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Reducing bias and mitigating the influence of excess of zeros in regression covariates with multi-outcome adaptive LAD-lasso

Author

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  • Jyrki Möttönen
  • Tero Lähderanta
  • Janne Salonen
  • Mikko J. Sillanpää

Abstract

Zero-inflated explanatory variables, as opposed to outcome variables, are common, for example, in environmental sciences. In this article, we address the problem of having excess of zero values in some continuous explanatory variables, which are subject to multi-outcome lasso-regularized variable selection. In short, the problem results from the failure of the lasso-type of shrinkage methods to recognize any difference between zero value occurring either in the regression coefficient or in the corresponding value of the explanatory variable. This kind of confounding will obviously increase the number of false positives – all non-zero regression coefficients do not necessarily represent true outcome effects. We present here the adaptive LAD-lasso for multiple outcomes, which extends the earlier work of multi-outcome LAD-lasso with adaptive penalization. In addition to well-known property of having less biased regression coefficients, we show that the adaptivity also improves method’s ability to recover from influences of excess of zero values measured in continuous covariates.

Suggested Citation

  • Jyrki Möttönen & Tero Lähderanta & Janne Salonen & Mikko J. Sillanpää, 2024. "Reducing bias and mitigating the influence of excess of zeros in regression covariates with multi-outcome adaptive LAD-lasso," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(13), pages 4730-4744, July.
  • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:13:p:4730-4744
    DOI: 10.1080/03610926.2023.2189059
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