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Quantile regression for longitudinal data using the asymmetric Laplace distribution.

Marco Geraci1, Matteo Bottai

  • 1Department of Epidemiology and Biostatistics, University of South Carolina, 800 Sumter Street, Columbia, SC 29208, USA. geraci@gwm.sc.edu

Biostatistics (Oxford, England)
|April 26, 2006
PubMed
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This study introduces a new quantile regression (QR) model with random effects for analyzing longitudinal data. The model accurately captures changes in response distribution over time, offering a robust alternative to traditional methods.

Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Longitudinal studies involve repeated measurements on individuals over time.
  • Analyzing the shape of response distributions and influencing factors is crucial.
  • Standard mixed-effects models may be insufficient for non-Gaussian distributions.

Purpose of the Study:

  • To propose a novel linear model for quantile regression (QR) incorporating random effects.
  • To account for the dependence between serial observations within subjects.
  • To provide a robust method for analyzing the conditional distribution of responses in longitudinal data.

Main Methods:

  • Developed a linear model for quantile regression (QR) with random effects.
  • Employed a likelihood-based estimation approach using the asymmetric Laplace density.

Related Experiment Videos

  • Utilized a simulation study to compare the proposed method with penalized fixed effects models.

    • Main Results:

    • The proposed QR model demonstrated an advantage in mean squared error compared to penalized fixed effects.
    • The model automatically selects an optimal degree of shrinkage for individual effects.
    • It serves as a robust alternative to mean regression with random effects for skewed distributions.

    Conclusions:

    • The novel random effects quantile regression model effectively analyzes longitudinal data with non-Gaussian distributions.
    • The method offers robust estimation and automatic selection of shrinkage parameters.
    • Applied successfully to labor pain measurements, demonstrating its practical utility.