IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/78063.html
   My bibliography  Save this paper

The Davies Problem: A New Test for Random Slope in the Hierarchical Linear Model

Author

Listed:
  • van Oest, R.D.
  • Franses, Ph.H.B.F.

Abstract

__Abstract__ Crucial inference for the hierarchical linear model concerns the null hypothesis of no random slope. We argue that the usually applied statistical test suffers from the so-called Davies problem, that is, a nuisance parameter is only identified under the alternative. We propose an easy-to-implement methodology that exploits this property. We provide the relevant critical values and demonstrate through simulations that our new methodology has better power properties.

Suggested Citation

  • van Oest, R.D. & Franses, Ph.H.B.F., 2015. "The Davies Problem: A New Test for Random Slope in the Hierarchical Linear Model," Econometric Institute Research Papers EI 2015-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:78063
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/78063/EI2015-01.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Beg, A B M Rabiul A & Silvapulle, Mervyn J & Silvapulle, Paramsothy, 2001. "Tests Against Inequality Constraints When Some Nuisance Parameters Are Present Only under the Alternative: Test of ARCH in ARCH-M Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 245-253, April.
    2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    3. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    4. Carrasco, Marine, 2002. "Misspecified Structural Change, Threshold, and Markov-switching models," Journal of Econometrics, Elsevier, vol. 109(2), pages 239-273, August.
    5. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    6. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    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. Lanouar Charfeddine & Dominique Guegan, 2008. "Is it possible to discriminate between different switching regressions models? An empirical investigation," PSE-Ecole d'économie de Paris (Postprint) halshs-00368358, HAL.
    2. Sun, Yixiao X, 2005. "Estimation and Inference in Panel Structure Models," University of California at San Diego, Economics Working Paper Series qt5tf1231k, Department of Economics, UC San Diego.
    3. Marine Carrasco, 2004. "Chi-square Tests for Parameter Stability," RCER Working Papers 508, University of Rochester - Center for Economic Research (RCER).
    4. Gabriel Vasco J. & Alexandre Fernando & Bação Pedro, 2008. "The Consumption-Wealth Ratio under Asymmetric Adjustment," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(4), pages 1-32, December.
    5. Antonio Diez De Los Rios & René Garcia, 2011. "Assessing and valuing the nonlinear structure of hedge fund returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 193-212, March.
    6. Donald W.K. Andrews & Werner Ploberger, 1994. "Testing for Serial Correlation Against an ARMA(1,1) Process," Cowles Foundation Discussion Papers 1077, Cowles Foundation for Research in Economics, Yale University.
    7. Burcu Kapar & William Pouliot, 2013. "Multiple Change-Point Detection in Linear Regression Models via U-Statistic Type Processes," Discussion Papers 13-13, Department of Economics, University of Birmingham.
    8. Philip Arestis & Andrea Cipollini & Bassam Fattouh, 2004. "Threshold Effects in the U.S. Budget Deficit," Economic Inquiry, Western Economic Association International, vol. 42(2), pages 214-222, April.
    9. Nicolas Million, 2010. "Test simultané de la non-stationnarité et de la non-linéarité : une application au taux d’intérêt réel américain," Économie et Prévision, Programme National Persée, vol. 192(1), pages 83-95.
    10. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    11. Deidda, Luca & Fattouh, Bassam, 2002. "Non-linearity between finance and growth," Economics Letters, Elsevier, vol. 74(3), pages 339-345, February.
    12. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Working Papers 9821, Department of Economics, Bilkent University.
    13. Martinez Oscar & Olmo Jose, 2012. "A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-39, September.
    14. González, Andrés & Teräsvirta, Timo & van Dijk, Dick & Yang, Yukai, 2005. "Panel Smooth Transition Regression Models," SSE/EFI Working Paper Series in Economics and Finance 604, Stockholm School of Economics, revised 11 Oct 2017.
    15. Bruce E. Hansen, 1996. "Estimation of TAR Models," Boston College Working Papers in Economics 325., Boston College Department of Economics.
    16. Pérez-Alonso Alicia & Di Sanzo Silvestro, 2010. "Unemployment and Hysteresis: A Nonlinear Unobserved Components Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(1), pages 1-29, December.
    17. Christoph Rothe & Philipp Sibbertsen, 2006. "Phillips-Perron-type unit root tests in the nonlinear ESTAR framework," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(3), pages 439-456, September.
    18. Pesaran, M. Hashem & Timmermann, Allan, 2009. "Testing Dependence Among Serially Correlated Multicategory Variables," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 325-337.
    19. Jonathan B. Hill, 2004. "Consistent Model Specification Tests Against Smooth Transition Alternatives," Econometrics 0402004, University Library of Munich, Germany, revised 05 Aug 2005.
    20. Rafael González-Val & Jose Olmo, 2015. "Growth in a Cross-section of Cities: Location, Increasing Returns or Random Growth?," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(2), pages 230-261, June.

    More about this item

    Keywords

    hierarchical linear model; random effects; slope variance; Davies problem;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ems:eureir:78063. 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: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    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.