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A simple test for random effects in regression models

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  • Simon N. Wood

Abstract

Testing that random effects are zero is difficult, because the null hypothesis restricts the corresponding variance parameter to the edge of the feasible parameter space. In the context of generalized linear mixed models, this paper exploits the link between random effects and penalized regression to develop a simple test for a zero effect. The idea is to treat the variance components not being tested as fixed at their estimates and then to express the likelihood ratio as a readily computed quadratic form in the predicted values of the random effects. Under the null hypothesis this has the distribution of a weighted sum of squares of independent standard normal random variables. The test can be used with generalized linear mixed models, including those estimated by penalized quasilikelihood. Copyright 2013, Oxford University Press.

Suggested Citation

  • Simon N. Wood, 2013. "A simple test for random effects in regression models," Biometrika, Biometrika Trust, vol. 100(4), pages 1005-1010.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:4:p:1005-1010
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    File URL: http://hdl.handle.net/10.1093/biomet/ast038
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    Cited by:

    1. Roel Verbelen & Katrien Antonio & Gerda Claeskens, 2018. "Unravelling the predictive power of telematics data in car insurance pricing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1275-1304, November.
    2. Baey, Charlotte & Cournède, Paul-Henry & Kuhn, Estelle, 2019. "Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 107-122.
    3. Umberto Amato & Anestis Antoniadis & Italia De Feis, 2016. "Additive model selection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 519-564, November.
    4. Kruse, René-Marcel & Silbersdorff, Alexander & Säfken, Benjamin, 2022. "Model averaging for linear mixed models via augmented Lagrangian," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    5. Giampiero Marra & Rosalba Radice & Till Bärnighausen & Simon N. Wood & Mark E. McGovern, 2017. "A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 484-496, April.
    6. Marra Giampiero & Radice Rosalba, 2017. "A joint regression modeling framework for analyzing bivariate binary data in R," Dependence Modeling, De Gruyter, vol. 5(1), pages 268-294, December.
    7. Marra, Giampiero & Radice, Rosalba, 2017. "Bivariate copula additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 99-113.
    8. Nathaniel E. Helwig, 2022. "Robust Permutation Tests for Penalized Splines," Stats, MDPI, vol. 5(3), pages 1-18, September.
    9. Christian Ritz & Rikke Pilmann Laursen & Camilla Trab Damsgaard, 2017. "Simultaneous inference for multilevel linear mixed models—with an application to a large-scale school meal study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 295-311, February.
    10. Jakob Peterlin & Nataša Kejžar & Rok Blagus, 2023. "Correct specification of design matrices in linear mixed effects models: tests with graphical representation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 184-210, March.
    11. Konrad Klotzke & Jean-Paul Fox, 2019. "Modeling Dependence Structures for Response Times in a Bayesian Framework," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 649-672, September.
    12. Semadeni-Davies, Annette & Jones-Todd, Charlotte & Srinivasan, M.S. & Muirhead, Richard & Elliott, Alexander & Shankar, Ude & Tanner, Chris, 2020. "CLUES model calibration and its implications for estimating contaminant attenuation," Agricultural Water Management, Elsevier, vol. 228(C).

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