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 struggle with the unit-sum constraint and zero values. This paper revisits the $\alpha$--regression framework, which uses a flexible power transformation parameterized by $\alpha$ to interpolate between raw data analysis and log-ratio methods, naturally handling zeros without imputation while allowing data-driven transformation selection. We formulate $\alpha$--regression as a non-linear least squares problem, provide efficient estimation via the Levenberg-Marquardt algorithm with explicit gradient and Hessian derivations, establish asymptotic normality of the estimators, and derive marginal effects for interpretation. The framework is extended to spatial settings through two models: the $\alpha$--spatially lagged X regression model, which incorporates spatial spillover effects via spatially lagged covariates with decomposition into direct and indirect effects, and the geographically weighted $\alpha$--regression, which allows coefficients to vary spatially for capturing local relationships. Application to Greek agricultural land-use data demonstrates that spatial extensions substantially improve predictive performance.

翻译：成分数据——即各分量非负且总和为一的向量——常见于科学应用中，其中协变量影响各成分的相对比例，但传统回归方法难以处理单位总和约束与零值问题。本文重新审视α-回归框架，该框架通过参数α控制的灵活幂变换，在原始数据分析和对数比方法之间进行插值，无需插补即可自然处理零值，同时支持数据驱动的变换选择。我们将α-回归表述为非线性最小二乘问题，通过Levenberg-Marquardt算法结合显式梯度与海森矩阵推导实现高效估计，建立估计量的渐近正态性，并推导用于解释的边际效应。该框架通过两种模型扩展至空间场景：α-空间滞后X回归模型通过空间滞后协变量纳入空间溢出效应，并将其分解为直接与间接效应；地理加权α-回归则允许系数随空间变化以捕捉局部关系。对希腊农业用地数据的应用表明，空间扩展模型能显著提升预测性能。