IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v82y2019i2d10.1007_s00184-018-0669-9.html
   My bibliography  Save this article

Inner workings of the Kenward–Roger test

Author

Listed:
  • Waseem Alnosaier

    (Institute of Public Administration)

  • David Birkes

    (Oregon State University)

Abstract

For testing a linear hypothesis about fixed effects in a normal mixed linear model, a popular approach is to use a Wald test, in which the test statistic is assumed to have a null distribution that is approximately chi-squared. This approximation is questionable, however, for small samples. In 1997 Kenward and Roger constructed a test that addresses this problem. They altered the Wald test in three ways: (a) adjusting the test statistic, (b) approximating the null distribution by a scaled F distribution, and (c) modifying the formulas to achieve an exact F test in two special cases. Alterations (a) and (b) lead to formulas that are somewhat complicated but can be explained by using Taylor series approximations and a few convenient assumptions. The modified formulas used in alteration (c), however, are more mysterious. Restricting attention to models with linear variance–covariance structure, we provide details of a derivation that justifies these formulas. We show that similar but different derivations lead to different formulas that also produce exact F tests in the two special cases and are equally justifiable. A simulation study was done for testing the equality of treatment effects in block-design models. Tests based on the different derivations performed very similarly. Moreover, the simulations confirm that alteration (c) is worthwhile. The Kenward–Roger test showed greater accuracy in its p values than did the unmodified version of the test.

Suggested Citation

  • Waseem Alnosaier & David Birkes, 2019. "Inner workings of the Kenward–Roger test," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 195-223, March.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:2:d:10.1007_s00184-018-0669-9
    DOI: 10.1007/s00184-018-0669-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-018-0669-9
    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/s00184-018-0669-9?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. Halekoh, Ulrich & Højsgaard, Søren, 2014. "A Kenward-Roger Approximation and Parametric Bootstrap Methods for Tests in Linear Mixed Models The R Package pbkrtest," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i09).
    2. Green, Paul E, 1974. "On the Design of Choice Experiments Involving Multifactor Alternatives," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 1(2), pages 61-68, Se.
    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. Paul E. Rose & James E. Brereton & Lewis J. Rowden & Ricardo Lemos Figueiredo & Lisa M. Riley, 2019. "What’s new from the zoo? An analysis of ten years of zoo-themed research output," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-10, December.
    2. Anoek Castelein & Dennis Fok & Richard Paap, 2020. "A multinomial and rank-ordered logit model with inter- and intra-individual heteroscedasticity," Tinbergen Institute Discussion Papers 20-069/III, Tinbergen Institute.
    3. Byron C. Jaeger & Lloyd J. Edwards & Kalyan Das & Pranab K. Sen, 2017. "An statistic for fixed effects in the generalized linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(6), pages 1086-1105, April.
    4. Haghani, Milad & Bliemer, Michiel C.J. & Rose, John M. & Oppewal, Harmen & Lancsar, Emily, 2021. "Hypothetical bias in stated choice experiments: Part I. Macro-scale analysis of literature and integrative synthesis of empirical evidence from applied economics, experimental psychology and neuroimag," Journal of choice modelling, Elsevier, vol. 41(C).
    5. Shehely Parvin & Paul Wang & Jashim Uddin, 2016. "Using best-worst scaling method to examine consumers’ value preferences: A multidimensional perspective," Cogent Business & Management, Taylor & Francis Journals, vol. 3(1), pages 1199110-119, December.
    6. King, K.W. & Hanrahan, B.R. & Stinner, J. & Shedekar, V.S., 2022. "Field scale discharge and water quality response, to drainage water management," Agricultural Water Management, Elsevier, vol. 264(C).
    7. Patterson, Paul M. & Martinez, Samuel Cardona, 2004. "State and Origin Branding in Hispanic Food Markets," Journal of Food Distribution Research, Food Distribution Research Society, vol. 35(3), pages 1-12, November.
    8. Wirth, Ferdinand F. & Davis, Kathy J., 2003. "Shrimp Purchasing Behavior And Preferences Of Seafood Dealers," 2003 Annual Meeting, February 1-5, 2003, Mobile, Alabama 35151, Southern Agricultural Economics Association.
    9. van Beek, Krijn W. H. & Koopmans, Carl C. & van Praag, Bernard M. S., 1997. "Shopping at the labour market: A real tale of fiction," European Economic Review, Elsevier, vol. 41(2), pages 295-317, February.
    10. Conlon, B.J. & Dellaert, B.G.C. & van Soest, A.H.O., 2001. "Optimal Effort in Consumer Choice : Theory and Experimental Evidence for Binary Choice," Discussion Paper 2001-51, Tilburg University, Center for Economic Research.
    11. Veisten, Knut, 2007. "Willingness to pay for eco-labelled wood furniture: Choice-based conjoint analysis versus open-ended contingent valuation," Journal of Forest Economics, Elsevier, vol. 13(1), pages 29-48, May.
    12. Wirth, Ferdinand F. & Stanton, John L. & Wiley, James B., 2011. "The Relative Importance of Search versus Credence Product Attributes: Organic and Locally Grown," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 40(1), pages 1-15, April.
    13. Govaerts, B. & Francq, B. & Marion, R. & Martin, M. & Thiel, M., 2020. "The essentials on linear regression, ANOVA, general linear and linear mixed models for the chemist," LIDAM Discussion Papers ISBA 2020012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. James Simpson & Megan Freeth & Kimberley Jayne Simpson & Kevin Thwaites, 2022. "Street edge subdivision: Structuring ground floor interfaces to stimulate pedestrian visual engagement," Environment and Planning B, , vol. 49(6), pages 1775-1791, July.
    15. Hee-Jong Yang & Seul-Ye Lim & Seung-Hoon Yoo, 2017. "The Environmental Costs of Photovoltaic Power Plants in South Korea: A Choice Experiment Study," Sustainability, MDPI, vol. 9(10), pages 1-13, September.
    16. Liu, Wei & Denizci Guillet, Basak & Xiao, Qu & Law, Rob, 2014. "Globalization or localization of consumer preferences: The case of hotel room booking," Tourism Management, Elsevier, vol. 41(C), pages 148-157.
    17. Jordan J. Louviere, 2013. "Modeling single individuals: the journey from psych lab to the app store," Chapters, in: Stephane Hess & Andrew Daly (ed.), Choice Modelling, chapter 1, pages 1-47, Edward Elgar Publishing.
    18. Rose Fiamohe & Tebila Nakelse & Aliou Diagne & Papa A. Seck, 2015. "Assessing the Effect of Consumer Purchasing Criteria for Types of Rice in Togo: A Choice Modeling Approach," Agribusiness, John Wiley & Sons, Ltd., vol. 31(3), pages 433-452, June.
    19. KESSELS, Roselinde & VAN HERCK, Pieter & DANCET, Eline & ANNEMANS, Lieven & SERMEUS, Walter, 2014. "How to reform western care payment systems according to physicians, policy makers, healthcare executives and researchers: A discrete choice experiment," Working Papers 2014022, University of Antwerp, Faculty of Business and Economics.
    20. Bairagi, Subir K. & Mohanty, Samarendu & Ynion, Jhoanne & Demont, Matty, 2017. "Determinants of Consumer Preferences for Rice Attributes: Evidence from South and Southeast Asia," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258384, Agricultural and Applied Economics Association.

    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:82:y:2019:i:2:d:10.1007_s00184-018-0669-9. 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.