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The α–regression for compositional data: a unified framework for standard, spatially-lagged, spatial autoregressive and geographically-weighted regression models

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  • Michail Tsagris

  • Yannis Pantazis

Abstract

Compositional data–vectors of non-negative components summing to unity–frequently arise in scientific applications where covariates influence the relative proportions of components, yet traditional regression approaches face challenges regarding the unit-sum constraint and zero values. This paper revisits the α–regression framework, which uses a flexible power transformation parameterized by α to interpolate between raw data analysis and log-ratio methods, naturally handling zeros without imputation while allowing data-driven transformation selection. We formulate α–regression as a non-linear least squares problem, study its asymptotic properties, provide efficient estimation via the Levenberg-Marquardt algorithm, and derive marginal effects for interpretation.

Suggested Citation

  • Michail Tsagris & Yannis Pantazis, 2026. "The α–regression for compositional data: a unified framework for standard, spatially-lagged, spatial autoregressive and geographically-weighted regression models," Working Papers 2603, University of Crete, Department of Economics.
    • Handle: RePEc:crt:wpaper:2603
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    References listed on IDEAS

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    2. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Improved classi cation for compositional data using the $\alpha$-transformation," MPRA Paper 67657, University Library of Munich, Germany.
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    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • R15 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Econometric and Input-Output Models; Other Methods

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