Experimental Design with Constraints

[nayeem]

In some stated choice experiments, certain alternatives may systematically outperform others on some attributes (e.g., travel time reliability, travel time), while being worse on others (e.g., cost, frequency). For example, a bullet train service may always be faster and more reliable than a conventional train, but also more expensive.

In this case, is it better to use constraints in experimental design or select attribute levels in a way that one alternative has always superior levels in one attribute and inferior levels of another attribute compared to a reference alternative?

For instance, one possible experimental design involves a choice between the current option and an alternative that is cheaper but has equal or worse levels of service:

Code: Select all

Design
? This game involves choice between the current option and an alternative that is Cheaper but with lower or equal level-of-service in the rest of the attributes
? Cost is in Euros per shipment
? Transit time is in days
? Magnitude of delay in days
? Frequency is in number of weekly departures
;alts = alt1, alt2
;rows = 12
;eff = (mnl,d)
;model:
U(alt1) = b_cost[-0.00347] *  cost.ref[700]             +     b_time[-0.357] * time.ref[4]           + b_delay[-0.107] * delay.ref[2]             + b_freq[0.255] * frequency.ref[3]/
U(alt2) = b_cost           *  cost.piv[-25%,-15%,-10%]  +     b_time         * time.piv[1,2,3]       + b_delay         * delay.piv[-2%,-5%,-10%]  + b_freq        * frequency.piv[-2,-1,0]

$

Another experimental design involves the current option and an alternative that is more expensive but offers better levels of service:

Code: Select all

Design
? This game involves choice between the current option and an alternative that involves a higher cost but offers better conditions for the other attributes considered
? Transit time is in days
? Magnitude of delay in days
? Frequency is in number of weekly departures
;alts = alt1, alt2
;rows = 12
;eff = (mnl,d)
;model:
U(alt1) = b_cost[-0.00347] *  cost.ref[700]         +     b_time[-0.357] * time.ref[4]           + b_delay[-0.107] * delay.ref[2]             + b_freq[0.255] * frequency.ref[3]/
U(alt2) = b_cost           *  cost.piv[5%,10%,20%]  +     b_time         * time.piv[-2,-1,0]      + b_delay         * delay.piv[0%,5%,7%]    + b_freq        * frequency.piv[-1,0,1]

$

Alternatively, should these two cases be combined into a single experiment with three alternatives: the current option, a premium alternative (higher cost but better service), and a discount alternative (lower cost but inferior service)? From a design and modeling perspective, which approach is preferable: separate experiments reflecting asymmetric trade-offs, or a single combined experiment that presents both types of alternatives simultaneously?

[Michiel Bliemer]

If you are mainly interested in willingness to pay, you can use an unlabelled experiment (option A, option B) wherein the second option is sometimes cheaper (and worse in other attributes) and sometimes more expensive (and better in other attributes) than the current option. Ngene can automatically avoid dominant alternatives in an unlabelled experiment by using ;alts = alt1*, alt2* (adding an asterisk after each alternative name), assuming that non-zero priors are given to indicate the preference order of the attribute levels.

If you are interested in demand forecasting for different services, e.g. premium versus basic, then you have a labelled experiment and alternative-specific constants will need to be added to capture the label effect. In that case, you can again conduct a single experiment with three alternatives.

Michiel