IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v71y2014icp1159-1167.html
   My bibliography  Save this article

Computing efficient exact designs of experiments using integer quadratic programming

Author

Listed:
  • Harman, Radoslav
  • Filová, Lenka

Abstract

A new method for computing exact experimental designs for linear regression models by integer quadratic programming is proposed. The key idea is to use the criterion of DQ-optimality, which is a quadratic approximation of the criterion of D-optimality in the neighbourhood of the approximate D-optimal information matrix. Several numerical examples are used to demonstrate that the D-efficiency of exact DQ-optimal designs is usually very high. An important advantage of this method is that it can be applied to situations with general linear constraints on permissible designs, including marginal and cost constraints.

Suggested Citation

  • Harman, Radoslav & Filová, Lenka, 2014. "Computing efficient exact designs of experiments using integer quadratic programming," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1159-1167.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:1159-1167
    DOI: 10.1016/j.csda.2013.02.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313000777
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.02.021?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Martin-Martin, R. & Torsney, B. & Lopez-Fidalgo, J., 2007. "Construction of marginally and conditionally restricted designs using multiplicative algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5547-5561, August.
    2. Turkington,Darrell A., 2002. "Matrix Calculus and Zero-One Matrices," Cambridge Books, Cambridge University Press, number 9780521807883, September.
    3. L. Imhof & J. Lopez‐Fidalgo & W. K. Wong, 2001. "Efficiencies of Rounded Optimal Approximate Designs for Small Samples," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(3), pages 301-318, November.
    4. Pace, R. Kelley & LeSage, James P., 2004. "Chebyshev approximation of log-determinants of spatial weight matrices," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 179-196, March.
    5. R. A. Bailey, 2007. "Designs for two‐colour microarray experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 365-394, August.
    6. Grace Montepiedra, 1998. "Application of genetic algorithms to the construction of exact D-optimal designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(6), pages 817-826.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Radoslav Harman & Eva Benková, 2017. "Barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 201-225, February.
    2. Harman, Radoslav & Prus, Maryna, 2018. "Computing optimal experimental designs with respect to a compound Bayes risk criterion," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 135-141.
    3. Belmiro P. M. Duarte, 2023. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    4. Lenka Filová & Radoslav Harman, 2020. "Ascent with quadratic assistance for the construction of exact experimental designs," Computational Statistics, Springer, vol. 35(2), pages 775-801, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Haoying Wang & Guohui Wu, 2022. "Modeling discrete choices with large fine-scale spatial data: opportunities and challenges," Journal of Geographical Systems, Springer, vol. 24(3), pages 325-351, July.
    2. Sgrignoli, Paolo & Metulini, Rodolfo & Schiavo, Stefano & Riccaboni, Massimo, 2015. "The relation between global migration and trade networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 245-260.
    3. Víctor Casero-Alonso & Jesús López-Fidalgo, 2015. "Experimental designs in triangular simultaneous equations models," Statistical Papers, Springer, vol. 56(2), pages 273-290, May.
    4. Duarte, Belmiro P.M. & Sagnol, Guillaume & Wong, Weng Kee, 2018. "An algorithm based on semidefinite programming for finding minimax optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 99-117.
    5. Ohtsuka, Yoshihiro & Oga, Takashi & Kakamu, Kazuhiko, 2010. "Forecasting electricity demand in Japan: A Bayesian spatial autoregressive ARMA approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2721-2735, November.
    6. Belmiro P. M. Duarte, 2023. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    7. Maller, Ross & Roberts, Steven & Tourky, Rabee, 2016. "The large-sample distribution of the maximum Sharpe ratio with and without short sales," Journal of Econometrics, Elsevier, vol. 194(1), pages 138-152.
    8. Konno, Akio & Kato, Hironori & Takeuchi, Wataru & Kiguchi, Riku, 2021. "Global evidence on productivity effects of road infrastructure incorporating spatial spillover effects," Transport Policy, Elsevier, vol. 103(C), pages 167-182.
    9. Monchuk, Daniel C. & Miranowski, John A., 2003. "Spatial Labor Markets And Technology Spillovers - Analysis From Us Midwest," 2003 Annual meeting, July 27-30, Montreal, Canada 22250, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    10. López-Fidalgo, J. & Rivas-López, M.J., 2014. "Optimal experimental designs for partial likelihood information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 859-867.
    11. Godolphin, J.D. & Warren, H.R., 2014. "An efficient procedure for the avoidance of disconnected incomplete block designs," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1134-1146.
    12. Lukas Dargel, 2021. "Revisiting estimation methods for spatial econometric interaction models," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-41, December.
    13. Philip L. H. Yu & W. K. Li & F. C. Ng, 2017. "The Generalized Conditional Autoregressive Wishart Model for Multivariate Realized Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 513-527, October.
    14. D. Stephen G. Pollock, 2021. "Multidimensional Arrays, Indices and Kronecker Products," Econometrics, MDPI, vol. 9(2), pages 1-15, April.
    15. CUERVO, Daniel Palhazi & GOOS, Peter & SÖRENSEN, Kenneth, 2013. "An iterated local search algorithm for the construction of large scale D-optimal experimental designs," Working Papers 2013006, University of Antwerp, Faculty of Business and Economics.
    16. Luc Anselin, 2012. "From SpaceStat to CyberGIS," International Regional Science Review, , vol. 35(2), pages 131-157, April.
    17. repec:asg:wpaper:1047 is not listed on IDEAS
    18. Stephen Pollock, 2011. "On Kronecker Products, Tensor Products And Matrix Differential Calculus," Discussion Papers in Economics 11/34, Division of Economics, School of Business, University of Leicester, revised Jul 2011.
    19. Millo, Giovanni, 2014. "Maximum likelihood estimation of spatially and serially correlated panels with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 914-933.
    20. Víctor Casero-Alonso & Jesús López-Fidalgo, 2015. "Optimal designs subject to cost constraints in simultaneous equations models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 701-713, December.
    21. Yehua Dennis Wei & Weiye Xiao & Ming Wen & Ran Wei, 2016. "Walkability, Land Use and Physical Activity," Sustainability, MDPI, vol. 8(1), pages 1-16, January.

    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:eee:csdana:v:71:y:2014:i:c:p:1159-1167. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.