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Alternatives to the usual likelihood ratio test in mixed linear models

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  • Stein, Markus Chagas
  • da Silva, Michel Ferreira
  • Duczmal, Luiz Henrique

Abstract

The small-sample performance of alternatives to the usual likelihood ratio test in mixed linear models is investigated. Specifically, the following tests for fixed effects are considered: (i) a bootstrap-based test, (ii) the Bartlett-corrected usual test, and (iii) an adjusted profile likelihood ratio test. The last test is derived using an approximation to the modified profile likelihood proposed by Barndorff-Nielsen, based on the work of Severini. Bootstrap resampling is performed to numerically construct a Bartlett correction factor for the usual test statistic, and also to obtain a critical value that does not rely on first-order asymptotics. The numerical evidence presented in the paper slightly favors the Bartlett-corrected usual test. An application to real longitudinal data is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:184-197
    DOI: 10.1016/j.csda.2013.08.002
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    References listed on IDEAS

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    1. S. J. Welham & R. Thompson, 1997. "Likelihood Ratio Tests for Fixed Model Terms using Residual Maximum Likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 701-714.
    2. Guolo, Annamaria & Brazzale, Alessandra R. & Salvan, Alessandra, 2006. "Improved inference on a scalar fixed effect of interest in nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1602-1613, December.
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    5. N. Sartori, 2003. "Modified profile likelihoods in models with stratum nuisance parameters," Biometrika, Biometrika Trust, vol. 90(3), pages 533-549, September.
    6. Cribari-Neto, Francisco & Frery, Alejandro C. & Silva, Michel F., 2002. "Improved estimation of clutter properties in speckled imagery," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 801-824, October.
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    Cited by:

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    3. 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.

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