Constraints in Labelled Experiments with D-Efficient Design

[nayeem]

I am designing a labelled choice experiment to estimate WTP for more reliable freight transport along a particular corridor. There are three labelled alternatives:

• Normal Road Transport
  Normal Intermodal Transport
  High speed Intermodal Transport

There are no status quo alternatives. The different attributes are:

• Transport Cost
  Transport time (origin to destination)
  Travel time reliability (mean-variance method)

I want a D-efficient design. Should I add a constraint so that within each alternative, higher reliability of service and lower travel time is always accompanied by higher costs charged to the users?

[Michiel Bliemer]

You would usually only include constraints to make choice tasks more realistic. So if you think that the profiles would become too unrealistic, then you can certainly impose constraints. However, note that to be able to estimate choice models, one would need sufficient variation in the data and therefore imposing constraints could hinder model estimation if the constraints are too strict. But as long as you do not perfectly correlate attribute levels you should still be fine in most cases. If you generate an efficient design, and your D-error is finite, then you will be able to estimate the model.

You can also consider constraints to avoid dominant alternatives. Ngene does this automatically for unlabelled experiments, but with labels there is usually no issue with dominance. In your case, if you would use generic coefficients across your labelled alternatives, you could still apply dominance checks across the three alternatives in Ngene.

Michiel

[nayeem]

Can I use a generic cost attribute when the attribute levels of the alternatives are different? For example in my DCE, cost(high speed intermodal transport) > cost(normal road transport) > cost(normal intermodal transport). For the time attribute its the opposite, time(normal road transport) > time(high speed intermodal transport) > time(normal high speed intermodal transport). When do we use a generic attribute and when do we use a mode specific attribute? Is there any thumb rule in this case? The cost and time spent in transporting freight doesn’t seem to be distinguishable across modes unlike in passenger transport where time spent inside an auto can be qualitatively different compared to time spent inside a public transport vehicle.

And how can I use Ngene to make dominance checks for generic attributes in my labelled alternatives?

In my DCE the range of the cost attribute is different for the alternatives. For example, cost(normal road transport) varied from 160 USD to 240 USD (over 5 levels) while for cost(normal intermodal transport) varied from 184 USD to 220 USD (over 3 levels). Could this create a problem in model estimation when I have collected sufficient data?

Nayeem

[Michiel Bliemer]

For labelled alternatives, you would usually estimate alternative-specific coefficients and then conduct hypothesis testing to see if they are statistically different. If not, you replace them with a generic coefficient when estimating the model. So in the design phase you can consider them alternative-specific, and during the model estimation phase you can test whether they need to be generic or not.

For cost, often a generic coefficient is used because economists would argue that a dollar is a dollar, no matter what you spend it on. But this is not always true (for example, toll cost and fuel cost are perceived differently, with more aversion towards toll costs). So if you are unsure, it may be best to consider them alternative-specific in the design phase and again test during the model estimation phase.

The hypothesis testing is simply:
H0: b1 = b2, or: H0: b1-b2 = 0.

Using the Delta method, you can calculate the variance V = Var(b1-b2) = Var(b1) + Var(b2) - 2 * Cov(b1,b2) and use a standard t-test, t = abs(b1-b2) / sqrt(V) > 1.96 for a test at the 5% significance level.

Dominance checks formally do not exist for labelled alternatives. For example. a Bus with a travel time of 10 minutes is not necessarily dominant over a Car with a travel time of 20 minutes. Because of the label-specific constant, a labelled alternative cannot be strictly dominant.

You can use a generic parameter even if the levels of the numerical attribute are different across alternatives, or if the number of levels is diferent. The differences in range in your case are not very large so I do not foresee any issues. If the costs are very different, e.g. 100-200 versus 200-500 then you may want to test for nonlinearities, e.g. by using log(cost), and consider estimating alternative-specific coefficients.

Michiel