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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Carrasco, Marine, 2002. "Misspecified Structural Change, Threshold, and Markov-switching models," Journal of Econometrics, Elsevier, vol. 109(2), pages 239-273, August.
    4. 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.
    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. 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.
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    Keywords

    hierarchical linear model; random effects; slope variance; Davies problem;
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