Use of compositional covariates in linear regression: problems and solutions

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

Health, Econometrics and Data Group (HEDG) Working Papers from HEDG, c/o Department of Economics, University of York

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.

Keywords: compositional data; CoDA; age group proportion; isometric log-ratio (search for similar items in EconPapers)
JEL-codes: C13 C18 I10 (search for similar items in EconPapers)
Date: 2023-11
New Economics Papers: this item is included in nep-ecm
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