IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v124y2014icp166-178.html
   My bibliography  Save this article

An optimal test for variance components of multivariate mixed-effects linear models

Author

Listed:
  • Aryal, Subhash
  • Bhaumik, Dulal K.
  • Mathew, Thomas
  • Gibbons, Robert D.

Abstract

In this article we derive an optimal test for testing the significance of covariance matrices of random-effects of two multivariate mixed-effects linear models. We compute the power of this newly derived test via simulation for various alternative hypotheses in a bivariate set up for unbalanced designs and observe that power responds sharply when sample size and alternative hypotheses are changed. For some balanced designs we compare power of the optimal test to that of the likelihood ratio test via simulation, and find that the proposed test has greater power than the likelihood ratio test. The results are illustrated using real data on human growth. Other relevant applications of the model are highlighted.

Suggested Citation

  • Aryal, Subhash & Bhaumik, Dulal K. & Mathew, Thomas & Gibbons, Robert D., 2014. "An optimal test for variance components of multivariate mixed-effects linear models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 166-178.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:166-178
    DOI: 10.1016/j.jmva.2013.10.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13002212
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.10.014?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. Mathew, T. & Niyogi, A. & Sinha, B. K., 1994. "Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 83-101, October.
    2. Franklin Satterthwaite, 1941. "Synthesis of variance," Psychometrika, Springer;The Psychometric Society, vol. 6(5), pages 309-316, October.
    Full references (including those not matched with items on IDEAS)

    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. Lada, Emily K. & Wilson, James R., 2006. "A wavelet-based spectral procedure for steady-state simulation analysis," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1769-1801, November.
    2. Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
    3. Julia Volaufova, 2009. "Heteroscedastic ANOVA: old p values, new views," Statistical Papers, Springer, vol. 50(4), pages 943-962, August.
    4. Yuan, Ke-Hai & Chan, Wai, 2008. "Structural equation modeling with near singular covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4842-4858, June.
    5. Marc Hallin & Abdessamad Saidi, 2005. "Testing Non‐Correlation and Non‐Causality between Multivariate ARMA Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 83-105, January.
    6. Joseph Fleiss, 1970. "Estimating the reliability of interview data," Psychometrika, Springer;The Psychometric Society, vol. 35(2), pages 143-162, June.
    7. J. Davenport & J. Webster, 1975. "The Behrens-Fisher problem, an old solution revisited," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 22(1), pages 47-54, December.
    8. Chiou, Paul, 1997. "Interval estimation of scale parameters following a pre-test for two exponential distributions," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 477-489, February.
    9. Mikkel Helding Vembye & James Eric Pustejovsky & Therese Deocampo Pigott, 2023. "Power Approximations for Overall Average Effects in Meta-Analysis With Dependent Effect Sizes," Journal of Educational and Behavioral Statistics, , vol. 48(1), pages 70-102, February.
    10. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    11. repec:mpr:mprres:6510 is not listed on IDEAS
    12. Jacob M. Paul & Martijn Ackooij & Tuomas C. Cate & Ben M. Harvey, 2022. "Numerosity tuning in human association cortices and local image contrast representations in early visual cortex," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    13. Bentler, Peter M. & Xie, Jun, 2000. "Corrections to test statistics in principal Hessian directions," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 381-389, May.
    14. Kubokawa, Tatsuya & Tsai, Ming-Tien, 2006. "Estimation of covariance matrices in fixed and mixed effects linear models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2242-2261, November.
    15. Rodríguez, Julio, 2003. "A powerful test for conditional heteroscedasticity for financial time series with highly persistent volatilities," DES - Working Papers. Statistics and Econometrics. WS ws036716, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Melisa Stevanovic & Samuel Tuhkanen & Milla Järvensivu & Emmi Koskinen & Camilla Lindholm & Jenny Paananen & Enikö Savander & Taina Valkeapää & Kaisa Valkiaranta, 2022. "Making Food Decisions Together: Physiological and Affective Underpinnings of Relinquishing Preferences and Reaching Decisions," SAGE Open, , vol. 12(1), pages 21582440221, February.
    17. Zhu, Fukang & Wang, Dehui, 2010. "Diagnostic checking integer-valued ARCH(p) models using conditional residual autocorrelations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 496-508, February.
    18. Katayama, Shota & Kano, Yutaka & Srivastava, Muni S., 2013. "Asymptotic distributions of some test criteria for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 410-421.
    19. Christiane B Wiebel-Herboth & Matti Krüger & Patricia Wollstadt, 2021. "Measuring inter- and intra-individual differences in visual scan patterns in a driving simulator experiment using active information storage," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-24, March.
    20. Jolynn Pek & Hao Wu, 2015. "Profile Likelihood-Based Confidence Intervals and Regions for Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1123-1145, December.
    21. Pan, Wei, 2002. "Approximate confidence intervals for one proportion and difference of two proportions," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 143-157, July.

    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:124:y:2014:i:c:p:166-178. 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.