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

Michail Tsagris () and Yannis Pantazis

No 2603, Working Papers from University of Crete, Department of Economics

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.

Keywords: compositional data; α–transformation; spatial regression (search for similar items in EconPapers)
JEL-codes: C21 C31 C51 R15 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2026-03-07
New Economics Papers: this item is included in nep-ecm
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