I've followed the work of the transport economist Marc Gaudry with great interest for several years now. He has a recent report (available on ResearchGate - https://tinyurl.com/bdhfzzp4) that identifies four properties of the logit model (some are generalizable to other probability models). I thought the topic would interest some on the forum. I summarize them below.

1. "An unlikely genealogy of random coefficient model ancestors" This is largely focused on the origins of the logit model formulation. I see this point as rooted in a lack of a common global language - not a bad thing in general terms, but it means that some important work sometimes gets missed. As a Canadian with only basic French skills, I would have a hard time following Abraham's work from the 1960s.

2. "Missing constants and the unlikely functional form of network variables". This is a point about linearity (or logarithmic) functional form assumptions for time and cost variables, which is common in the transportation literature. Marc has made this argument for many years and it's a point well taken. We had a recent correspondence on the parallels in recent work by Chandra Bhat and colleagues applied to probit and using Yao-Johnson transformations (vs. the Box-Cox applied to logit in Marc's 1970s work on the topic).

3. "A random utility function error generating non-stochastic pi and elasticities". This is one I hadn't thought about, but I agree is, in a way, strange. Probabilistic choice models include random error terms, but they generate deterministic outcomes so that elasticities are "sample elasticities" rather than expectations. Marc estimates mean, variance, and skewness for other models that admit their derivation.

4. "A Log-sum term generally not unique for a given estimated model". The issue arises when socioeconomic variables enter the equation. The logsum term is no longer unique because the specification (in which alternative(s) one puts socioeconomic indicator variables) affects the outcome. There is no problem for ASC. The report has some nice examples. This non-uniqueness becomes a problem when estimating nested logit models. It sounds like Huw Williams provided some comments on the paper.

His conclusion also has some good "food for thought".

Thank you. Some comments to your numbered bullets.

1. Every Logit model, like the Gravity Model, IPF, ODME, etc. can be stated as a Maximum Entropy model which produces the most probable set of solutions, a meso-state, among all possible random solutions, micro-states, not the only unique solution. (I tried to include a URL to an old presentation https://www.trbappcon.org/oldsite/2009conf/TRB2009presentations/s2/02_be..., but that URL is broken. But I am a pack rat and the PPT for that link is attached. The Logit Model is the 13th slide. )

1. A Logit Model only misses coefficients if its cost/utility function does not also include these coefficients. The fact that they are close to zero and often not included in cost functions does not mean that they do not exist.

1. Logit models are of course random. See First bullet.

1. Logit model solutions are of course not unique. See First bullet.

From: jason.hawkins=unl.edu@mg.tmip.org On Behalf Of jfhawkin

Sent: Friday, September 1, 2023 12:03 PM

To: TMIP

Subject: [TMIP] Four "Strange Properties" of the Logit Model

I've followed the work of the transport economist Marc Gaudry with great interest for several years now. He has a recent report (available on ResearchGate - https://tinyurl.com/bdhfzzp4) that identifies four properties of the logit model (some are generalizable to other probability models). I thought the topic would interest some on the forum. I summarize them below.

1. "An unlikely genealogy of random coefficient model ancestors" This is largely focused on the origins of the logit model formulation. I see this point as rooted in a lack of a common global language - not a bad thing in any sense, but it means that some important work sometimes gets missed. As a Canadian with only basic French skills, I would have a hard time following Abraham's work from the 1960s.

2. "Missing constants and the unlikely functional form of network variables". This is a point about linearity (or logarithmic) functional form assumptions for time and cost variables, which is common in the transportation literature. Marc has made this argument for many years and it's a point well taken. We had a recent correspondence on the parallels in recent work by Chandra Bhat and colleagues applied to probit and using Yao-Johnson transformations (vs. the Box-Cox applied to logit in Marc's 1970s work on the topic).

3. "A random utility function error generating non-stochastic pi and elasticities". This is one I hadn't thought about, but I agree is in a way strange. Probabilistic choice models include random error terms, but they generate deterministic outcomes so that elasticities are "sample elasticities" rather than expectations. Marc estimates mean, variance, and skewness for other models that admit their derivation.

4. "A Log-sum term generally not unique for a given estimated model". The issue arises when socioeconomic variables enter the equation. The logsum term is no longer unique because the specification (in which alternative(s) one puts socioeconomic indicator variables) affects the outcome. There is no problem for ASC. The report has some nice examples. This non-uniqueness becomes a problem when estimating nested logit models. It sounds like Huw Williams provided some comments on the paper.

His conclusion also has some good "food for thought".

--

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Thanks for the comments.

To clarify, point 2 is not about the omission of cost variables. It's about their misspecification in models producing non-intuitive signs or scale invariant time estimates (2 minutes has the same effect relative to both 10 minutes and 100 minutes base times). Alex Anas showed the equivalence between logit and entropy maximization some years ago, and I don't think Gaudry disagrees.

The lack of randomness is in the probability value - it is derived from a random quantity but has no randomness itself. The issue here is that the elasticity cannot be calculated as an expectation - see a 1968 paper by Goldberger on the topic.

Point 4 is not about the uniqueness in the sense used in maximum entropy, which is a function of system states. It's a question of different (though economically equivalent) utility specifications resulting in different results.

________________________________

From: Daniel Beagan

Sent: Friday, September 1, 2023 1:05 PM

To: Jason Hawkins ; TMIP

Subject: RE: [TMIP] Four "Strange Properties" of the Logit Model

Non-NU Email

________________________________

Thank you. Some comments to your numbered bullets.

1. Every Logit model, like the Gravity Model, IPF, ODME, etc. can be stated as a Maximum Entropy model which produces the most probable set of solutions, a meso-state, among all possible random solutions, micro-states, not the only unique solution. (I tried to include a URL to an old presentation https://www.trbappcon.org/oldsite/2009conf/TRB2009presentations/s2/02_be..., but that URL is broken. But I am a pack rat and the PPT for that link is attached. The Logit Model is the 13th slide. )

1. A Logit Model only misses coefficients if its cost/utility function does not also include these coefficients. The fact that they are close to zero and often not included in cost functions does not mean that they do not exist.

1. Logit models are of course random. See First bullet.

1. Logit model solutions are of course not unique. See First bullet.

From: jason.hawkins=unl.edu@mg.tmip.org On Behalf Of jfhawkin

Sent: Friday, September 1, 2023 12:03 PM

To: TMIP

Subject: [TMIP] Four "Strange Properties" of the Logit Model

I've followed the work of the transport economist Marc Gaudry with great interest for several years now. He has a recent report (available on ResearchGate - https://tinyurl.com/bdhfzzp4) that identifies four properties of the logit model (some are generalizable to other probability models). I thought the topic would interest some on the forum. I summarize them below.

1. "An unlikely genealogy of random coefficient model ancestors" This is largely focused on the origins of the logit model formulation. I see this point as rooted in a lack of a common global language - not a bad thing in any sense, but it means that some important work sometimes gets missed. As a Canadian with only basic French skills, I would have a hard time following Abraham's work from the 1960s.

2. "Missing constants and the unlikely functional form of network variables". This is a point about linearity (or logarithmic) functional form assumptions for time and cost variables, which is common in the transportation literature. Marc has made this argument for many years and it's a point well taken. We had a recent correspondence on the parallels in recent work by Chandra Bhat and colleagues applied to probit and using Yao-Johnson transformations (vs. the Box-Cox applied to logit in Marc's 1970s work on the topic).

3. "A random utility function error generating non-stochastic pi and elasticities". This is one I hadn't thought about, but I agree is in a way strange. Probabilistic choice models include random error terms, but they generate deterministic outcomes so that elasticities are "sample elasticities" rather than expectations. Marc estimates mean, variance, and skewness for other models that admit their derivation.

4. "A Log-sum term generally not unique for a given estimated model". The issue arises when socioeconomic variables enter the equation. The logsum term is no longer unique because the specification (in which alternative(s) one puts socioeconomic indicator variables) affects the outcome. There is no problem for ASC. The report has some nice examples. This non-uniqueness becomes a problem when estimating nested logit models. It sounds like Huw Williams provided some comments on the paper.

His conclusion also has some good "food for thought".

--

Full post: https://tmip.org/content/four-strange-properties-logit-model

Manage my subscriptions: https://tmip.org/mailinglist

Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/14043