Combining experiments and feasibility of using nested logit structure

[Gabriel Souza]

Hi!

I'm working on a SP survey which consists of two DCEs:
1 - The first and principal one is a mode choice experiment, with two alternatives (actual mode vs train) with two attributes (total time and cost)
2 - The second one is kind of a route choice experiment, with two alternatives (train 1 vs train 2) with two attributes (travel time and access time)

The reason to split it in two parts instead of just using travel time and access time in the principal one is to reduce cognitive burden.
So I was thinking what would be the best way to combine the data collected from these two experiments to consider travel time and access time coefficients in train's utility in the mode choice model.

It seems to me that I could use apollo_combineModels function to achieve this. In the first model, I would specify train's utility as U_train = [beta_time_access * alfa + beta_time_travel * (1 - alfa)] * time_total + beta_cost * cost. In the second model, it would be directly U_train = beta_time_acess * time_acess + beta_time_travel * time_travel. Alfa would be a parameter to be estimated by the model.

Questions:
1 - Would this approach work? Do you suggest some modification or even a whole other approach?
2 - Should I add a scaling parameter for each experiment (of course, normalizing one of them) multiplying the utilities? The respondents will be the same, but since the experiments are different, I believe the answer is yes, but I'd like to confirm this.

Now, another question I have related to the first experiment is about the feasibility to use a nested logit model with the data collected from this experiment. Each respondent will only see 2 alternatives (his actual vs train), but we'll collect data from 3 actual modes (car, public bus and charter bus). So I'd like to test some nested structures to end up with a single model for the 4 modes (car, public bus, charter bus and train).

I did some tests filtering apollo_modeChoiceData database to keep rows where respondents had only 2 alternatives available to choose, and I was still able to estimate a nested logit model with all the 4 modes that are in the database. So I guess it would be possible to use nested logit with the data collected from my experiment.

The question is: does it make sense? I mean, I didn't observe choices considering the 4 modes as alternatives. Even though I can estimate a single model with the 4 modes, should it be used?

Looking forward to your thoughts. Thanks!

[stephanehess]

Hi

not sure what your aim is re the alpha parameter, but otherwise, combining the models would be fine, of course with a scale parameter. There's an example on the Apollo website

Regarding NL, this won't really work. As you'll only ever have two alternatives available at a time, the probs would be the same as for MNL except in those cases where the nested alternatives are present at the same time

Stephane

[Gabriel Souza]

Thanks for the reply, Stephane.

Regarding the alpha parameter, the idea is to create a link between the total travel time used in the mode choice experiment and the decomposed time components used in the route choice experiment.

Since access and in-vehicle time are not available in the first experiment, my idea was to express the time coefficient for the train in the mode choice model as a weighted combination of the coefficients identified in the route choice experiment:
β_time_train = α·β_access + (1−α)·β_travel

So the train utility in the first experiment would be:
U_train = [α·β_access + (1−α)·β_travel] · time_total + β_cost · cost

While in the second experiment the utilities would be specified directly as:
U_train = β_access · time_access + β_travel · time_travel.

The parameter α would therefore capture the extent to which the total travel time presented in the mode choice experiment is behaviourally perceived as access time versus in-vehicle time, allowing the two experiments to inform the same underlying time sensitivities.


Regarding the NL, I'd like to make sure I understood your point correctly.

I realised that, in the test I previously mentioned, even after filtering the apollo_modeChoiceData database to keep only observations where respondents had two alternatives available, I still ended up with all possible pairwise combinations of modes in the dataset.

In my actual experiment, however, one of the alternatives will always be train, so the observed pairs would only be:
car vs train
public bus vs train
charter bus vs train

This means that alternatives within a, let's say, bus nest (public vs charter) would never be observed together. Am I correct in thinking that this is the issue, i.e., that without observing choices between alternatives within the same nest, the nesting parameter would not be identified?

[stephanehess]

Hi

your approach with alpha will work on the assumption that there is no other heterogeneity in sensitivities between the two experiments.

Re NL, the issue is that you only ever have two alternatives available at a time

Stephane