IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v91y2004i2p383-392.html
   My bibliography  Save this article

Multimodality of the likelihood in the bivariate seemingly unrelated regressions model

Author

Listed:
  • Mathias Drton

Abstract

We analyse the simplest two-equation seemingly unrelated regressions model and demonstrate that its likelihood may have up to five stationary points, and thus there may be up to three local modes. Consequently the estimates obtained via iterative estimation methods may depend on starting values. We further show that the probability of multimodality vanishes asymptotically. Monte Carlo simulations suggest that multimodality rarely occurs if the seemingly unrelated regressions model is true, but can become more frequent if the model is misspecified. The existence of multimodality in the likelihood for seemingly unrelated regressions models contradicts several claims in the literature. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Mathias Drton, 2004. "Multimodality of the likelihood in the bivariate seemingly unrelated regressions model," Biometrika, Biometrika Trust, vol. 91(2), pages 383-392, June.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:2:p:383-392
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Søren Højsgaard & Steffen L. Lauritzen, 2008. "Graphical Gaussian models with edge and vertex symmetries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 1005-1027, November.
    2. Rolf Sundberg, 2010. "Flat and Multimodal Likelihoods and Model Lack of Fit in Curved Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 632-643, December.
    3. Piotr Zwiernik & Caroline Uhler & Donald Richards, 2017. "Maximum likelihood estimation for linear Gaussian covariance models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1269-1292, September.
    4. Lin Zhang & Andrew DiLernia & Karina Quevedo & Jazmin Camchong & Kelvin Lim & Wei Pan, 2021. "A random covariance model for bi‐level graphical modeling with application to resting‐state fMRI data," Biometrics, The International Biometric Society, vol. 77(4), pages 1385-1396, December.
    5. Søren Johansen & Anders Ryghn Swensen, 2021. "Adjustment coefficients and exact rational expectations in cointegrated vector autoregressive models," CREATES Research Papers 2021-10, Department of Economics and Business Economics, Aarhus University.
    6. Focacci, Chiara Natalie & Santarelli, Enrico, 2021. "Job Training, Remote Working, and Self-Employment: Displaced Workers Beyond Employment Hysteresis," GLO Discussion Paper Series 780, Global Labor Organization (GLO).
    7. Drton, Mathias & Andersson, Steen A. & Perlman, Michael D., 2006. "Conditional independence models for seemingly unrelated regressions with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 385-411, February.
    8. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, 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:oup:biomet:v:91:y:2004:i:2:p:383-392. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.