Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Contributions to Probabilistic Discrete Choice
KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport and Location Analysis.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. , x, 20 p.
Series
TRITA-TSC-PHD, 12:001
National Category
Transport Systems and Logistics
Identifiers
URN: urn:nbn:se:kth:diva-95402ISBN: 978-91-85539-86-4 (print)OAI: oai:DiVA.org:kth-95402DiVA: diva2:528102
Public defence
2012-06-01, D2, Lindstedtsvägen 5, KTH, Stockholm, 09:15 (English)
Opponent
Supervisors
Funder
TrenOp, Transport Research Environment with Novel Perspectives
Note

QC 20120524

Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2016-01-20Bibliographically approved
List of papers
1. Invariance of achieved utility in random utility models
Open this publication in new window or tab >>Invariance of achieved utility in random utility models
1995 (English)In: Environment and planning A, ISSN 0308-518X, E-ISSN 1472-3409, Vol. 27, 121-142 p.Article in journal (Refereed) Published
National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-78500 (URN)
Note
NR 20140805Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2017-12-08Bibliographically approved
2. Extreme values, invariance and choice probabilities
Open this publication in new window or tab >>Extreme values, invariance and choice probabilities
2011 (English)Report (Other academic)
Abstract [en]

Since the pioneering work of McFadden (1974), discretechoice random-utility models have become work horses in many areas in economics.In these models, the random variables enter additively or multiplicatively, and the noise distributions take a particular parametric form. We show that the same qualitative results, with closed-form choice probabilities, can be obtained for a wide class of distributions without such specifications. This class generalizes the statistically independent distributions where any two c.d.f.:s are powers of each others to a class that allows for statistical dependence, in a way analogous to how GEV distributions generalize Gumbel distributions. We show that this generalization is sufficient, and under statistical independence also necessary, for the following invariance property: all conditional random variables, when conditioning upon a certain alternative having been chosen, are identically distributed. In our general framework, proofs become simpler, more direct and transparent, well-known results are obtained as special cases, and one can characterize the Gumbel, Fréchet and Weibull distributions.

National Category
Transport Systems and Logistics Economics
Identifiers
urn:nbn:se:kth:diva-95383 (URN)
Funder
TrenOp, Transport Research Environment with Novel Perspectives
Note
QC 20120523Available from: 2012-05-23 Created: 2012-05-23 Last updated: 2012-06-12Bibliographically approved
3. Random Utility Models, IIA, Mattsson-Weibull-Li Distributionsand a Conjecture by Luce and Suppes
Open this publication in new window or tab >>Random Utility Models, IIA, Mattsson-Weibull-Li Distributionsand a Conjecture by Luce and Suppes
2012 (English)Report (Other academic)
Abstract [en]

In recent papers, Mattsson and Weibull, and independently Li, have introduced a class of independent distributions, where the individual cdf’s are powers of each other. For this class they have showed that the choice probabilities are of “Luce form”, i.e. the form following from the Independence from Irrelevant Alternatives (IIA) assumption. We show a converse to this result. For a class of “independent” Random Utility (RU) Models, allowing non-uniform expansion, and where the cdf’s in question are well-behaved in a certain sense, the only possibility is that the cdf’s are of the above mentioned Mattsson-Weibull-Li (MWL) type. This result resolves an old conjecture by Luce and Suppes. The result demands unbounded choice sets. For finite models, we show on the contrary, that any finite independent RU model with Luce form choice probabilities, there is a version with random terms that are not MWL-distributed

National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-95396 (URN)
Note
QC 20120524Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2012-05-24Bibliographically approved
4. Choice Probabilities in Random Utility Models: Necessary and Sufficient Conditions for a Much Used Formula, andImplications for the Conditional Distributions of Achieved Utility
Open this publication in new window or tab >>Choice Probabilities in Random Utility Models: Necessary and Sufficient Conditions for a Much Used Formula, andImplications for the Conditional Distributions of Achieved Utility
2012 (English)Report (Other academic)
Abstract [en]

Random Utility (RU) Models have reached a wide applicability in many areas of applied Economics. In all application areas, the formulas for the choice probabilities play a central role. For the formulas to be useful, the probabilities further need to sum up to 1. In this note, we give necessary and sufficient conditions for the validity of the classical choice probability formula (i.e. that the choice probabilities are the integrals of the partial derivatives of the cdf of the random term along the diagonal), and that the probabilities sum up to 1. Further, it is proved sufficient that the gradient of said cdf is continuous and piecewise differentiable with locally bounded gradient, along the diagonal. Along the way we prove many intermediate results relating different derivatives of the cdf. Finally the results are applied to derive formulas for the distribution of achieved utility conditioned on a given alternative being chosen.

National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-95397 (URN)
Note
QC 20120524Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2012-05-24Bibliographically approved
5. The Choice Axiom Revisited
Open this publication in new window or tab >>The Choice Axiom Revisited
2012 (English)Report (Other academic)
Abstract [en]

The famous Choice Axiom by Luce is now more than half a century old. We investigate the consequences of going back to Luce’s original formulation of the axiom, which had a more succinct formulation. Using this, what we term Strong Choice Axiom, we prove a sort of “lexicographic” version of the “Luce form” choice probabilities. Further, we study whether these extended choice probabilities are representable by Random Utility models.

National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-95399 (URN)
Note
QC 20120524Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2012-05-24Bibliographically approved
6. A simple derivation of the Williams-Daly-Zachery theorem
Open this publication in new window or tab >>A simple derivation of the Williams-Daly-Zachery theorem
2012 (English)Report (Other academic)
Abstract [en]

In this note we give a simple elementary proof of the Williams-Daly-Zachery theorem for additive random utility (ARU) models. This theorem says that the choice probabilities in an ARU model are the partial derivatives of the expected achieved utility. This is proved under the condition that the choice probabilities are continuous. We further prove that the choice probabilities are continuous exactly when the probability of ties is zero. Finally we prove that the probability of ties is zero if the cdf of the random term (of the ARU model) is differentiable with locally bounded gradient.

National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-95398 (URN)
Note
QC 20120524Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2012-05-24Bibliographically approved
7. A Note on Power Invariance in Random Utility Models
Open this publication in new window or tab >>A Note on Power Invariance in Random Utility Models
2012 (English)Report (Other academic)
Abstract [en]

Invariance in Random Utility (RU) Models is the property that the distribution of achievedutility is invariant across the alternatives chosen. In this note we study a generalization termedPower Invariance (PI). It generalizes the property, showed by Mattsson and Weibull, thatinvariance holds for an independent RU Model, where the cdf’s of the random terms arepositive powers of a given base cdf . The power invariant copulas turn out to be the copulasof Multivariate Extreme Value distributions. We further show that, under natural regularityconditions, the copulas of the marginal distributions of a PI copula are power invariant.

National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-95400 (URN)
Note
QC 20120524Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2012-05-24Bibliographically approved
8. Random Utility Invariance Revisited
Open this publication in new window or tab >>Random Utility Invariance Revisited
2012 (English)Report (Other academic)
National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-95401 (URN)
Note
QC 20120524Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2012-05-24Bibliographically approved

Open Access in DiVA

fulltext(583 kB)337 downloads
File information
File name FULLTEXT01.pdfFile size 583 kBChecksum SHA-512
a79fd7d910ab2fda4418a62c6672dd9bb5cddcb11ffacb8dcb178dd16afee74c7f0aeeb8a4139116669cf5ffe095f1011fd46dd909d13e168719aa0691bd7f9a
Type fulltextMimetype application/pdf
Abstract(15 kB)2 downloads
File information
File name SPIKBLAD01.pdfFile size 15 kBChecksum SHA-512
ce390294ac9e4f38f898bfb62d5d8c138d100c9fa557c7ce870191f8264f525bda21a4f12fcf7706e7cbdbb31ec3f47f1b1f8322ed5aa77a6ebce4626d6b7de4
Type spikbladMimetype application/pdf
Introductory presentation(207 kB)13 downloads
File information
File name FULLTEXT03.pdfFile size 207 kBChecksum SHA-512
82a5c5312f5aef2bfb76c68308a9c1e03c78f19c8267548296a092b5cc6888ed1aa7c35e7e16830ac6446fb2485ec1f7f5801b6a780d55376bc2236cb7984b03
Type attachmentMimetype application/pdf

Search in DiVA

By author/editor
Lindberg, Per Olov
By organisation
Transport and Location Analysis
Transport Systems and Logistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 350 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 588 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf