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