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Bayesian analysis of measurement error models using integrated nested Laplace approximations

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  • Stefanie Muff
  • Andrea Riebler
  • Leonhard Held
  • Håvard Rue
  • Philippe Saner

Abstract

type="main" xml:id="rssc12069-abs-0001"> To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge can be incorporated in the prior distributions. Recently, integrated nested Laplace approximations have been proven to be a computationally convenient alternative to sampling approaches for Bayesian inference in latent Gaussian models. We show how the most common approaches to adjust for ME, the classical and the Berkson ME, fit into this framework. This is achieved through a reformulation with augmented pseudo-observations and a suitable extension of the latent Gaussian field. Two specific classes are described, which allow for a particularly simple implementation using integrated nested Laplace approximations. We present three applications within the framework of generalized linear (mixed) models with ME. To illustrate the practical feasibility, R code is provided in on-line supplementary material.

Suggested Citation

  • Stefanie Muff & Andrea Riebler & Leonhard Held & Håvard Rue & Philippe Saner, 2015. "Bayesian analysis of measurement error models using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(2), pages 231-252, February.
    • Handle: RePEc:bla:jorssc:v:64:y:2015:i:2:p:231-252
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    File URL: http://hdl.handle.net/10.1111/rssc.2015.64.issue-2
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    Cited by:

    1. David Imo & Holger Dressel & Katarzyna Byber & Christine Hitzke & Matthias Bopp & Marion Maggi & Stephan Bose-O’Reilly & Leonhard Held & Stefanie Muff, 2018. "Predicted Mercury Soil Concentrations from a Kriging Approach for Improved Human Health Risk Assessment," IJERPH, MDPI, vol. 15(7), pages 1-14, June.
    2. Marcus Groß, 2016. "Modeling body height in prehistory using a spatio-temporal Bayesian errors-in variables model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 289-311, July.
    3. Edgar Santos‐Fernandez & Erin E. Peterson & Julie Vercelloni & Em Rushworth & Kerrie Mengersen, 2021. "Correcting misclassification errors in crowdsourced ecological data: A Bayesian perspective," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 147-173, January.
    4. Luis A. Barboza & Julien Emile-Geay & Bo Li & Wan He, 2019. "Efficient Reconstructions of Common Era Climate via Integrated Nested Laplace Approximations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 535-554, September.
    5. Muff, Stefanie & Ott, Manuela & Braun, Julia & Held, Leonhard, 2017. "Bayesian two-component measurement error modelling for survival analysis using INLA—A case study on cardiovascular disease mortality in Switzerland," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 177-193.
    6. Nian-Sheng Tang & De-Wang Li & An-Min Tang, 2017. "Semiparametric Bayesian inference on generalized linear measurement error models," Statistical Papers, Springer, vol. 58(4), pages 1091-1113, December.

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