Department of Economics

AUTHOR

Pantazis Yannis

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Statistics , Data Analytics - 2026

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

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.

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