the profiles to give the choice sets. One such design is given in Table 2. Thus the first choice set, using the attributes and uncoded levels, becomes {($350, 4 h, no food or drink, no entertainment, Boeing 737), ($650, 4 h, beverage and hot meal, audio only, Boeing 767)}.

Observe, however, that this pairing has resulted in the second attribute having the same level in all pairs

Strategy 2

The second design strategy is similar to the first but uses two different OMEPs, one to represent the profiles that appear as the first option in the choice sets and one to represent the profiles that appear as the second option in the choice sets. One such design is shown in Table 3. Note that each level of each attribute appears equally often in each option but it does not stop the possibility that all pairs may have the same level of one, or more, attributes. This problem is partially

Strategy 3

This strategy takes the profiles from an OMEP and pairs them manually in such a way that the pairs satisfy the minimal overlap property from Huber and Zwerina (1996), or as close to it as is possible. In effect, this means that for each attribute there should be the maximum number of different levels in the choice set. Each level appears either 0 or 1 times in each pair and, over the whole choice experiment, each option displays the possible levels of each attribute equally often. One set of

Strategy 4

The fourth strategy requires an OMEP for ten 4-level attributes. The smallest such design has 64 level combinations. For each level combination in the OMEP the first five attributes are used to represent the profiles of the first option and the final five attributes are used to represent the profiles of the second option. So there are 64 total pairs in the experiment. This strategy is sometimes called an LMA approach (see Louviere, Hensher, & Swait, 2000). As this design is large it is in the

Strategy 5

This strategy uses a software package like SAS (see Kuhfeld, 2004) to generate a starting OMEP and then construct choice sets using a search algorithm. The “goodness” of the design (efficiency) is given, but there is no indication if a design is the best (optimal) design. The user must nominate the number of profiles in the candidate set from which the search algorithm selects profiles for the choice sets. We tried a number of different candidate sets, and used the one with the highest

The information matrix and statistical efficiency

In general, each profile in each option in a choice set is described by k attributes and each choice set contains m options. We assume that the qth attribute has lq levels, represented by 0, 1, …, lq  1 and that attributes may have different numbers of levels (i.e., a design can be asymmetric).

We discuss experiments that are consistent with the multinomial logit model (MNL), where the results from a DCE are to be used to estimate the main effects or the main effects plus two-factor interactions.

Designs for estimating main effects

Burgess and Street (2005) provide an upper bound for det(C) for estimating main effects for any choice set size with any number of attributes each having any number of levels. The maximum value of the determinant of C isdet(C optimal)=q=1k(2Sqm2(lq1)i=1,iqkli)lq1whereSq={(m21)/4lq=2,m odd,m2/4lq=2,m even,(m2(lqx2+2xy+y))/22<lqm,m(m1)/2lqmand positive integers x and y satisfy the equation m = lqx + y for 0  y < lq. The value Sq is the largest number of pairs of profiles that can have

Designs for estimating main effects and two-factor interactions

The situation is more complicated if one wants to estimate both main effects and two factor interactions. If all attributes have two levels and choice sets are of size 2, the optimal designs consist of all pairs with (k + 1)/2 attributes different (if k is odd), or all pairs with either k/2 or k/2 + 1 attributes different (k even) as established in Street et al. (2001).

If all attributes have two levels, and choice sets have more than two options, the optimal design consists of all choice sets in

Comparison of strategies

In this section we compare the information matrices of DCEs constructed using Strategies 1, 2, 3, 4 and 5 with a design constructed using the method of Burgess and Street (Strategy 6). This comparison depends only on the design used and it is not dependent on the data collected. Each design is to be used to estimate only main effects. The results are shown in Table 12. An asterisk denotes a choice experiment in which the main effects cannot be estimated independently.

Table 12 shows that the

Discussion and conclusions

The Burgess and Street (2005) method of design construction for DCEs outlined in this paper will lead to “good” designs but not necessarily to designs that are the smallest and/or best possible (nor is it necessarily the case the smallest possible designs should be used, as noted by Louviere et al., 2000). However, these designs allow independent estimation of all effects, and they generally are superior to most designs in the published literature. Indeed, our review of that literature suggests

Acknowledgements

The authors gratefully acknowledge the support of the Australian Research Council, Grant Number DP0343632, entitled “Modelling the Choices of Individuals”.

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