Bevorzugter Zitierstil für diesen Vortrag

Transkript

1 Bevorzugter Zitierstil für diesen Vortrag Axhausen, K.W. (2008) What does similarity measure?, Invitational Workshop on Discrete Choice Models, EPF Lausanne, Lausanne, August Stunde 1 1

2 What does similarity measure? KW Axhausen IVT ETH Zürich August 2008

3 Stunde 1 3 Addressing the IIA property of the MNL/1 How similar are the ε jq? Ω = 2 ij... : σ Identical and independent or variabel and correlated Ω = nn n n n n ij σ σ σ σ σ σ σ σ σ... :

4 Addressing the IIA property of the MNL/2 Idea: Expand V i with a penalty term proportional to the average similarity with the other alternatives = ' + in in Cin in U V ϑ ε Stunde 1 4

5 But, how to measure it Temporal closeness of the time-space paths Spatial overlap of the time-space paths Overlap of level and style of pricing Control of time table and company Comfort Brand of the service Cost and quality of the service at the destination Kind and density of other services surrounding the destination Stunde 1 5

6 Example situation Stunde 1 6

7 Mechanisms Visibility of the alternative Stunde 1 7

8 Only visibility? Oberhausen (Wekeck/Friedrich) (BC) +/- Montreal (Wekeck/Friedrich) (BC) -/+ Zurich-based air travel (Wekeck/Friedrich) (BC) -/+ European air travel (Wekeck/Friedrich) (ln) +/0 Cycling route choice (PS) (ln) +/0 Stunde 1 8

9 Other mechanisms? Aggregation to form a generic alternative (and loss of visibility) (negative penalty) Aggregation in the time-space system (and joint incidence of breakdown and traffic volumes) (negative penalty) Aggregation to form a super-alternative (with a resulting larger capacity and chance for successful activity performance) (positive penalty) tip of iceberg effect (and increase in visibility of the alternative) (positive penalty) Stunde 1 9

10 New formulation One would want to test: = ' + β ϑ + ε in in Cin in U V ϑ Stunde 1 10

11 New formulation Possible implementation: Similarity in attributes Visibility among alternatives Closeness (and aggregation) in time-space system Gains/losses relative to the base situation Regret over a less-then-optimal choice (relative position) Rank (via tip-of-iceberg) ( Winner takes all ) Stunde 1 11

12 Route choice C-Logit (route overlap) PS-Logit (route overlap) Wekeck/Friedrich (schedule overlap, fare and travel time similarity) Stunde 1 12

13 Location choice Similarity in attributes (Batsell, 1981; Meyer and Eagle, 1982; Borgers and Timmermans, 1987) Attractiveness of the vicinity (Kitamura, 1988) Dominance/rank (Pagliara et al., 2006) Stunde 1 13

14 Dominanz With Rij = max(0, Xki Xkj ) = 0 R i = k j J R ij Stunde 1 14

15 Location choice: Validity of assumptions The availability of an alternative is a-priori unknown, which implies: Available capacity will be overestimated Overly positive assessment of the generalised costs on the way to a location Stunde 1 15

16 Location choice: Possibility of correction Iterative estimation (de Palma, Picard and Waddell, 2008) Penalty (Martinez, 2007) Stunde 1 16

17 Other implementations Field effects Prospect theory Regret Rank/dominance Stunde 1 17

18 Field effect With: Py ( )~ βx + W y + WX + Kε ki ki y j ì x j ì ki with y X i W i = = = Alternative k chosen by person i Attributes of alternative k weight matrix Stunde 1 18

19 Prospect theory with V = α f (max(0, X X )) + α f (min(0, X X )) + + i k k ki k0 k k ki k0 k where α f X ki Parameter; α + positive; α - negative funktion; f + concave; f - convex Attribukte k of alternative I Alternative 0 is a reference alternative, generally the status-quo Stunde 1 19

20 Regret with Rij = max(0, βk f( xkj xki )) k R = max ( R ) = V i j ij i where R ij f() k β regret for alternative i vis-à-vis alternative j Transformation, in Chorus et al. (2007) linear Attribute k of Alternative I Parameter Stunde 1 20

21 Swiss freight mode choice (Hettinger, 2008) Data: Recent telephone/cati SP experiments Current choice is reference Alternatives: Rail, Rail+Truck, Truck with Distance, weight, value, type of movement Cost Travel time Punctuality Stunde 1 21

22 Swiss freight mode choice Without panel-effect With panel-effect LL adj. 2 LL adj. 2 MNL / /0.529 CNL / /0.537 Dominance / /0.529 Batsell / /0.536 Prospect theory / /0.560 Stunde 1 22

23 Summary and outlook 1 prospect theory, regret and dominance are a continuum similarity and capacity utilisation terms are a continuum Can we unify the approaches? Are they consistent with utility maximisation? Are the elasticities correct? Stunde 1 23

24 Summary and outlook 2 Which mechanism is appropriate? Can we give guidance? Can we automate the iterative processes? Can we identify the appropriate model form? Stunde 1 24

25 Literature Batsell, R. R. (1981l) A Multiattribute Extension ofthe Luce Model which Simultaneously Scales Utility and Substitutability, Working Paper, J. H. Jones Graduate School of Administration, Rice University. Ben-Akiva, M. E. and M. Bierlaire (1999) Discrete choice methods and their applications to short-term travel decisions, in R. Hall (ed.) Handbook of Transportation Science, 5 34,Kluwer, Dordrecht. Borgers, A.W. J. and H. J. P. Timmermans (1987) Choice model specification, substitution and spatial structure effects: A simulation experiment, Regional Science and Urban Econimics,17, Cascetta, E., A. Nuzzola, F. Russo and A. Vitetta (1996) A modified logit route choice model overcoming path overlapping problems: Specification and some calibration results for interurban networks, in J. B. Lesort (ed.) Proceedings of the 13th International Symposium on Transportation and Traffic Theory, , Pergamon, Oxford. Cascetta, E., F. Paliara and K. W. Axhausen (2007) The use of dominance variables in choice set generation, in WCTRS (ed.) the 11th World Conference on Transportation Research, Berkeley, Jun Stunde 1 25

26 Literature Cascetta, E. and A. Papola (2003) A joint mode-transit service choice model incorporating the effect of regional transport service timetables, Transportation Research Part B, 37 (7) Cascetta, E. and A. Papola (2005) Dominance among alternatives in random utility models: A general framework and an application to destination choice, in ETC (ed.) European Transport Conference, Strasbourg, Oct Dugundji, E. R. and J. L. Walker (2005) Discrete choice with social and spatial network interdepencies: An empirical example using mixed gev models with field and "panel" effects,in TRB (ed.) the 84th Annual Meeting of the Transportation Research Board, Washington, D.C., Jan Fotheringham, A. S. (1988) Consumer store choice and choice set definition, Marketing Science, 7 (3) Frejinger, E. and M. Bierlaire (2007) Capturing correlation with subnetworks in route choice models, Transportation Research Part B, 41 (3) Friedrich, M., I. Hofsäss and S. Wekeck (2001) Timetable-based transit assignment using branch and bound techniques, Transportation Research Record, 1752, Hettinger, T. (2008) Konsistenz von Entscheidungsmodellen, Masterarbeit MSc Angewandte Mathematik, IVT, ETH Zürich, Zürich, Wintersemester Stunde 1 26

27 Literature Hoogendoorn-Lanser, S. and P. H. L. Bovy (2007) Modeling overlap in multi-modal route choice by inclusion of trip part specific path size factors, in TRB (ed.) the 86th Annual Meeting of the Transportation Research Board, Washington, D.C., Jan Hoogendoorn-Lanser, S., R. van Nes and P. H. L. Bovy (2005) Path size and overlap in multimodal transport networks, in H. S. Mahmassani (ed.) Flow, Dynamics and Human Interaction - Proceedings of the 16th International Symposium on Transportation and Traffic Theory, 63 83, Elsevier, Oxford. Kitamura, R. (1984) Incorporating trip chaining into analysis of destination choice, Transportation Research Part B, 18 (1) Meyer, R. J. and T. C. Eagle (1982) Context-Induced Parameter Instability in a Disaggregate-Stochastic Model of Store Choice, Journal of Marketing Research, 19, Martinez, F. (2007) The Constrained Multinomial Logit: a semi-compensatory choice model, paper to be presented at the 87th Annual Meeting of the Transportation Research Board, Washington, D.C., January Meyer, R. J. and T. C. Eagle (1982) Context-Induced Parameter Instability in a Disaggregate-Stochastic Model of Store Choice, Journal of Marketing Research, 19, Stunde 1 27

28 Literature Ramming, M. S. (2002) Network knowledge and route choice, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge. van Eggermond, M., N. Schüssler and K.W. Axhausen (2007) Accounting for similarities in air transport route choice, Working Paper, 456, IVT, ETH Zurich, Zurich. Vrtic, M. (2003) Simultanes Routen- und Verkehrsmittelwahlmodell, Ph.D. Thesis, Technical University Dresden, Dresden. Weis, C. (2006) Routenwahl im ÖV, Master Thesis, IVT, ETH Zurich, Zurich. Stunde 1 28

29 Appendix Stunde 1 29

30 C-Logit 1 (Cascetta et al., 1996) als: CF in = β 0 ln a Γ i la L i N an Mit: CF in l a L i Ähnlichkeit für Route i zwischen OD-Paar n Länge von Strecke a auf Route i Länge der Route i N an Anzahl der Routen zwischen OD-Paar n, die Strecke a beinhalten Satz der Strecken der Route i Г i Stunde 1 30

31 C-Logit 2 (Cascetta et al., 1996) als: CF in L ij = α ln 1+ 1/2 1/2 j i, ε C L n i L j γ Mit: CF in L ij L i C n Ähnlichkeit für Route i zwischen OD-Paar n Gemeinsame Länge der Routen i und j Länge der Route i Satz der Routen zwischen OD-Paar n α, γ Parameter Stunde 1 31

32 Path Size Logit (Ben-Akiva and Bierlaire, 1999) Wobei: Mit: l a 1 PS in= * a Γ L i i L δ aj L PS in path size -Faktor für Route i zwischen OD-Paar n l a Länge von Strecke a auf Route i L i Länge der Route i L* C n Länge der kürzesten Route zwischen OD-Paar n, δ aj 1, falls Strecke a zu Route j gehört; sonst 0 Г i Satz der Strecken der Route i Satz der Routen zwischen OD-Paar n C n j C n C j n Stunde 1 32

33 Eigenständigkeit einer Verbindung (Friedrich et al., 2000) wobei IND() c 1 1 = = f ( c') 1 + f ( c') c c' C c' C; c' c c Mit Überlapppung des Zeitfensters x c (c ), wahrgenommener Reisezeit y c (c ) und Fahrpreis z c (c ) f c ( c ) ( c' ) yc( c' ) zc( c' ) x + ' 1 = 1 γ min 1, + c s x sy sz s x, s y und s z beschränken die Wirkung von x c (c ), y c (c ) und z c (c ) s y und s z hängen vom Vorzeichen von y c (c ) und z c (c ) ab γ Gewichtsfaktor Stunde 1 33

34 Eigenständigkeit einer Verbindung (Friedrich et al., 2000) Überlappung des Zeitfensters: Nähe des Fahrpreises: x ( c') = 0.5( dt dt + at at ) c c c' c c' Mit dt at c z ( c') = c c c c c' Abfahrtszeit Ankunftszeit Fahrpreis Stunde 1 34

35 Eigenständigkeit einer Verbindung (Friedrich et al., 2000) Nähe der empfundenen Reisezeit erz c y ( c') = erz erz c c c' erz = fz + α uz + β u c Mit: fz Fahrzeit uz Umsteigezeit u Anzahl Umsteigen α,β Parameter; Bei Friedrich et al. jeweils gleich 2 Stunde 1 35

36 Zielwahl: Ähnlichkeit 1 Batsell (1981): ln 1 A = β X X J 1 i k jk ik j J k K Mit A i J K X β k Ähnlichkeit von Ziel i Satz aller betrachteten Ziele Satz der Attribute Wert des Attributs X Parameter für Attribut k Stunde 1 36

37 Zielwahl: Ähnlichkeit 2 Meyer und Eagle (1982): Mit A i J r ij β A i 1 = 0.5 rij 1 J 1 j J Ähnlichkeit von Ziel i Satz aller betrachteten Ziele Korrelation der Attribute der Ziele i und j Parameter für Attribut k β Stunde 1 37

38 Zielwahl: Ähnlichkeit 3 Borgers and Timmermans (1987): 1 A = X X k K J 1 j J i ik jk β k Mit A i J K X ij β k Ähnlichkeit von Ziel i Satz aller betrachteten Ziele Satz der Attribute Wert des Attributs k des Ziels i Parameter für Attribut k Stunde 1 38

39 Umgebungsangebot und -qualität Kitamura (1988) berücksichtigt die Erreichbarkeit vom Zielort aus A i c ij c ij,max = ln i X e j c ij Mit c ij,max X j c ij Maximale generalisierte Kosten Gelegenheiten am Ort j Generalisierte Kosten von I nach j, im einfachsten Fall: β(reisezeit ij ) Stunde 1 39

40 Zielwahl mit Kapazitätsstrafen (Martinez, 2007) Es sei: 1 Vi = β Xki + ln φki ( Xk ) + εi μ Mit X Ф Eigenschaften k von Ziel i Strafe mit: φ = φ T φ H ki ki ki k Stunde 1 40

41 Zielwahl mit Kapazitätsstrafen (Martinez, 2007) Mit: ( a X + ) T k ki ki k φ ki = 11+ e ω ρ ( X b + ) H k ki ki k φ ki = 11+ e ω ρ Und a b ρ ω Obere Grenze Untere Grenze Toleranz Parameter Stunde 1 41