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A method for determining groups in nonparametric regression curves: Application to prefrontal cortex neural activity

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Summary

This study introduces a novel method for grouping individuals based on similar nonlinear relationships between variables. The approach automatically determines the optimal number of groups using bootstrapping, enhancing generalized additive models.

Keywords:
clustering of regression curvesfactor-by-curve interactiongeneralized additive modelmultiple regression curvesnonlinear regressionnumber of groups

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Area of Science:

  • Statistics
  • Biostatistics
  • Machine Learning

Background:

  • Generalized additive models (GAMs) offer flexible interpretation of nonlinear relationships between responses and covariates.
  • The effect of continuous covariates often varies across groups defined by categorical variables.
  • Comparing regression curves becomes crucial when numerous groups and factor-by-curve interactions are present in GAMs.

Purpose of the Study:

  • To develop a method for grouping individuals with similar regression functions when factor-by-curve interactions are significant in GAMs.
  • To enable automatic selection of the number of groups.
  • To provide a robust approach for analyzing complex covariate effects across populations.

Main Methods:

  • Proposed a novel statistical method for clustering individuals based on regression function similarity.
  • Employed bootstrapping for automatic determination of the optimal number of clusters.
  • Validated the method through extensive simulation studies.

Main Results:

  • The proposed method effectively identifies groups with shared regression functions.
  • Simulation studies demonstrated the method's validity and performance.
  • The approach successfully handles situations with numerous groups and factor-by-curve interactions.

Conclusions:

  • The developed method offers an automated and reliable way to group individuals based on covariate effects.
  • This technique enhances the interpretability of GAMs in the presence of complex interactions.
  • Applicable to diverse fields, including neurology, for analyzing experimental data.