Constructing Efficient Stated Choice Experimental Designs

Abstract

Stated choice (SC) experiments are often used in transportation studies for estimating and forecasting behaviour of travellers, road authorities, etc. This kind of experiment relies on underlying experimental designs. Whilst orthogonal designs are mainstream for practitioners, many researchers now realize that so‐called efficient designs are able to produce more efficient data in the sense that more reliable parameter estimates can be achieved with an equal or lower sample size. This paper describes several processes for generating SC experiments and is intended to give an overview of the current state‐of‐the‐art. Different methods are described.

Notes

1. Labelled choice experiments involve studies where the names of the alternatives on offer convey meaning to the respondents beyond the order in which they are shown to respondents (e.g. the alternatives may be labelled as car, bus and train). In unlabelled choice experiments, the names of the alternatives are only meaningful insofar as they relate the order of the alternative as shown to the respondent (e.g. Option A, Option B, etc.). In the latter case, each alternative may actually represent a car or a bus or a train in terms of the attribute levels shown to the respondent, but the fact that the alternative resembles one of these modes is not explicitly stated to the respondent. An exception to this rule exists where the different alternatives are treated as an attribute in the experiment. Also, in many SC experiments, a type or brand of alternative is often mentioned in the scenario descriptor of the task. In such cases, all the alternatives represent different versions of the same type or brand (e.g. Option A, Option B, etc., represent different alternative buses).

2. One of the reviewers suggests that this distinction is due to historical reasons, with Western Europeans, led predominately by John Bates in the early 1980s, adopting the column‐based approach whilst the row‐based approach remained a legacy from the traditional conjoint methods used by marketing researchers elsewhere in the world. We also note that the different design formats also correspond as to the use of either equations to derive the asymptotic variance–covariance (AVC) matrix (representing the column‐based approach) or matrix algebra (corresponding to the row‐based approach). We discuss the importance of the AVC matrix later in the paper.

3. In some cases, this definition of an orthogonal design may be relaxed to define orthogonality as occurring when all attribute correlations are zero within alternatives but not necessarily between alternatives; see Louviere et al. (2000) for a discussion on sequential versus simultaneous generation of orthogonal designs.

4. The attribute level values used in the design are based on orthogonal coding in this example. More details on different types of coding can be found in Bliemer and Rose (2006).

5. This holds only when the design is generated using effects coding (see, e.g. Bliemer and Rose, 2006).

6. The log‐likelihood of other discrete choice models may be similarly written out, with the discussion that follows applying equally.

7. For example, see Rose and Bliemer (2006) with regard to the MNL model and Bliemer et al. (in press) for the nested logit model. For the mixed logit model assuming independent choice situations, the choice index also is not required for the calculation of the expected AVC matrix; however it is required when the choice situations are considered not to be independent within respondents; see Bliemer and Rose (submitted).

8. This is possible as McFadden showed that the AVC matrices of discrete choice models are asymptotically divisible by N. Hence, if you construct the AVC matrix for a design assuming a single respondent, one can theoretically calculate the AVC matrix for that same design given any sample size, N, simply by dividing the elements in the matrix by N.

9. For example, the authors once constructed a survey where the two alternatives represented different potential dates. One attribute in the experiment was that the potential date either had children or did not. Because the design required that one potential date always had children whilst the other did not, problems arose, particularly with younger respondents, who always selected the date without children. This occurred to the point where no information could be gained on the other attributes of the design.

10. The attributes alongside the parameters influence the choice probabilities obtained from the design. The choice probabilities are in turn instrumental in the calculation of the AVC matrix for the design. Nevertheless, efficient and optimal choice probability designs are optimized based on the attribute levels selected, and hence the specific selection of the attribute levels is less likely to impact upon the results reported here relative to the selection of different prior parameter estimates. For this reason, we discuss in Section ‘Misspecification of Prior Parameter Estimates’ the impact on efficiency of misspecifying the prior parameter estimates. The interested reader is directed to Bliemer and Rose (2006, submitted) who discuss the impact of imposing different attribute levels on designs.

11. This statement is strictly not true.

12. Note that this strategy is not the same as adaptive conjoint which attempts to optimize the design within respondent.