Compositional and noncompositional covariates in multiple linear regression

Le résumé fourni par la source

Abstract Empirical studies in the social sciences often include covariates that are compositional in nature—vectors of shares that sum to a constant—alongside noncompositional covariates. A common approach to handling compositional data in linear regression is to omit one component to avoid perfect multicollinearity. I demonstrate why these coefficients (along with standard errors and t-statistics) can be highly sensitive to the choice of omitted category. Transforming the compositional data using additive logarithmic ratios (ALR) yields permutation-invariant regressions and permits counterfactual changes in the implied composition that remain within the simplex. Furthermore, I demonstrate that applying a simple scale factor to the ALR coefficients generates the coefficients and standard errors associated with isometric logarithmic ratios (ILR) for the variables of interest. Finally, using log-ratios does not exacerbate inherent problems of multicollinearity associated with compositional data. Economic growth regressions incorporating compositional and noncompositional covariates are used to illustrate.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.