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Multimodality of the likelihood in the bivariate seemingly unrelated regressions model

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  • 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
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    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. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.
    6. 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.
    7. 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).
    8. 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.

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