IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v19y1985i3p278-292.html
   My bibliography  Save this article

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surveys is expensive and time consuming, and once the survey data are collected and compiled the matrices are rapidly outdated.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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.19.3.278
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.19.3.278?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Tao Li, 2017. "A Demand Estimator Based on a Nested Logit Model," Transportation Science, INFORMS, vol. 51(3), pages 918-930, August.
    10. 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.
    11. 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.
    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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:19:y:1985:i:3:p:278-292. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.