Heterogenous pivot design around multiple ref alts.

[nayeem]

I defined the travel time reliability (TTR) attribute using five equiprobable outcomes (interpretable as five shipments), as follows:

• Very high reliability: 4/5 times on time, 1/5 times 2 hours late

• High reliability: 3/5 times on time, 2/5 times 3 hours late

• Medium reliability: 2/5 times on time, 3/5 times 3 hours late

• Low reliability: 2/5 times on time, 3/5 times 4 hours late

• Very Low reliability: 1/5 times on time, 4/5 times 5 hours late

And included the reliability attribute in the experimental design as shown:

Code: Select all

design   
? mode choice of shippers with HOMOGENOUS DESIGN CODING   
;alts=truck, train, etrain
;rows=24
;block=3
;eff=(mnl,d)
;con
;model: ?model using DESIGN CODING
U(truck)=  b1.dummy[0|0|0|0]       *  COST1[0,1,2,3,4]                               
        +  b2.dummy[0|0|0|0]       *  TIME1[0,1,2,3,4]                               
        +  b3.dummy[0|0]           *  TTR1[0,1,2,3,4]                                   
        +  b4.dummy[0]             *  risk[1,0]                                     
        /
U(train)=  con_train                                                                 
        +  b5.dummy[0|0]           *  COST2[0,1,2]                                   
        +  b6.dummy[0|0|0]         *  TIME2[0,1,2,3]                                 
        +  b3.dummy                *  TTR1                                           
        +  b7.dummy[0|0]           *  frequency[0,1,2]
        /
U(etrain)= con_etrain                                                               
        +  b5.dummy                *  COST2                                         
        +  b8.dummy[0|0]           *  TIME3[0,1,2]                                   
        +  b9.dummy[0]             *  TTR2[0,1]                                     
        +  b7.dummy                *  frequency                                     
$

One alternative (etrain) has first two levels only (Very high reliability, High reliability)
Since both high and medium reliability have the same standard deviations (although they differ in number of on time arrivals), can I breakdown the reliability attribute into two separate attributes like:

• Option 1: Probability of on-time arrivals (in fractions or percents) and magnitude of delay (in hours)

• Option 2: Standard deviation of travel time and a categorical variable to differentiate between first two levels of reliability (Very high, High) and last three levels of reliability (Medium, Low, Very Low) for alternatives truck and train since etrain only has first two levels of reliability

Are these options methodologically sound given my experimental design or do I have to stick to a single attribute of reliability as in my experimental design?

[Michiel Bliemer]

In the transport literature, travel time reliability for road transport is most commonly included in utility functions by including two attributes:
* The MEAN of the distribution
* The STANDARD DEVIATION of the distribution

The coefficient of the mean is typically used to compute a value of time, while the coefficient of the standard deviation is used to compute the value of reliability.

U = ... b1 * mean(TT) + b2 * stdev(TT) ...

For public transport, one sometimes considers on-time arrival or lateness variables.

You can consider nonlinearities as well, for example using the categorical variable you proposed:

U = ... b1 * mean(TT) + (b2 + b3 * HighOrVeryHighReliability) * stdev(TT) ...

There are other ways to include travel time distributions into the utility function, but it is best to consult the literature on what is considered acceptable. These are two articles may be useful:

https://www.sciencedirect.com/science/a ... 6415000142
https://www.sciencedirect.com/science/a ... 0X21001625

[nayeem]

In the original research article, you mentioned in your reply (Khan et al., 2021), they have used an external candidate set in Ngene. In this case even though a travel time distribution is used to represent both time and travel time reliability in the SP survey, the utility specification has separate variables for mean and standard deviation of the same travel time distribution. Since each unique distribution is represented by both mean time and standard deviation and there are often large numbers of choice tasks in external candidate sets (67 tasks in the paper mentioned above), how do we represent the levels of the variables mean and standard deviation of travel time in the Ngene code below?

Code: Select all

design
;alts   =  urbanRoad, motorWay
;rows   =  18
;blocks =  3
;eff    = (mnl,d)
;alg    = mfederov(candidates =choice_task.csv)
;model:
U(urbanRoad) = b1[-0.08]   * toll[0]
             + b2[-0.02]   * meantime[.....]
             + b3[-0.04]   * stdDeviation[....]
             /
U(motorWay)  = b1          * toll[1,2,3]
             + b2          * meantime[6]
             + b3          * stdDeviation[0]
$

• Khan, F., Bliemer, M. C., Beck, M. J., Hess, S., & Van Lint, J. W. C. (2021). Stated choices and simulated experiences: Differences in the value of travel time and reliability. Transportation Research Part C: Emerging Technologies, 128, 103145.

• Choice Tasks: https://drive.google.com/file/d/1Nunkwz ... view?pli=1

[Michiel Bliemer]

We first designed the distributions, for example: (4,4,10,12,12).

Then we calculated (in Excel) the mean and stdev for each distribution. In the example distribution above:
mean(4,4,10,12,12) = 8.4
sddev(4,4,10,12,12) = 4.1

We calculated this for all distributions and created a candidate set with columns for mean and stdev for both alternatives. We made sure that all values for the mean and stdev appear in the Ngene script, so 8.4 is included in the script for attribute meantime and 4.1 is included in the script for attribute stdDeviation.

Michiel

[nayeem]

Like other designs, if priors are not available, I can start with zero priors for my pilot study?

[Michiel Bliemer]

Yes, absolutely, you can use zero priors.

In the candidate set, you may also want to make sure that you avoid any dominant alternatives, e.g. an alternative with a lower toll, lower mean, and lower stdev. Similarly, you may also want to remove any stochastically dominant alternatives, e.g. (4,6,8,8,8) stochastically dominates (8,8,8,8,8) because the travel time is always lower (or the same). Despite the latter alternative being better in terms of stdev (more reliable). We removed such alternatives from our candidate set in the paper that you cite.

Another paper where we discuss stochastically dominant alternatives is in this paper:
https://link.springer.com/article/10.10 ... 21-10206-3

Michiel