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Ultrahigh Dimensional Variable Selection for Interpolation of Point Referenced Spatial Data: A Digital Soil Mapping

Benjamin R Fitzpatrick1,2,3, David W Lamb2,4, Kerrie Mengersen1,2,3,5

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This study efficiently uses the Least Angle Regression (LAR) algorithm to select environmental covariates for interpolating soil carbon observations. LAR simplifies complex soil mapping by effectively identifying key variables with minimal computational cost.

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Area of Science:

  • Geosciences
  • Environmental Science
  • Computational Statistics

Background:

  • Modern soil mapping requires interpolating geostatistical data using numerous environmental covariates.
  • Similar interpolation challenges exist in biogeography and environmental science.
  • Exhaustive model searches with many covariates are computationally intensive.

Purpose of the Study:

  • To demonstrate the efficiency of the Least Angle Regression (LAR) algorithm for variable selection in soil mapping.
  • To apply LAR for fitting Least Absolute Shrinkage and Selection Operator (LASSO) penalized Multiple Linear Regression models.
  • To aid the interpolation of geostatistical soil carbon observations.

Main Methods:

  • Employed the Least Angle Regression (LAR) algorithm.
  • Utilized Least Absolute Shrinkage and Selection Operator (LASSO) penalized Multiple Linear Regression.
  • Applied methods to a dataset with 800 potential covariates and 60 observations.

Main Results:

  • The LAR algorithm efficiently selected relevant covariates for interpolating soil carbon data.
  • LASSO variable selection proved computationally inexpensive.
  • Demonstrated the practical application of LAR in complex geostatistical modeling.

Conclusions:

  • The LAR algorithm is a highly efficient tool for covariate selection in geostatistical soil mapping.
  • LASSO regularization significantly reduces computational burden in model building.
  • This approach enhances the accuracy and feasibility of soil carbon interpolation.