Calibrating trip distribution models to trip length distribution (TLD)?

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louismerlin
Calibrating trip distribution models to trip length distribution (TLD)?

Hello TMIPers,

I frequently come across publications in both research and practice where
the impedance function has been calibrated to the trip length distribution
(TLD).

However, I have not been able to find a justification for this approach.

(Note: Ortuzar and Willumsen (2011) do suggest allowing travel cost bins
for ranges of travel length pp. 188, 195; but they do not suggest fitting
an impedance function to the TLD)

Could anyone out there point me to papers and/or book chapters that
recommend and justify the calibration of the impedance function to the trip
length distribution?

Thanks!

Louis Merlin
Assistant Professor
Florida Atlantic University

covomopez

Louis
Here is a link to a paper I wrote some time ago that bears on this topic.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.457.4387&rep=re...
If you cannot access the paper via the link, I could send it to you directly, so let me know,  

The basic idea is that each parameter of the impedance function can be associated with a statistical moment of the trip cost distribution. For example a negative exponential function of cost is associated with the mean cost, a power function with the mean log cost etc. As the complexity of the parameters increases, more and more moments of the trip cost distribution are required in order to estimate them all.
Hope this is helpful.
Geoff HymanGeoffrey Hyman Consultancy 

-----Original Message-----
From: louismerlin
To: TMIP
Sent: Fri, 5 Jul 2019 20:15
Subject: [TMIP] Calibrating trip distribution models to trip length distribution (TLD)?

Hello TMIPers,I frequently come across publications in both research and practice where
the impedance function has been calibrated to the trip length distribution
(TLD).However, I have not been able to find a justification for this approach.(Note: Ortuzar and Willumsen (2011) do suggest allowing travel cost bins
for ranges of travel length pp. 188, 195; but they do not suggest fitting
an impedance function to the TLD)Could anyone out there point me to papers and/or book chapters that
recommend and justify the calibration of the impedance function to the trip
length distribution?Thanks!Louis Merlin
Assistant Professor
Florida Atlantic University--
Full post: https://tmip.org/content/calibrating-trip-distribution-models-trip-lengt...
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Pilo Willumsen

This is a somewhat strange question. Section 5.5.2 of the Ortúzar &
Willumsen book is called ³Calibration techniques² and describes one
(Hyman¹s) for the standard gravity model in simple terms using observed Trip
Length Distribution. This may not be a very comprehensive treatment of the
calibration task and the reader is referred to commercial packages. All
commercial software have modules for distribution model calibration offering
solutions for different impedance/deterrence functions, for example in
Chapter 6 of my (old) version of TransCAD User¹s Manual.

Luis

From: on behalf of louismerlin

Date: Friday, 5 July 2019 at 20:13
To: TMIP
Subject: [TMIP] Calibrating trip distribution models to trip length
distribution (TLD)?

Hello TMIPers,

I frequently come across publications in both research and practice where
the impedance function has been calibrated to the trip length distribution
(TLD).

However, I have not been able to find a justification for this approach.

(Note: Ortuzar and Willumsen (2011) do suggest allowing travel cost bins
for ranges of travel length pp. 188, 195; but they do not suggest fitting
an impedance function to the TLD)

Could anyone out there point me to papers and/or book chapters that
recommend and justify the calibration of the impedance function to the trip
length distribution?

Thanks!

Louis Merlin
Assistant Professor
Florida Atlantic University
--
Full post:
https://tmip.org/content/calibrating-trip-distribution-models-trip-lengt...
stribution-tld
Manage my subscriptions: https://tmip.org/mailinglist
Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/13171

winufuwub

I think Louis Merlin´s original question referred to a sort of
"theoretical" reason for using the TLD as a basis for calibrating the trip
distribution (TD) model.

If this is the question, to me a good answer in that direction is given by
looking at the entropy maximising derivation of the TD model, where beta,
the sensitivity parameter of the TD model is the Lagrange multiplier
associated with the cost of the system (which is, in turn, associated with
trip lengths), and so it is obvious to estimate it on the basis of fitting
the TLD.

If you replace beta by several parameters associated with cost bins, you
obviously get a better fit and the theoretical derivation can be done the
same way (as proposed in a question in the aforementioned book, "Modelling
Transport").

Cheers

Juan de Dios

El lun., 8 jul. 2019 a las 13:08, Pilo Willumsen ()
escribió:

> This is a somewhat strange question. Section 5.5.2 of the Ortúzar &
> Willumsen book is called ³Calibration techniques² and describes one
> (Hyman¹s) for the standard gravity model in simple terms using observed
> Trip
> Length Distribution. This may not be a very comprehensive treatment of the
> calibration task and the reader is referred to commercial packages. All
> commercial software have modules for distribution model calibration
> offering
> solutions for different impedance/deterrence functions, for example in
> Chapter 6 of my (old) version of TransCAD User¹s Manual.
>
> Luis
>
> From: on behalf of louismerlin
>
> Date: Friday, 5 July 2019 at 20:13
> To: TMIP
> Subject: [TMIP] Calibrating trip distribution models to trip length
> distribution (TLD)?
>
> Hello TMIPers,
>
> I frequently come across publications in both research and practice where
> the impedance function has been calibrated to the trip length distribution
> (TLD).
>
> However, I have not been able to find a justification for this approach.
>
> (Note: Ortuzar and Willumsen (2011) do suggest allowing travel cost bins
> for ranges of travel length pp. 188, 195; but they do not suggest fitting
> an impedance function to the TLD)
>
> Could anyone out there point me to papers and/or book chapters that
> recommend and justify the calibration of the impedance function to the trip
> length distribution?
>
> Thanks!
>
> Louis Merlin
> Assistant Professor
> Florida Atlantic University
> --
> Full post:
> https://tmip.org/content/calibrating-trip-distribution-models-trip-lengt...
>
> stribution-tld
> Manage my subscriptions: https://tmip.org/mailinglist
> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/13171
> --
> Full post:
> https://tmip.org/content/calibrating-trip-distribution-models-trip-lengt...
> Manage my subscriptions: https://tmip.org/mailinglist
> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/13171
>

covomopez

Juan's discussion of the entropy maximisation derivation of the distributionmodel was indeed the initial thinking behind my paper. But the whole idea neededto be inverted. Instead of entropy we have hypothesis testing of the parameters ofan already specified impedance function. Instead of constrains, leading to the Lagrandian,we have first order conditions arising from a maximum likelihood estimation of the parameters.Essentially we end up with a dual of entropy maximisation. But in statistical terms, I think the motivation is clearer. Perhaps for physicists it is the other way round, but the strong duality suggests they are looking at opposite sides of the same coin. 
Meanwhile the derivation of the destination choice model has/had moved into the real of random utility theory, along with much of travel choice models. Interestingly, Cochran's formulation of the economic basis for the gravity model appeared at almost the same time as Wilson's paper on the statistical theory of spatial distribution models. Both of these preceded my calibration paper. 
Cheers
Geoff Hyman

-----Original Message-----
From: winufuwub
To: TMIP
Sent: Mon, 8 Jul 2019 21:18
Subject: Re: [TMIP] Calibrating trip distribution models to trip length distribution (TLD)?

I think Louis Merlin´s original question referred to a sort of
"theoretical" reason for using the TLD as a basis for calibrating the trip
distribution (TD) model.If this is the question, to me a good answer in that direction is given by
looking at the entropy maximising derivation of the TD model, where beta,
the sensitivity parameter of the TD model is the Lagrange multiplier
associated with the cost of the system (which is, in turn, associated with
trip lengths), and so it is obvious to estimate it on the basis of fitting
the TLD.If you replace beta by several parameters associated with cost bins, you
obviously get a better fit and the theoretical derivation can be done the
same way (as proposed in a question in the aforementioned book, "Modelling
Transport").CheersJuan de DiosEl lun., 8 jul. 2019 a las 13:08, Pilo Willumsen ()
escribió:> This is a somewhat strange question. Section 5.5.2 of the Ortúzar &
> Willumsen book is called ³Calibration techniques² and describes one
> (Hyman¹s) for the standard gravity model in simple terms using observed
> Trip
> Length Distribution. This may not be a very comprehensive treatment of the
> calibration task and the reader is referred to commercial packages. All
> commercial software have modules for distribution model calibration
> offering
> solutions for different impedance/deterrence functions, for example in
> Chapter 6 of my (old) version of TransCAD User¹s Manual.
>
> Luis
>
> From: on behalf of louismerlin
>
> Date: Friday, 5 July 2019 at 20:13
> To: TMIP
> Subject: [TMIP] Calibrating trip distribution models to trip length
> distribution (TLD)?
>
> Hello TMIPers,
>
> I frequently come across publications in both research and practice where
> the impedance function has been calibrated to the trip length distribution
> (TLD).
>
> However, I have not been able to find a justification for this approach.
>
> (Note: Ortuzar and Willumsen (2011) do suggest allowing travel cost bins
> for ranges of travel length pp. 188, 195; but they do not suggest fitting
> an impedance function to the TLD)
>
> Could anyone out there point me to papers and/or book chapters that
> recommend and justify the calibration of the impedance function to the trip
> length distribution?
>
> Thanks!
>
> Louis Merlin
> Assistant Professor
> Florida Atlantic University
> --
> Full post:
> https://tmip.org/content/calibrating-trip-distribution-models-trip-lengt...
>
> stribution-tld
> Manage my subscriptions: https://tmip.org/mailinglist
> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/13171
> --
> Full post:
> https://tmip.org/content/calibrating-trip-distribution-models-trip-lengt...
> Manage my subscriptions: https://tmip.org/mailinglist
> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/13171
>--
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