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Modelling and estimation of nonlinear quantile regression with clustered data.

Marco Geraci1

  • 1Arnold School of Public Health, Department of Epidemiology and Biostatistics, University of South Carolina, COlumbia SC, USA.

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|July 31, 2019
PubMed
Summary

This study introduces a novel method for estimating nonlinear quantile regression models with clustered data. The approach simplifies complex calculations, offering a more efficient way to analyze hierarchical data in various scientific fields.

Keywords:
Asymmetric Laplace distributionCOnditional percentilesMultilevel designsRandom effects

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Nonlinearity and correlated observations pose computational challenges in regression, particularly for nonsmooth objective functions like those in quantile regression.
  • Analyzing clustered data in two-level nested designs requires specialized modeling techniques.

Purpose of the Study:

  • To develop methods for modeling and estimating nonlinear conditional quantile functions in the presence of clustered data.
  • To address computational challenges associated with nonsmooth objective functions in quantile regression for hierarchical data.

Main Methods:

  • A novel estimation algorithm combining a smoothing algorithm for quantile regression and a second-order Laplacian approximation for nonlinear mixed models.
  • Reducing the nonsmooth optimization problem to an approximated L2 problem for computational efficiency.
  • An iterative optimization approach with a simple analytic form for the objective function.

Main Results:

  • The proposed method effectively handles nonlinearity and correlation in clustered data for quantile regression.
  • The optimization approach simplifies complex nonsmooth problems into solvable L2 problems.
  • The methods were validated through simulation studies and practical applications.

Conclusions:

  • The developed methods provide an efficient and robust approach for analyzing nonlinear quantile regression with clustered data.
  • The technique is applicable to diverse fields, including pharmacokinetics and agricultural growth curve modeling.
  • This work advances the statistical toolkit for complex data structures in regression analysis.