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Robust estimation for longitudinal data based upon minimum Hellinger distance.

Joonsung Kang1

  • 1Department of Information Statistics, Gangneung-Wonju National University, Gangneung, Republic of Korea.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a robust Bayesian estimation method for mixed models, improving accuracy with longitudinal data, especially when outliers are present. The new approach offers better performance than standard methods in simulations and real-world analyses.

Keywords:
Linear mixed modelkernel density estimationminimum Hellinger distanceoutlierspseudo posterior

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Generalized linear mixed models (GLMMs) are crucial for analyzing correlated data, particularly longitudinal and repeated measures.
  • Standard linear mixed models are sensitive to outliers, which can significantly distort results.
  • Robust estimation methods like M-estimators and minimum Hellinger distance estimators offer alternatives, but often involve trade-offs in efficiency or robustness.

Purpose of the Study:

  • To propose a robust Bayesian parameter estimation method for linear mixed models using a pseudo-posterior distribution based on the minimum Hellinger distance.
  • To enhance robustness against outliers and missing values in longitudinal data analysis.
  • To evaluate the proposed method's performance against traditional methods like Restricted Maximum Likelihood (REML).

Main Methods:

  • Developed a Bayesian estimation approach incorporating minimum Hellinger distance.
  • Utilized nonparametric kernel density estimation and cross-validation for estimating longitudinal data distributions.
  • Applied the proposed method to simulated data and real-world orthodontic and Alzheimer's Disease (AD) datasets.

Main Results:

  • The proposed Bayesian method demonstrated smaller biases, mean squared errors, and standard errors compared to REML in simulation studies with outliers and missing values.
  • Real data analysis showed lower standard errors and variance-covariance components for the proposed method in both orthodontic and AD datasets.
  • The method effectively accommodates nonparametric kernel density estimation for longitudinal data.

Conclusions:

  • The proposed robust Bayesian estimation method offers superior performance over REML, particularly in the presence of outliers and missing data in longitudinal studies.
  • This approach provides a more reliable alternative for analyzing complex correlated data in fields like biostatistics and public health.
  • The minimum Hellinger distance-based pseudo-posterior distribution enhances the reliability of parameter estimation in mixed models.