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Inference for generalized additive mixed models via penalized marginal likelihood

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  • Stringer, Alex

Abstract

The Laplace approximation is sometimes not sufficiently accurate for smoothing parameter estimation in generalized additive mixed models. A novel estimation strategy is proposed that solves this problem and leads to estimates exhibiting the correct statistical properties.

Suggested Citation

  • Stringer, Alex, 2025. "Inference for generalized additive mixed models via penalized marginal likelihood," Statistics & Probability Letters, Elsevier, vol. 224(C).
    • Handle: RePEc:eee:stapro:v:224:y:2025:i:c:s0167715225000884
    DOI: 10.1016/j.spl.2025.110443
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    References listed on IDEAS

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    1. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    2. H. E. Ogden, 2017. "On asymptotic validity of naive inference with an approximate likelihood," Biometrika, Biometrika Trust, vol. 104(1), pages 153-164.
    3. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    4. Göran Kauermann & Tatyana Krivobokova & Ludwig Fahrmeir, 2009. "Some asymptotic results on generalized penalized spline smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 487-503, April.
    5. Blair Bilodeau & Alex Stringer & Yanbo Tang, 2024. "Stochastic Convergence Rates and Applications of Adaptive Quadrature in Bayesian Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 690-700, January.
    6. Jiming Jiang & Matt P. Wand & Aishwarya Bhaskaran, 2022. "Usable and precise asymptotics for generalized linear mixed model analysis and design," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 55-82, February.
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