Interactions

[vigneshkesavan]

Dear Prof Michiel and team,

In line with the topics on Prior values, Interactions, and Pilot study, I have a few questions. Kindly clarify the doubts.

My question is specifically about the interaction specification in Ngene efficient design. For example, I am using the following source to understand the interaction : https://www.sciencedirect.com/science/article/pii/S0965856408000049, where the authors used RP data and Nested logit model for estimation. My question is concerning the 'TABLE 3'.

1. First, I need to clarify the total number of interactions in the model. Explicitly, there are five interaction terms such as Toll², Time², (Time) X (income), (Toll) X (Time), (Time) X (Dep. time) in the lower nest. Apart, Is it right to say that implicitly for 'each' parameter, there are 3 interactions- for example: to estimate the 'Toll' parameter under the 'cash- Pre-work' - I need to have a part of utility equation like 'Beta_Toll* Tolldata*Dummy(cash)*Dummy(Pre)*Dummy(work)', where dummy takes 1 if yes or 0. Does the above utility specification stand right ? and will it count as a '4' interaction for finding this 'single' parameter? If the term 'Interaction' is unsuitable for this case, how and what should be used when using Ngene in a similar case?

2. As said before, the cited source uses RP data. If a Discrete choice experiment is planned with the Time, Toll Cost, Departure time, and Early or late arrival as 4 attributes, the conventional Ngene efficient design will include these 4 attributes and the explicit interactions like Time², Toll cost², (Toll cost) X (Time), (Time) X (Dep. time) are possible. But if I need to bring the elements which are 'not included in choice experiment' like Cash (dummy) or Work( dummy) or anything, how do I handle this while designing the efficient design in Ngene? Ngene manual (Page number: 115) explains the code for efficient design and interactions, but only with 'attributes' added in the discrete choice experiment (DSE); how to add the above-mentioned 'out of DSE' elements in design?

3. If adding out of DSE elements is possible, what type of difference is required to address between the 'dummy' elements and 'real' value elements? For example, work or leisure is a dummy but an interaction like (Time x Income) where Income carries a different value and is not part of DSE. I wish to know how prior specifications should be in these cases.

4. In reference to Tabe 3 in the same paper, estimation results give 12 values for each parameter. I can note 144 values only in the lower nest ( 12 parameters with 12 combinations). For example, Toll has 12 values with the combination of 'work-leisure' with 'pre-peak-post' along the 'ez pass and cash'. Is it right to say, in estimation, I have 12 'different' beta parameters only for toll, as 12 unique values should be from 12 unique beta parameters? If I am right the model needs 144 beta parameters only for the lower nest and, additionally, some 48 values in the upper nest and 24 values in inclusive parameters. Do we need to have these many separate beta parameters to be specified in the estimation model, or is there any other way to get these values without many separate beta parameters? Sorry for asking an estimation question in this forum.
As Prior values for the main survey are informed from either a pilot study or a previous study, if I get many attribute values with interactions, how should the priors be fixed in the design part in Ngene?

5. If more beta parameters, as in the above case, are required, what model is recommended in design for 'pivot' efficient in Ngene? MNl or nested logted or error component or any other? Sorry for the genric question.

Thank you for your time.

[Michiel Bliemer]

Hi,

I am afraid that I do not have time to read that paper to try to understand their utility function, which seems quite complex, so I cannot answer your specific questions about that study.

Note that you need to make a distinction between attributes and socio-demographic variables. It sounds like income and work are socio-demographic variables that you add to the utility function after the data collection, which are generally ignored at the experimental design stage because they are not available (unless you create a separate design for each population segment). So you would merely consider interactions between attributes. Ngene does allow using socio-demographics using the .covar syntax, I refer to section 8.4 in the Ngene manual. The way to do this is quite restrictive though, and it is rarely done.

The priors for these attributes would be an average across the population, so you would need to combine the parameters of interactions with socio-demographic variables to obtain a population-averaged prior. For example, if V = -0.5*cost -0.2*cost*lowincome, where lowincome is a dummy that equals 1 if the respondent has a low income (with high income the base), then the prior for high income respondents is -0.5 and the prior for low income respondents is -0.7. If you know how many respondents will have low and high income, you can compute the population average prior. For example, if both income classes appear 50-50%, then the population average prior for cost is -0.6.

When generating a design, I would typically always assume an mnl model as it is very difficult to optimise for other types of designs (because of computational complexity or inability to get priors for certain variables such as inclusive value or error component). An mnl optimised design is typically also reasonably efficient to estimate other logit models. If your model will have many parameters, then I would simply use a large number of rows in the design to ensure that there is sufficient variation to estimate all interactions and also to estimate more advanced models.

Michiel

[vigneshkesavan]

Thank you Prof Michiel for your detailed answer.
1. I am searching for the research paper(s) that developed theoretical or statistical constructs for "PIVOT" discrete choice experiments. I can trace the theory and applied studies back to the papers of Prof Hensher, Prof Rose, Prof Train, Prof Wilson, etc. However, I can't find the analytical model supporting the pivot design. Rose, Bliemer, Hensher, and Collins (2008) " Designing efficient stated choice experiments in the presence of reference alternatives" explains the pivot element but elaborates on the computation only for efficient design. Train and Wilson (2008) "Estimation on stated-preference experiments constructed from revealed-preference choices" focuses only on the estimation part. Hence, kindly inform about any papers that developed the mathematical support for pivot design.

2. I am quoting your answer from the previous chat

If you include early/late arrival in the utility function, which is common, then you would, of course, not include departure time in the utility function because this is confounded with early/late arrival and travel time and you cannot estimate a separate parameter for departure time.

Early arrival = max{PAT-deptime-traveltime,0}
Late arrival = max{deptime+traveltime-PAT,0}
where PAT is preferred arrival time. In other words, you can include early/late arrival time and you can include travel time, but you cannot include deptime because this is not an independent variable and the model would suffer from multicollinearity.

I design the pivot efficient with NGene for the experiment with 4 attributes Time, Cost, Departure time, and Early/late arrival. I understand from your above-quoted answer that departure time will not have a 'separate parameter' in estimation even though it is included as an attribute in discrete choice table. My question is if i need to set the prior (by pilot), how should i fix the priors of departure time in design (both in design for pilot study and main study) when it can't be estimated as a separate parameter. I understand priors are only for parameters to be estimated, if no parameters, then no priors. But I wish to clarify this clearly. Sorry for this question, if it is less meaningful.

3. I hope it is generally followed that Early or late arrival will be considered as a single attribute, where respondents may get the combination of late and early for different alternatives in the same task. Of course, it will be captured as a single parameter. Is it right to give the single prior for that parameter as it includes both early and late ?

Thank you for your time

[Michiel Bliemer]

The calculation of the D-error of a pivot design is the same as for a regular design, the equations are not different.

For a pivot design in Ngene, one of the alternatives has reference values, so the utility of this alternative is constant.
For the reference alternatives, the attribute levels are simply pivoted around the reference values and hence become values again like in any other design. A pivot design is therefore not different from any other design.

Your utility function will look something like:
U(deptime7) = b1 * traveltime[...] + b2 * (PAT[9] - deptime[7] - traveltime) + b3 * (deptime[7] + traveltime - PAT[9])
U(deptime8) = ...

where the terms multiplied by b2 should be set to 0 if negative, and the terms multiplied by b3 should be set to 0 if negative. In Ngene this could possibly be done by imposing constraints, but I have not done this previously for such complex utility functions. You will need to carefully think about the utility functions you are estimating, I do not believe that you have a parameter specifically for departure time, but you know the model that you want to estimate better than I do.

Michiel

[Michiel Bliemer]

Note that you can only edit utility functions in Ngene, not in the online version of SurveyEngine.
Generating an efficient design where your variables are functions of attributes is complicated.

Note that your utility functions are somewhat similar to the ones in this article:
https://www.researchgate.net/publication/227580330_Rewarding_instead_of_charging_road_users_A_model_case_study_investigating_effects_on_traffic_conditions

The choice experiment for the model in the above article is described in this PhD thesis, see a screenshot of the choice experiment on page 47:
https://repository.tudelft.nl/islandora/object/uuid%3A80b846c8-43a7-4613-8a2d-c7f01367d0c0

The design for that choice experiment was based on an orthogonal array. With an orthogonal array you do not need to set priors and the utility function that you specify does not matter, so you could use SurveyEngine to generate it.

Michiel

[vigneshkesavan]

Thank you Prof Michiel for clarifying the doubts.