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. 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.
    2. 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).
    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. Martin, Manon & Govaerts, Bernadette, 2019. "LiMM-PCA : combining ASCA+ and linear mixed models to analyse high dimensional designed data," LIDAM Discussion Papers ISBA 2019021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. 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.
    3. Manalo, Alberto B., 1989. "Benefits Sought by Apple Consumers," Working Papers 115908, Regional Research Project NE-165 Private Strategies, Public Policies, and Food System Performance.
    4. 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.
    5. Vetschera, Rudolf & Weitzl, Wolfgang & Wolfsteiner, Elisabeth, 2014. "Implausible alternatives in eliciting multi-attribute value functions," European Journal of Operational Research, Elsevier, vol. 234(1), pages 221-230.
    6. Menictas, Con & Wang, Paul Z. & Louviere, Jordan J., 2012. "Assessing the validity of brand equity constructs," Australasian marketing journal, Elsevier, vol. 20(1), pages 3-8.
    7. 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.
    8. 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).
    9. Burton, Michael P. & Marsh, Sally P. & Patterson, Josie, 2000. "Community attitudes towards water management in the Moore Catchment, WA," 2000 Conference (44th), January 23-25, 2000, Sydney, Australia 123616, Australian Agricultural and Resource Economics Society.
    10. 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.
    11. Milena Pavlova & Wim Groot & Godefridus Merode, 2005. "An Application of Rating Conjoint Analysis to Study the Importance of Quality-, Access- and Price-attributes to Health Care Consumers," Economic Change and Restructuring, Springer, vol. 37(3), pages 267-286, September.
    12. Lenth, Russell V., 2016. "Least-Squares Means: The R Package lsmeans," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i01).
    13. Sebastian Loth & Katharina Jettka & Manuel Giuliani & Stefan Kopp & Jan P de Ruiter, 2018. "Confidence in uncertainty: Error cost and commitment in early speech hypotheses," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-30, August.
    14. 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).
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. G.E. Kersten & S.J. Noronha, 1997. "Negotiation Via the World Wide Web: A Cross-Cultural Study of Decision Making," Working Papers ir97052, International Institute for Applied Systems Analysis.
    20. 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.

    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.