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Robust designs for generalized linear models with possible overdispersion and misspecified link functions

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  • Adewale, Adeniyi J.
  • Xu, Xiaojian

Abstract

We discuss robust designs for generalized linear models with protection for possible departures from the usual model assumptions. Besides possible inaccuracy in an assumed linear predictor, both problems of overdispersion and misspecification in link function are addressed. For logistic and Poisson models, as examples, we incorporate the variance function prescribed by a superior model similar to a generalized linear mixed model to address overdispersion, and adopt a parameterized generalized family of link functions to deal with the problem of link misspecification. The design criterion is the average mean squared prediction error (AMSPE). The exact optimal design, which minimizes the AMSPE, is also presented using examples on the toxicity of ethylene oxide to grain beetles, and on Ames Salmonella Assay.

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  • Adewale, Adeniyi J. & Xu, Xiaojian, 2010. "Robust designs for generalized linear models with possible overdispersion and misspecified link functions," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 875-890, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:875-890
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    References listed on IDEAS

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    1. Dette, Holger & Biedermann, Stefanie & Pepelyshev, Andrey, 2004. "Some robust design strategies for percentile estimation in binary response models," Technical Reports 2004,19, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Joy King & Weng-Kee Wong, 2000. "Minimax D-Optimal Designs for the Logistic Model," Biometrics, The International Biometric Society, vol. 56(4), pages 1263-1267, December.
    3. Adewale, Adeniyi J. & Wiens, Douglas P., 2006. "New criteria for robust integer-valued designs in linear models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 723-736, November.
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    Cited by:

    1. Amalan Mahendran & Helen Thompson & James M. McGree, 2023. "A model robust subsampling approach for Generalised Linear Models in big data settings," Statistical Papers, Springer, vol. 64(4), pages 1137-1157, August.
    2. Diego Ramos Canterle & Fábio Mariano Bayer, 2019. "Variable dispersion beta regressions with parametric link functions," Statistical Papers, Springer, vol. 60(5), pages 1541-1567, October.
    3. Kwame Asiam Addey & William Nganje, 2023. "The role of the U.S. exchange‐rate equity market volatility on agricultural exports and forecasts," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 71(1), pages 25-47, March.
    4. Sanjoy Sinha, 2013. "Robust designs for multivariate logistic regression," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 157-173, September.

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