IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v180y2020ics0047259x2030244x.html
   My bibliography  Save this article

Locally optimal designs for multivariate generalized linear models

Author

Listed:
  • Idais, Osama

Abstract

The multivariate generalized linear model is considered. Each univariate response follows a generalized linear model. In this situation, the linear predictors and the link functions are not necessarily the same. The quasi-Fisher information matrix is obtained by using the method of generalized estimating equations. Then locally optimal designs for multivariate generalized linear models are investigated under the D- and A-optimality criteria. It turns out that under certain assumptions the optimality problem can be reduced to the marginal models. More precisely, a locally optimal saturated design for the univariate generalized linear models remains optimal for the multivariate structure in the set of all saturated designs. Moreover, the general equivalence theorem provides a necessary and sufficient condition under which the saturated design is locally D-optimal in the set of all designs. The results are applied for multivariate models with gamma-distributed responses. Furthermore, we consider a multivariate model with univariate gamma models having seemingly unrelated linear predictors. Under this constraint, locally D- and A-optimal designs are found as product of all D- and A-optimal designs, respectively for the marginal counterparts.

Suggested Citation

  • Idais, Osama, 2020. "Locally optimal designs for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:jmvana:v:180:y:2020:i:c:s0047259x2030244x
    DOI: 10.1016/j.jmva.2020.104663
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X2030244X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2020.104663?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. Silvio S. Zocchi & Anthony C. Atkinson, 1999. "Optimum Experimental Designs for Multinomial Logistic Models," Biometrics, The International Biometric Society, vol. 55(2), pages 437-444, June.
    2. Holger Dette & Laura Hoyden & Sonja Kuhnt & Kirsten Schorning, 2017. "Optimal designs for thermal spraying," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 53-72, January.
    3. Imhof, Lorens, 2000. "Optimum Designs for a Multiresponse Regression Model," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 120-131, January.
    4. Krafft, Olaf & Schaefer, Martin, 1992. "D-Optimal designs for a multivariate regression model," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 130-140, July.
    5. Soumaya, Moudar & Gaffke, Norbert & Schwabe, Rainer, 2015. "Optimal design for multivariate observations in seemingly unrelated linear models," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 48-56.
    6. Yue, Rong-Xian & Liu, Xin & Chatterjee, Kashinath, 2014. "D-optimal designs for multiresponse linear models with a qualitative factor," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 57-69.
    7. Valerii V. Fedorov & Robert C. Gagnon & Sergei L. Leonov, 2002. "Design of experiments with unknown parameters in variance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 18(3), pages 207-218, July.
    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. Ioannis Passas & Konstantina Ragazou & Eleni Zafeiriou & Alexandros Garefalakis & Constantin Zopounidis, 2022. "ESG Controversies: A Quantitative and Qualitative Analysis for the Sociopolitical Determinants in EU Firms," Sustainability, MDPI, vol. 14(19), pages 1-17, October.
    2. Sergio Pozuelo-Campos & Víctor Casero-Alonso & Mariano Amo-Salas, 2021. "Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine," Mathematics, MDPI, vol. 9(9), pages 1-15, April.
    3. Konstantina Ragazou & Ioannis Passas & Alexandros Garefalakis & Eleni Zafeiriou & Grigorios Kyriakopoulos, 2022. "The Determinants of the Environmental Performance of EU Financial Institutions: An Empirical Study with a GLM Model," Energies, MDPI, vol. 15(15), pages 1-15, July.

    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. Kao, Ming-Hung & Khogeer, Hazar, 2021. "Optimal designs for mixed continuous and binary responses with quantitative and qualitative factors," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    2. Yue, Rong-Xian & Liu, Xin, 2010. "-optimal designs for a hierarchically ordered system of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3458-3465, December.
    3. Linda M. Haines & Inna Perevozskaya & William F. Rosenberger, 2003. "Bayesian Optimal Designs for Phase I Clinical Trials," Biometrics, The International Biometric Society, vol. 59(3), pages 591-600, September.
    4. Soumaya, Moudar & Gaffke, Norbert & Schwabe, Rainer, 2015. "Optimal design for multivariate observations in seemingly unrelated linear models," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 48-56.
    5. Andreas Falke & Harald Hruschka, 2017. "Setting prices in mixed logit model designs," Marketing Letters, Springer, vol. 28(1), pages 139-154, March.
    6. Bodunwa, O. K. & Fasoranbaku, O. A., 2020. "D-optimal Design in Linear Model With Different Heteroscedasticity Structures," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(2), pages 1-7, March.
    7. Guiteras, Raymond P. & Levine, David I. & Polley, Thomas H., 2016. "The pursuit of balance in sequential randomized trials," Development Engineering, Elsevier, vol. 1(C), pages 12-25.
    8. Cong Han & Kathryn Chaloner, 2004. "Bayesian Experimental Design for Nonlinear Mixed-Effects Models with Application to HIV Dynamics," Biometrics, The International Biometric Society, vol. 60(1), pages 25-33, March.
    9. Katarzyna Filipiak & Augustyn Markiewicz & Anna Szczepańska, 2009. "Optimal designs under a multivariate linear model with additional nuisance parameters," Statistical Papers, Springer, vol. 50(4), pages 761-778, August.
    10. Konrad Engel & Sylke Gierer, 1993. "Optimal designs for models with block-block resp. treatment-treatment correlations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 349-359, December.
    11. Peter F. Thall & Randall E. Millikan & Peter Mueller & Sang-Joon Lee, 2003. "Dose-Finding with Two Agents in Phase I Oncology Trials," Biometrics, The International Biometric Society, vol. 59(3), pages 487-496, September.
    12. Yue, Rong-Xian & Liu, Xin & Chatterjee, Kashinath, 2014. "D-optimal designs for multiresponse linear models with a qualitative factor," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 57-69.
    13. Han, Cong, 2003. "A note on optimal designs for a two-part model," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 343-351, December.
    14. Wolfgang Bischoff, 1995. "Determinant formulas with applications to designing when the observations are correlated," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 385-399, June.
    15. Shun Matsuura & Hiroshi Kurata, 2020. "Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 79-99, March.
    16. Imhof, Lorens, 2000. "Optimum Designs for a Multiresponse Regression Model," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 120-131, January.
    17. Xin Liu & Rong-Xian Yue, 2013. "A note on $$R$$ -optimal designs for multiresponse models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 483-493, May.
    18. Yue, Rong-Xian, 2002. "Model-robust designs in multiresponse situations," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 369-379, July.
    19. Lin, Chun-Sui & Huang, Mong-Na Lo, 2010. "Optimal designs for estimating the control values in multi-univariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1055-1066, May.

    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:jmvana:v:180:y:2020:i:c:s0047259x2030244x. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.