Project Meeting 2025.03.13

Agenda

• Explicit error terms methodology

Technical

• Joel presented slides on the Phase 10 scope for representing explicit error terms

Monte Carlo simulation versus explicit error terms

• Presentation: https://docs.google.com/presentation/d/1F4HhiDQN_pfCvwbk1On3O4RcsVcsuNrL/edit
• Monte Carlo current method -- probability for each alternative, create cumulative probability distribution, draw realization from CDF.
• Pseudo random number generator (Mersenne Twister)
• Showed example of simple 3-alternative mode choice model. No-build choice of auto changes to walk in the build alternative even though the positive change in utility was to transit. In fact, the probability of walk went down. The random number did not change, but the ordering of alternatives in the cumulative distribution made the difference. Cross tab of 1000 tours of base vs build. 100 tours switch from auto to walk, which does not make sense, even though marginal shares change in the right direction. Does not make sense for individual decision makers.
• Simulation with explicit error terms – deterministic component and unobserved error term. The error term is treated as a random component. Logit model uses the Gumbel distribution for the error term. Draw random error terms from inverse cumulative density function and add to the measurable utility.
• Showed same 3-mode example using the random draws for the error terms and the resultant total utility. Alternative with highest utility is the choice. Same example as above, but with explicit error term draws, no decision maker switches to an alternative with a utility that did not increase. Can be used to cross tab changes between baseline and build.
• Examples are illustrative and simplistic. Nested logit model would be more complex and is commonly used. Total number of decision makers does not change, but could in some build scenarios. Upstream changes would not be held constant in real world.

Expected Use Cases for Explicit Random Error Method

• User Benefits Calculations – rule of half to calculate benefits for travelers who change modes. User Benefits calculations was the original motivation for this (Jan Zill, Australian context); Jan indicated that there are some theoretical benefits as well.
• Understanding who is changing their choice in a build alt to provide more information for decision making – e.g. income groups who change auto ownership, or primary mode, or auto vs. tolled path.

Overview of the scope of work

• Design phase
• Initial meeting on methodology and random number seeds (today)
• User features and gather feedback week of March 31
• Rec software solutions and prototype April 14, Tech memo

Key issues to address in design: Computational

• There are more calculations required for explicit error terms – random number draws for each alternative and two log calcs; more for nested models; need to exponentiate for logsums
• May investigate more modern random number generators

Key issues to address in design: Computational

• Circumstances when it is (or not) appropriate to compare outcomes across base versus build scenarios
• Straightforward for choices that are always made, but more challenging when the upstream choices change between scenarios (e.g., different numbers or types of tours)
• Are there software features that make the comparisons more meaningful for those cases? Flexibility in how random number drawn
• Recommendations when comparisons are meaningful and not

Key issues other:

• Logsums – expected value or inclusive error terms (taste heterogeneity)
• User features – control over what method is applied by model component

Discussion

• May not be able to address all the key issues under this scope. Recommendation is to run the prototype on a full model (time permitting).
• April 3 has been proposed as the next time to update the group on this task.
• Tuesday 3/18 is time for next Roadmap update.