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FSR Methods for Second-Order Regression Models.

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This study introduces forward selection algorithms for complex regression models, managing many predictors effectively. These methods control uninformative effects and balance selection rates in higher-order models.

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Area of Science:

  • Statistics
  • Regression Analysis

Background:

  • Traditional variable selection methods primarily address first-order linear regression models.
  • Including interaction and quadratic terms significantly increases the number of candidate predictors, complicating variable selection.
  • Existing techniques struggle with the rapid growth of predictors in higher-order models.

Purpose of the Study:

  • To develop and evaluate forward selection algorithms for second-order regression models.
  • To control the rate of uninformative effect entry in complex models.
  • To equalize false selection rates between first-order and second-order terms.

Main Methods:

  • Development of forward selection algorithms that enforce natural hierarchies in second-order models.
  • Monte Carlo simulations to assess method performance.
  • Application to real-world data from Cox regression and response surface experiments.

Main Results:

  • The proposed algorithms effectively manage the increased number of predictors in second-order models.
  • Demonstrated control over the entry rate of uninformative effects.
  • Achieved equalization of false selection rates between first-order and second-order terms.

Conclusions:

  • Forward selection algorithms with hierarchical structures offer a robust approach to variable selection in complex regression models.
  • These methods are suitable for models including interaction and quadratic terms.
  • The approach is validated through simulation and practical examples.