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Homogeneity pursuit and variable selection in regression models for multivariate abundance data.

Francis K C Hui1, Luca Maestrini1, Alan H Welsh1

  • 1Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, ACT 2601, Australia.

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Summary
This summary is machine-generated.

This study introduces a new regression method for ecological data, grouping species with similar responses to environmental factors and selecting key predictors. This approach improves biodiversity modeling and prediction accuracy.

Keywords:
correlated data analysisgeneralized estimating equationspenalizationregularizationsparsity

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Area of Science:

  • Ecology
  • Statistical Modeling
  • Biodiversity Research

Background:

  • Multivariate abundance data in ecology requires accounting for species correlations.
  • Species often show homogeneous responses to environmental predictors, with many species influenced by only a subset of these predictors.

Purpose of the Study:

  • To propose a generalized estimating equation (GEE) approach for simultaneous homogeneity pursuit and variable selection in regression models for multivariate abundance data.
  • To group species with similar coefficient values while allowing differing groups for different covariates and to encourage sparsity across covariates.

Main Methods:

  • Utilizing generalized estimating equations (GEEs) to account for between-response correlations via a reduced-rank working correlation matrix.
  • Augmenting GEEs with adaptive fused lasso and adaptive lasso-type penalties for coefficient clustering and covariate sparsity.

Main Results:

  • Numerical studies show strong finite sample performance compared to existing methods for multivariate abundance data.
  • Application to Great Barrier Reef data reveals significant homogeneity and sparsity in species-environmental relationships.

Conclusions:

  • The proposed method provides a more parsimonious model for understanding environmental drivers of seabed biodiversity.
  • The approach leads to stronger out-of-sample predictive performance by accommodating homogeneity and sparsity.