IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v139y2015icp45-55.html
   My bibliography  Save this article

A mixed model for complete three or higher-way layout with two random effects factors

Author

Listed:
  • Güven, Bilgehan

Abstract

The classical F-test for testing the hypothesis of no fixed main effects in a mixed model is valid under normality, variance homogeneity and symmetry assumption. We consider a mixed model in which one fixed and two random main effects are crossed. A new test procedure for testing the hypothesis of no fixed main effects is developed under violations of normality, variance homogeneity and symmetry assumptions. The asymptotic distribution of the proposed test statistic is studied under the condition that the numbers of levels of two main random effects are large. The asymptotic distribution of the test statistic is the chi-square distribution. The theory presented in this article is applicable for complete four or higher-way layout with two random factors.

Suggested Citation

  • Güven, Bilgehan, 2015. "A mixed model for complete three or higher-way layout with two random effects factors," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 45-55.
  • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:45-55
    DOI: 10.1016/j.jmva.2015.02.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15000640
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2015.02.018?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. Rao, C. Radhakrishna, 1971. "Estimation of variance and covariance components--MINQUE theory," Journal of Multivariate Analysis, Elsevier, vol. 1(3), pages 257-275, September.
    2. Gupta, Arjun K. & Harrar, Solomon W. & Fujikoshi, Yasunori, 2006. "Asymptotics for testing hypothesis in some multivariate variance components model under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 148-178, January.
    3. Arnold, Steven, 1984. "The asymptotic validity of invariant procedures for the repeated measures model and multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 15(3), pages 325-335, December.
    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. Trent Gaugler & Michael G. Akritas, 2011. "Testing for Interaction in Two-Way Random and Mixed Effects Models: The Fully Nonparametric Approach," Biometrics, The International Biometric Society, vol. 67(4), pages 1314-1320, December.
    2. D. Rasch & O. Mašata, 2006. "Methods of variance component estimation," Czech Journal of Animal Science, Czech Academy of Agricultural Sciences, vol. 51(6), pages 227-235.
    3. Wu, Jixiang & Wu, Dongfeng & Jenkins, Johnie N. & McCarty, Jack Jr., 2006. "A recursive approach to detect multivariable conditional variance components and conditional random effects," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 285-300, January.
    4. Gelein, Brigitte & Haziza, David & Causeur, David, 2014. "Preserving relationships between variables with MIVQUE based imputation for missing survey data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 197-208.
    5. Matthew Reimherr & Dan Nicolae, 2016. "Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 407-422, March.
    6. Teng, Suyan & Lee, Loo Hay & Chew, Ek Peng, 2010. "Integration of indifference-zone with multi-objective computing budget allocation," European Journal of Operational Research, Elsevier, vol. 203(2), pages 419-429, June.
    7. Ping Wu & Li Xing Zhu, 2010. "An Orthogonality‐Based Estimation of Moments for Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 253-263, June.
    8. Chun-Lung Su, 2021. "Bayesian multi-way balanced nested MANOVA models with random effects and a large number of the main factor levels," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 663-692, July.
    9. Yahia S El-Horbaty & Eman M Hanafy, 2018. "Some Estimation Methods and Their Assessment in Multilevel Models: A Review," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 5(3), pages 69-76, February.
    10. Fei-Yu TANG & Wang-Cheng MO & Wen-Jun XIAO, 2016. "Genetic effects of high fibre strength breeding lines in crosses with transgenic Bt cotton cultivars (Gossypium hirsutum L.)," Czech Journal of Genetics and Plant Breeding, Czech Academy of Agricultural Sciences, vol. 52(1), pages 14-21.
    11. Luis Nobre Pereira & Pedro Simoes Coelho, 2010. "Small area estimation of mean price of habitation transaction using time-series and cross-sectional area-level models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(4), pages 651-666.
    12. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    13. L. Rob Verdooren, 2020. "History of the Statistical Design of Agricultural Experiments," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 457-486, December.
    14. Davis, Peter, 2002. "Estimating multi-way error components models with unbalanced data structures," Journal of Econometrics, Elsevier, vol. 106(1), pages 67-95, January.
    15. Wayan Somayasa & Gusti N. Adhi Wibawa & La Hamimu & La Ode Ngkoimani, 2016. "Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-16, September.
    16. Solomon Harrar & Arjun Gupta, 2007. "Asymptotic Expansion for the Null Distribution of the F-statistic in One-way ANOVA under Non-normality," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 531-556, September.
    17. Tsai, Ming-Tien, 2004. "Maximum likelihood estimation of covariance matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 292-303, May.
    18. Bathke, Arne C. & Harrar, Solomon W. & Wang, Haiyan & Zhang, Ke & Piepho, Hans-Peter, 2010. "Series of randomized complete block experiments with non-normal data," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1840-1857, July.
    19. Solomon Harrar & Arne Bathke, 2012. "A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 135-165, February.
    20. H. Baltagi, Badi & Heun Song, Seuck & Cheol Jung, Byoung, 2001. "The unbalanced nested error component regression model," Journal of Econometrics, Elsevier, vol. 101(2), pages 357-381, April.

    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:139:y:2015:i:c:p:45-55. 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.