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Model selection in multivariate semiparametric regression.

Zhuokai Li1, Hai Liu2, Wanzhu Tu3

  • 11 Duke Clinical Research Institute, Durham, USA.

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|February 7, 2017
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Summary
This summary is machine-generated.

This study introduces a new method for selecting variables in complex longitudinal data models, improving accuracy for multiple correlated outcomes. It helps determine if joint modeling is needed and simplifies nonlinear effects, aiding clinical data analysis.

Keywords:
Adaptive least absolute shrinkage and selection operatoradaptive group least absolute shrinkage and selection operatorexpectation-maximization algorithmmixed effectsmultivariate data

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Variable selection in semiparametric mixed models with multiple correlated outcomes is complex.
  • Existing methods struggle to simultaneously select fixed and random effects efficiently.

Purpose of the Study:

  • To develop a novel model selection procedure for semiparametric mixed models with longitudinal data.
  • To simultaneously select fixed and random effects and determine the necessity of joint modeling for correlated outcomes.
  • To accommodate and simplify joint nonlinear effects using penalized likelihood and adaptive group LASSO.

Main Methods:

  • A maximum penalized likelihood method with adaptive LASSO penalty for simultaneous fixed and random effects selection.
  • Incorporation of a bivariate nonparametric component approximated by tensor product splines.
  • An adaptive group LASSO for reducing bivariate components to additive ones.
  • A two-stage expectation-maximization algorithm for implementation.

Main Results:

  • The proposed method effectively performs variable selection for both fixed and random effects.
  • Random effects selection identifies the correlation structure, guiding joint model necessity.
  • The adaptive group LASSO successfully simplifies complex nonlinear interactions.
  • Simulation studies demonstrate the method's operating characteristics.

Conclusions:

  • The developed procedure offers a robust approach to variable selection in semiparametric mixed models for longitudinal data.
  • It effectively handles multiple correlated outcomes and nonlinear effects.
  • The method is validated through simulations and applied to a pediatric blood pressure study.