IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v84y2021i3d10.1007_s00184-020-00777-z.html
   My bibliography  Save this article

On the equivalence between the LRT and F-test for testing variance components in a class of linear mixed models

Author

Listed:
  • Fares Qeadan

    (University of Utah)

  • Ronald Christensen

    (University of New Mexico)

Abstract

For the special case of balanced one-way random effects ANOVA, it has been established that the generalized likelihood ratio test (LRT) and Wald’s test are largely equivalent in testing the variance component. We extend these results to explore the relationships between Wald’s F test, and the LRT for a much broader class of linear mixed models; the generalized split-plot models. In particular, we explore when the two tests are equivalent and prove that when they are not equivalent, Wald’s F test is more powerful, thus making the LRT test inadmissible. We show that inadmissibility arises in realistic situations with common number of degrees of freedom. Further, we derive the statistical distribution of the LRT under both the null and alternative hypotheses $$H_0$$ H 0 and $$H_1$$ H 1 where $$H_0$$ H 0 is the hypothesis that the between variance component is zero. Providing an exact distribution of the test statistic for the LRT in these models will help in calculating a more accurate p-value than the traditionally used p-value derived from the large sample chi-square mixture approximations.

Suggested Citation

  • Fares Qeadan & Ronald Christensen, 2021. "On the equivalence between the LRT and F-test for testing variance components in a class of linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 313-338, April.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:3:d:10.1007_s00184-020-00777-z
    DOI: 10.1007/s00184-020-00777-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-020-00777-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-020-00777-z?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. Molenberghs, Geert & Verbeke, Geert, 2007. "Likelihood Ratio, Score, and Wald Tests in a Constrained Parameter Space," The American Statistician, American Statistical Association, vol. 61, pages 22-27, February.
    2. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    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. Benjamin R. Saville & Amy H. Herring, 2009. "Testing Random Effects in the Linear Mixed Model Using Approximate Bayes Factors," Biometrics, The International Biometric Society, vol. 65(2), pages 369-376, June.
    2. Oliver E. Lee & Thomas M. Braun, 2012. "Permutation Tests for Random Effects in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 68(2), pages 486-493, June.
    3. Baey, Charlotte & Cournède, Paul-Henry & Kuhn, Estelle, 2019. "Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 107-122.
    4. Gumedze, Freedom N. & Welham, Sue J. & Gogel, Beverley J. & Thompson, Robin, 2010. "A variance shift model for detection of outliers in the linear mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2128-2144, September.
    5. Ghosal, Rahul & Maity, Arnab, 2022. "A Score Based Test for Functional Linear Concurrent Regression," Econometrics and Statistics, Elsevier, vol. 21(C), pages 114-130.
    6. Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    7. Zanin, Luca & Marra, Giampiero, 2012. "Assessing the functional relationship between CO2 emissions and economic development using an additive mixed model approach," Economic Modelling, Elsevier, vol. 29(4), pages 1328-1337.
    8. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    9. Miao-Yu Tsai & Chuhsing Hsiao, 2008. "Computation of reference Bayesian inference for variance components in longitudinal studies," Computational Statistics, Springer, vol. 23(4), pages 587-604, October.
    10. Yeojin Chung & Sophia Rabe-Hesketh & Vincent Dorie & Andrew Gelman & Jingchen Liu, 2013. "A Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 685-709, October.
    11. Chunlin Wang & Paul Marriott & Pengfei Li, 2022. "A note on the coverage behaviour of bootstrap percentile confidence intervals for constrained parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 809-831, October.
    12. Sonja Greven & Ciprian Crainiceanu, 2013. "On likelihood ratio testing for penalized splines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 387-402, October.
    13. Sun-Joo Cho & Sarah Brown-Schmidt & Woo-yeol Lee, 2018. "Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 751-771, September.
    14. Matthew K. Heun & João Santos & Paul E. Brockway & Randall Pruim & Tiago Domingos & Marco Sakai, 2017. "From Theory to Econometrics to Energy Policy: Cautionary Tales for Policymaking Using Aggregate Production Functions," Energies, MDPI, vol. 10(2), pages 1-44, February.
    15. Federico Belotti & Giuseppe Ilardi & Andrea Piano Mortari, 2019. "Estimation of Stochastic Frontier Panel Data Models with Spatial Inefficiency," CEIS Research Paper 459, Tor Vergata University, CEIS, revised 30 May 2019.
    16. Long Qu & Tobias Guennel & Scott L. Marshall, 2013. "Linear Score Tests for Variance Components in Linear Mixed Models and Applications to Genetic Association Studies," Biometrics, The International Biometric Society, vol. 69(4), pages 883-892, December.
    17. Benjamin Säfken & Thomas Kneib, 2020. "Conditional covariance penalties for mixed models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 990-1010, September.
    18. Zhenzhen Zhang & Thomas M. Braun & Karen E. Peterson & Howard Hu & Martha M. Téllez-Rojo & Brisa N. Sánchez, 2018. "Extending Tests of Random Effects to Assess for Measurement Invariance in Factor Models," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 634-650, December.
    19. Sanjoy Sinha & Abdus Sattar, 2015. "Inference in semi-parametric spline mixed models for longitudinal data," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 377-395, December.
    20. Chen, Haiqiang & Fang, Ying & Li, Yingxing, 2015. "Estimation And Inference For Varying-Coefficient Models With Nonstationary Regressors Using Penalized Splines," Econometric Theory, Cambridge University Press, vol. 31(4), pages 753-777, August.

    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:spr:metrik:v:84:y:2021:i:3:d:10.1007_s00184-020-00777-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.