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A Regression Formulation of the Matrix Estimation Problem

Author

Listed:
  • Sue McNeil

    (Princeton University, Princeton, New Jersey)

  • Chris Hendrickson

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania)

Abstract

Matrices are widely used in transportation planning to represent the distribution of characteristics or as origin-destination matrices. Developing such matrices by means of surveys is expensive and time consuming, and once the survey data are collected and compiled the matrices are rapidly outdated. Other methods which are commonly used are unable to include all available data or to provide a measure of the uncertainty of the estimates. This paper formulates a quadratic programming method to estimate matrix entry estimates as an equivalent constrained generalized least squares estimation problem. As well as being able to include any available information in the form of constraints, the variance-covariance matrix of the entry estimates may be found and confidence intervals calculated for matrix entry estimates with some added distributional assumptions. The problem of updating the proportions of nationwide automobile trips by purpose and trip length from 1970 to 1977 is included as a simple example to illustrate the method.

Suggested Citation

  • Sue McNeil & Chris Hendrickson, 1985. "A Regression Formulation of the Matrix Estimation Problem," Transportation Science, INFORMS, vol. 19(3), pages 278-292, August.
    • Handle: RePEc:inm:ortrsc:v:19:y:1985:i:3:p:278-292
    DOI: 10.1287/trsc.19.3.278
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    Citations

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    Cited by:

    1. Zhang, Michael & Nie, Yu & Shen, Wei & Lee, Ming S. & Jansuwan, Sarawut & Chootinan, Piya & Pravinvongvuth, Surachet & Chen, Anthony & Recker, Will W., 2008. "Development of A Path Flow Estimator for Inferring Steady-State and Time-Dependent Origin-Destination Trip Matrices," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3nr033sc, Institute of Transportation Studies, UC Berkeley.
    2. Maryam Abareshi & Mehdi Zaferanieh & Mohammad Reza Safi, 2019. "Origin-Destination Matrix Estimation Problem in a Markov Chain Approach," Networks and Spatial Economics, Springer, vol. 19(4), pages 1069-1096, December.
    3. Hai Yang & Qiang Meng & Michael G. H. Bell, 2001. "Simultaneous Estimation of the Origin-Destination Matrices and Travel-Cost Coefficient for Congested Networks in a Stochastic User Equilibrium," Transportation Science, INFORMS, vol. 35(2), pages 107-123, May.
    4. Sherali, Hanif D. & Narayanan, Arvind & Sivanandan, R., 2003. "Estimation of origin-destination trip-tables based on a partial set of traffic link volumes," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 815-836, November.
    5. Xie, Chi & Kockelman, Kara M. & Waller, S. Travis, 2011. "A maximum entropy-least squares estimator for elastic origin–destination trip matrix estimation," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1465-1482.
    6. Doblas, Javier & Benitez, Francisco G., 2005. "An approach to estimating and updating origin-destination matrices based upon traffic counts preserving the prior structure of a survey matrix," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 565-591, August.
    7. Li, Tao & Wan, Yan, 2019. "Estimating the geographic distribution of originating air travel demand using a bi-level optimization model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 267-291.
    8. Lundgren, Jan T. & Peterson, Anders, 2008. "A heuristic for the bilevel origin-destination-matrix estimation problem," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 339-354, May.
    9. Lo, H. P. & Zhang, N. & Lam, W. H. K., 1996. "Estimation of an origin-destination matrix with random link choice proportions: A statistical approach," Transportation Research Part B: Methodological, Elsevier, vol. 30(4), pages 309-324, August.
    10. Walpen, Jorgelina & Mancinelli, Elina M. & Lotito, Pablo A., 2015. "A heuristic for the OD matrix adjustment problem in a congested transport network," European Journal of Operational Research, Elsevier, vol. 242(3), pages 807-819.
    11. Tao Li, 2017. "A Demand Estimator Based on a Nested Logit Model," Transportation Science, INFORMS, vol. 51(3), pages 918-930, August.
    12. Maryam Abareshi & Mehdi Zaferanieh & Bagher Keramati, 2017. "Path Flow Estimator in an Entropy Model Using a Nonlinear L-Shaped Algorithm," Networks and Spatial Economics, Springer, vol. 17(1), pages 293-315, March.

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