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Use of compositional covariates in linear regression: problems and solutions

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  • Zhao, T.;
  • Sutton, M.;
  • Meacock, M.;

Abstract

Compositional variables such as proportions by age group are commonly included as covariates in aggregate-level health research. Since these proportions sum to one and only contain relative information, directly including them as covariates violates the fundamental assumptions made in linear regression analysis. We explain the compositional nature of such data and, using practice-level elective admissions rates in England as an example outcome variable, demonstrate the consequences of directly using proportions in regressions. We also provide an overview of compositional data analysis (CoDA) techniques with a focus on isometric log-ratio (ILR) transformation. Applying ILR to our example data shows that the regression results can differ significantly from those obtained using raw proportions. Health economists should apply appropriate CoDA methods when using compositional data in their research.

Suggested Citation

  • Zhao, T.; & Sutton, M.; & Meacock, M.;, 2023. "Use of compositional covariates in linear regression: problems and solutions," Health, Econometrics and Data Group (HEDG) Working Papers 23/16, HEDG, c/o Department of Economics, University of York.
    • Handle: RePEc:yor:hectdg:23/16
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    References listed on IDEAS

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    1. K. Hron & P. Filzmoser & K. Thompson, 2012. "Linear regression with compositional explanatory variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1115-1128, November.
    2. Sean Urwin & Yiu‐Shing Lau & Gunn Grande & Matt Sutton, 2023. "Informal caregiving, time use and experienced wellbeing," Health Economics, John Wiley & Sons, Ltd., vol. 32(2), pages 356-374, February.
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    More about this item

    Keywords

    compositional data; CoDA; age group proportion; isometric log-ratio;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • I10 - Health, Education, and Welfare - - Health - - - General

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