Linear-in-Parameters Logit Model Derived from the Efficiency Principle

  • Sven Erlander
Part of the Applied Optimization book series (APOP, volume 63)


The linear-in-parameters logit model is a discrete choice model which can be derived in many ways, e.g. by the additive random utility maximizing approach. It can also be derived from the efficiency principle. The efficiency approach offers a new way of testing the model against observations. This paper derives the linear-inparameters logit model from the efficiency principle and shows how the basic efficiency assumption, and hence the linear-in-parameters logit model, can be tested against observations.


Logit Model Choice Probability Travel Demand Observable Quantity Negative Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ben-Akiva, M. and Lerman, S.R. (1985). Discrete Choice Analysis: Theory and Application to Travel Demand. Cambridge, Massachusetts: The MIT Press. Erlander, S. (1985). On the principle of monotone likelihood and loglinear models,Mathematical Programming, 21: 137–151.Google Scholar
  2. Erlander, S. (1998). Efficiency and the logit model, Annals of Operations Research, 82: 203–218.CrossRefGoogle Scholar
  3. Erlander, S. (2000). A graphical test for utility maximizing behavior, Technical report LiTH-MAT-R-2000–11, Department of Mathematics, Linköping University, Linköping, Sweden.Google Scholar
  4. Erlander, S. and Smith, T.E. (1990). General representation theorems for efficient population behavior, Applied Mathematics and Computation, 36: 173–217.CrossRefGoogle Scholar
  5. Erlander, S. and Lundgren, J.T. (2000). Cost minimizing behavior in random discrete choice modeling, Technical Report LiTH-MAT-R-2000–08, Department of Mathematics, Linköping University, Linköping, Sweden.Google Scholar
  6. Florian, M. (1974). On modelling congestion in dial’s probabilistic assignment model, Transportation Research, 8: 85–86.CrossRefGoogle Scholar
  7. Florian, M. and Fox, B. (1976). On the probabilistic origin of dial’s multipath traffic assignment model, Transportation Research, 10: 339–341.CrossRefGoogle Scholar
  8. Florian, M. (1977). A traffic equilibrium model of travel by car and public transit modes, Transportation Science, 8: 166–179.CrossRefGoogle Scholar
  9. Kullback, S. (1959). Information Theory and Statistics: New York: Wiley.Google Scholar
  10. Lehmann, E.L. (1983). Theory of Point Estimation. New York: Wiley.Google Scholar
  11. Luce, R.D. (1959). Individual Choice Behavior: A Theoretical Analysis. New York: Wiley.Google Scholar
  12. Lundgren, J.T. (1989). Optimization Approaches to Travel Demand Modelling, PhD thesis, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden.Google Scholar
  13. McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior, in: Zarembka, P. (ed.), Frontiers of Econometrics, pages 105–142. New York: Academic Press.Google Scholar
  14. Smith, T.E. (1978). A cost-efficiency principle of spatial interaction behavior, Regional Science and Urban Economics, 8: 313–337.CrossRefGoogle Scholar
  15. Smith, T.E. (1983). A cost-efficiency approach to the analysis of congested spatial-interaction behavior, Environment and Planning A, 15: 435–464.CrossRefGoogle Scholar
  16. Smith, T.E. (1988). A cost-efficiency theory of dispersed network equilibria, Environment and Planning A, 20: 231–266.CrossRefGoogle Scholar
  17. Stuart, A. and Ord, J.K. (1987). Kendall’s Advanced Theory of Statistics. Volume 1. Distribution Theory. London: Charles Griffin.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Sven Erlander

There are no affiliations available

Personalised recommendations