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Comparison and Contrast of Two General Functional Regression Modeling Frameworks.

Jeffrey S Morris1

  • 1The University of Texas, MD Anderson Cancer Center, Unit 1411, PO Box 301402, Houston, TX 77230-1402.

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|July 25, 2017
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Summary

This study compares two functional regression frameworks: generalized additive models and functional mixed models. It highlights their strengths, weaknesses, and ideal applications for researchers.

Keywords:
Bayesian modelingFunctional data analysisFunctional regressionLinear Mixed Models

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Generalized additive models (GAMs) provide a flexible framework for regression.
  • Functional regression extends regression to functions as predictors or responses.
  • Existing functional regression methods have varying levels of generality and applicability.

Purpose of the Study:

  • To compare and contrast two general frameworks for functional regression.
  • To illuminate the characteristics, strengths, and weaknesses of each approach.
  • To provide recommendations for choosing between the frameworks in different settings.

Main Methods:

  • Comparison of a generalized additive modeling (GAM) based functional regression framework with functional mixed models.
  • Analysis of similarities and differences between the two frameworks.
  • Evaluation of applicability based on specific research scenarios.

Main Results:

  • Both frameworks offer general approaches to functional regression.
  • Key differences exist in their underlying assumptions and flexibility.
  • Specific scenarios favor one framework over the other due to distinct advantages.

Conclusions:

  • The choice between GAM-based functional regression and functional mixed models depends on the specific research question and data structure.
  • Understanding the nuances of each framework is crucial for effective functional data analysis.
  • Both approaches contribute significantly to the field of functional regression.