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Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood

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  • David M. Zucker
  • Offer Lieberman
  • Orly Manor

Abstract

The mixed linear model is a popular method for analysing unbalanced repeated measurement data. The classical statistical tests for parameters in this model are based on asymptotic theory that is unreliable in the small samples that are often encountered in practice. For testing a given fixed effect parameter with a small sample, we develop and investigate refined likelihood ratio (LR) tests. The refinements considered are the Bartlett correction and use of the Cox–Reid adjusted likelihood; these are examined separately and in combination. We illustrate the various LR tests on an actual data set and compare them in two simulation studies. The conventional LR test yields type I error rates that are higher than nominal. The adjusted LR test yields rates that are lower than nominal, with absolute accuracy similar to that of the conventional LR test in the first simulation study and better in the second. The Bartlett correction substantially improves the accuracy of the type I error rates with either the conventional or the adjusted LR test. In many cases, error rates that are very close to nominal are achieved with the refined methods.

Suggested Citation

  • David M. Zucker & Offer Lieberman & Orly Manor, 2000. "Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 827-838.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:4:p:827-838
    DOI: 10.1111/1467-9868.00267
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    Cited by:

    1. Ito, Tsubasa & Sugasawa, Shonosuke, 2021. "Improved confidence regions in meta-analysis of diagnostic test accuracy," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    2. Yoshifumi Ukyo & Hisashi Noma & Kazushi Maruo & Masahiko Gosho, 2019. "Improved Small Sample Inference Methods for a Mixed-Effects Model for Repeated Measures Approach in Incomplete Longitudinal Data Analysis," Stats, MDPI, vol. 2(2), pages 1-15, March.
    3. Melo, Tatiane F.N. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2009. "Improved testing inference in mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2573-2582, May.
    4. Stein, Markus Chagas & da Silva, Michel Ferreira & Duczmal, Luiz Henrique, 2014. "Alternatives to the usual likelihood ratio test in mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 184-197.
    5. David M. Zucker & Jonathan Denne, 2002. "Sample–Size Redetermination for Repeated Measures Studies," Biometrics, The International Biometric Society, vol. 58(3), pages 548-559, September.
    6. Vargas, Tiago M. & Ferrari, Silvia L.P. & Lemonte, Artur J., 2014. "Improved likelihood inference in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 110-124.

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