A practically tractable expression of the covariances of the Cross-Nested Logit model

Transportation Research Part B: Methodological

Volumn 57, Issue , 2013, Pages 1-11

  Marzano, Vittorio ^a   Papola, Andrea ^a   Simonelli, Fulvio ^b   Vitillo, Roberta ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b UNIVERSITY OF SANNIO   (Italy)

Author keywords

Covariance correlation calculation; Cross Nested Logit; GEV models

Indexed keywords

DISTRIBUTION FUNCTIONS; FUNCTIONS; PROBABILITY DISTRIBUTIONS;

COMPUTER SPREADSHEETS; COVARIANCE STRUCTURES; CROSS NESTED LOGIT MODEL; CUMULATIVE DISTRIBUTION FUNCTION; MATHEMATICAL PROCEDURES; NESTED LOGIT; PROBABILITY FUNCTIONS; TRANSPORTATION RESEARCH;

ONE DIMENSIONAL;

CORRELATION; COVARIANCE ANALYSIS; LOGIT ANALYSIS; PROBABILITY; SPREADSHEET; TRANSPORTATION PLANNING;

EID: 84884407592     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2013.08.017     Document Type: Article

References (30)

1. Abbe E., Bierlaire M., Toledo T. Normalization and correlation of Cross-Nested Logit models. Transportation Research Part B 2007, 41(7):795-808.
2. Ben-Akiva M., Lerman S.R. Discrete Choice Analysis: Theory and Application to Predict Travel Demand 1985, MIT Press, Cambridge, MA.
3. Bierlaire M. A general formulation of the Cross-nested Logit model. Annals of Operations Research 2006, 144(1):287-300.
4. Cascetta E. Transportation Systems Analysis: Models and Application 2009, Springer. second ed.
5. Daganzo C., Kusnic M. Two properties of the nested logit model. Transportation Science 1993, 27(4):395-400.
6. Daganzo C., Sheffi Y. On stochastic models of traffic assignment. Transportation Science 1977, 11(2):253-274.
7. Daly, A., 2001. Recursive Nested EV Model. Working Paper ITS 559, Institute for Transport Studies, University of Leeds, UK.
8. Daly A., Bierlaire M. A general and operational representation of Generalised Extreme Value models. Transportation Research Part B 2006, 40(4):285-305.
9. Daly A.J., Zachary S. Improved multiple choice models. Determinants of Travel Choice 1978, Saxon House. D.A. Hensher, M.Q. Dalvi (Eds.).
10. Guevara C.A., Ben-Akiva M. Sampling of alternatives in Multivariate Extreme Value (MEV) models. Transportation Research Part B 2013, 48:31-52.
11. Hoeffding, W., 1940. Masstabinvariante Korrelationtheorie. Schriften Mathematical Institute, University of Berlin, vol. 5, pp. 181-233.
12. Joe H. Multivariate extreme value distributions and coverage of ranking probabilities. Journal of Mathematical Psychology 2001, 45(1):180-188.
13. Kendall M., Stuart A. The Advanced Theory of Statistics 1979, Griffin ed., London.
14. Lemp J.D., Kockelman K.M., Damien P. The continuous cross-nested logit model: formulation and application for departure time choice. Transportation Research Part B 2010, 44(6):646-661.
15. Manski C.F., McFadden D.L. Structural Analysis of Discrete Data and Econometric Applications 1981, The MIT Press, Cambridge.
16. Marzano, V., Daly, A., 2007. Addressing homoskedasticity in invariant random utility models. In: Proceedings of ETC Conference, Strasbourg (under review for publication in the Journal of choice modelling).
17. Marzano V., Papola A. On the covariance structure of the Cross-Nested Logit model. Transportation Research Part B 2008, 42(2):83-98.
18. McFadden D. Modelling the choice of residential location. Spatial Interaction Theory and Residential Location 1978, 75-96. North-Holland, Amsterdam. A. Karlquist (Ed.).
19. McFadden, D., 1981. Econometric models of proabilistic choice. In: Manski, C.F., McFadden, D. (Eds.), Structural analysis of discrete data with econometric applications. MIT Press, Cambridge, MA (Chapter 5).
20. Müller S., Haase K., Seidel F. Exposing unobserved spatial similarity: evidence from German school choice data. Geographical Analysis 2012, 44(1):65-86.
21. Newman J.P. Normalization of network generalized extreme value models. Transportation Research Part B 2008, 42(10):958-969.
22. Papola A. Some developments of the cross-nested logit model. Transportation Research Part B 2004, 38(12):833-851.
23. Papola A., Marzano V. A Network Generalized Extreme Value model for route choice allowing implicit route enumeration. Computer-Aided Civil and Infrastructure Engineering 2013, 28:560-580.
24. Pinjari A.R. Generalized extreme value (GEV)-based error structures for multiple discrete-continuous choice models. Transportation Research Part B 2011, 45(3):474-489.
25. Sener I.N., Pendyala R.M., Bhat C.R. Accommodating spatial correlation across choice alternatives in discrete choice models: an application to modeling residential location choice behaviour. Journal of Transport Geography 2011, 19(2):294-303.
26. Small K. A discrete choice model for ordered alternatives. Econometrica 1987, 55(2):409-424.
27. Train K. Discrete Choice Methods with Simulation 2009, Cambridge University Press, MA.
28. Vovsha, P., 1997. Cross-nested logit model: an application to mode choice in the Tel-Aviv metropolitan area. In: Proceedings of 76th Annual Meeting of the Transportation Research Board, Washington, DC.
29. Wen C.H., Koppelman F.S. The Generalized Nested Logit model. Transportation Research Part B 2001, 35(12):627-641.
30. Williams H.C.W.L. On the formation of travel demand models and economic evaluation measures of user benefit. Environment and Planning A 1977, 9(2):285-344.