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Semiparametric Approach to a Random Effects Quantile Regression Model.

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This study introduces a flexible semiparametric method for analyzing clustered data using random effects quantile regression and empirical likelihood. The approach provides robust estimation of population-average effects and cluster-specific deviations without assuming Gaussian random effects.

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Clustered data presents unique analytical challenges in regression modeling.
  • Quantile regression is valuable for understanding covariate effects across the entire distribution.
  • Existing methods often rely on restrictive distributional assumptions for random effects.

Purpose of the Study:

  • To develop a semiparametric random effects quantile regression model for clustered data.
  • To incorporate empirical likelihood for robust estimation.
  • To provide a flexible and computationally simple analytical framework.

Main Methods:

  • Utilized a semiparametric approach combining random effects quantile regression with empirical likelihood.
  • Formulated random coefficient estimation using estimating equations.
  • Employed Markov Chain Monte Carlo (MCMC) samplers within a Bayesian framework for estimation.

Main Results:

  • Developed a likelihood-like criterion function that is asymptotically concave.
  • Proposed a quasi-posterior mean estimator derived from MCMC sampling.
  • Demonstrated asymptotic normality for population-level parameter estimators.
  • Showed first-order asymptotic shrinkage of random coefficient estimators towards population-level parameters.

Conclusions:

  • The proposed empirical likelihood method offers a flexible and computationally efficient alternative for analyzing clustered data.
  • The approach accommodates non-Gaussian random effects and avoids assumptions about error densities.
  • Validated through real-data examples, highlighting its practical applicability.