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Robust estimation of fixed effect parameters and variances of linear mixed models: the minimum density power divergence approach

Author

Listed:
  • Giovanni Saraceno

    (University of Trento
    University at Buffalo)

  • Abhik Ghosh

    (Indian Statistical Institute)

  • Ayanendranath Basu

    (Indian Statistical Institute)

  • Claudio Agostinelli

    (University of Trento)

Abstract

Many real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measures the discrepancy between two probability density functions, has been successfully used to build robust estimators with high stability associated with minimal loss in efficiency. Here, we develop the minimum DPD estimator (MDPDE) for independent but non-identically distributed observations for LMMs according to the variance components model. We prove that the theoretical properties hold, including consistency and asymptotic normality of the estimators. The influence function and sensitivity measures are computed to explore the robustness properties. As a data-based choice of the MDPDE tuning parameter $$\alpha$$ α is very important, we propose two candidates as “optimal” choices, where optimality is in the sense of choosing the strongest downweighting that is necessary for the particular data set. We conduct a simulation study comparing the proposed MDPDE, for different values of $$\alpha$$ α , with S-estimators, M-estimators and the classical maximum likelihood estimator, considering different levels of contamination. Finally, we illustrate the performance of our proposal on a real-data example.

Suggested Citation

  • Giovanni Saraceno & Abhik Ghosh & Ayanendranath Basu & Claudio Agostinelli, 2024. "Robust estimation of fixed effect parameters and variances of linear mixed models: the minimum density power divergence approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(1), pages 127-157, March.
  • Handle: RePEc:spr:alstar:v:108:y:2024:i:1:d:10.1007_s10182-023-00473-z
    DOI: 10.1007/s10182-023-00473-z
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    References listed on IDEAS

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    1. Koller, Manuel, 2016. "robustlmm: An R Package for Robust Estimation of Linear Mixed-Effects Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 75(i06).
    2. Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "New robust statistical procedures for the polytomous logistic regression models," Biometrics, The International Biometric Society, vol. 74(4), pages 1282-1291, December.
    3. Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2021. "Robust semiparametric inference for polytomous logistic regression with complex survey design," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 701-734, September.
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