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?