IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v54y2013i1p71-84.html
   My bibliography  Save this article

Testing normality in mixed models using a transformation method

Author

Listed:
  • Wangli Xu
  • Yanwen Li
  • Dawo Song

Abstract

Statistical inference often assumes the normality of the variables involved in the model under study. The existing tests are for independent observations and may not be readily extended to handle the case with correlated ones. In this paper, a transformation method is recommended for normality checking in the two-way analysis of variance model. Its sampling properties are investigated. Simulation studies are carried out to examine the performance of the proposed methodology. Copyright Springer-Verlag 2013

Suggested Citation

  • Wangli Xu & Yanwen Li & Dawo Song, 2013. "Testing normality in mixed models using a transformation method," Statistical Papers, Springer, vol. 54(1), pages 71-84, February.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:1:p:71-84
    DOI: 10.1007/s00362-011-0411-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-011-0411-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-011-0411-4?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. Hwang, Yi-Ting & Wei, Peir Feng, 2006. "A novel method for testing normality in a mixed model of a nested classification," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1163-1183, November.
    2. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    3. J. P. Royston, 1982. "The W Test for Normality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 176-180, June.
    4. Srivastava, M. S., 1984. "A measure of skewness and kurtosis and a graphical method for assessing multivariate normality," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 263-267, October.
    5. H. Holgersson, 2006. "A graphical method for assessing multivariate normality," Computational Statistics, Springer, vol. 21(1), pages 141-149, March.
    6. Dieter Rasch & Thomas Rusch & Marie Šimečková & Klaus Kubinger & Karl Moder & Petr Šimeček, 2009. "Tests of additivity in mixed and fixed effect two-way ANOVA models with single sub-class numbers," Statistical Papers, Springer, vol. 50(4), pages 905-916, August.
    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. Norbert Henze & Stefan Koch, 2020. "On a test of normality based on the empirical moment generating function," Statistical Papers, Springer, vol. 61(1), pages 17-29, February.
    2. Paulo Rodrigues & Elsa Moreira & Vera Jesus & João Mexia, 2014. "Structured orthogonal families of one and two strata prime basis factorial models," Statistical Papers, Springer, vol. 55(3), pages 603-614, August.

    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. Takayuki Yamada & Tetsuto Himeno, 2019. "Estimation of multivariate 3rd moment for high-dimensional data and its application for testing multivariate normality," Computational Statistics, Springer, vol. 34(2), pages 911-941, June.
    2. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & György H. Terdik, 2021. "Asymptotic theory for statistics based on cumulant vectors with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 708-728, June.
    3. Manuel Denzer & Constantin Weiser, 2021. "Beyond F-statistic - A General Approach for Assessing Weak Identification," Working Papers 2107, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. Tanya Araujo & João Dias & Samuel Eleutério & Francisco Louçã, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Working Papers Department of Economics 2012/21, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    5. Wanfang Chen & Marc G. Genton, 2023. "Are You All Normal? It Depends!," International Statistical Review, International Statistical Institute, vol. 91(1), pages 114-139, April.
    6. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study," Mathematics, MDPI, vol. 9(23), pages 1-20, November.
    7. Tanya Ara'ujo & Jo~ao Dias & Samuel Eleut'erio & Francisco Louc{c}~a, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Papers 1207.1202, arXiv.org.
    8. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    9. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.
    10. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    11. Kim, Namhyun, 2016. "A robustified Jarque–Bera test for multivariate normality," Economics Letters, Elsevier, vol. 140(C), pages 48-52.
    12. Minguez, Ana & Javier Sese, F., 2022. "Why do you want a relationship, anyway? Consent to receive marketing communications and donors’ willingness to engage with nonprofits," Journal of Business Research, Elsevier, vol. 148(C), pages 356-367.
    13. 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.
    14. Gustavo Castilho Beruski & Luis Miguel Schiebelbein & André Belmont Pereira, 2020. "Maize Yield Components as Affected by Plant Population, Planting Date and Soil Coverings in Brazil," Agriculture, MDPI, vol. 10(12), pages 1-20, November.
    15. Ali Derakhshan Asl & Kuan Yew Wong & Manoj Kumar Tiwari, 2016. "Unequal-area stochastic facility layout problems: solutions using improved covariance matrix adaptation evolution strategy, particle swarm optimisation, and genetic algorithm," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 799-823, February.
    16. repec:ers:journl:v:volumexxi:y:2018:i:issue4:p:622-636 is not listed on IDEAS
    17. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    18. J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, University Library of Munich, Germany.
    19. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2021. "Multivariate Hermite polynomials and information matrix tests," Working Paper series 21-12, Rimini Centre for Economic Analysis.
    20. Jacobovic, Royi & Kella, Offer, 2022. "A characterization of normality via convex likelihood ratios," Statistics & Probability Letters, Elsevier, vol. 186(C).
    21. Lauren Bin Dong & David E. A. Giles, 2004. "An Empirical Likelihood Ratio Test for Normality," Econometrics Working Papers 0401, Department of Economics, University of Victoria.

    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:stpapr:v:54:y:2013:i:1:p:71-84. 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.