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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2510.12663 |
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| _version_ | 1866914562192703488 |
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| author | Tsagris, Michail Pantazis, Yannis |
| author_facet | Tsagris, Michail Pantazis, Yannis |
| contents | The paper revisits the $α$--regression framework for compositional data. The model 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, derive marginal effects for interpretation, and provide a visual inspection of the effect of each predictor. We further discuss robustified versions, the inclusion of natural splines, and the incorporation of compositional predictors which further facilitate the formulation of a simple time series model. The framework is extended to spatial settings through four models. a) The $α$--spatially--lagged X regression model, which incorporates spatial spillover effects via spatially--lagged covariates, with decomposition into direct and indirect effects. b) The $α$--spatial autoregressive model that allows for spatial autocorrelation. c) The geographically--weighted $α$--regression, which allows coefficients to vary spatially for capturing local relationships. d) The $α$--eigenvector spatial filtering that is computationally efficient and captures spatial dependence via the eigenvectors of the kernelized distance matrix. Applications to four real datasets illustrate that the models perform on par with or outperform existing models in the literature. The examples showcase that spatial extensions capture the dependence and improve the predictive performance. Overall, the examples provide evidence that the log--ratio methodology does not lead to the optimal results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $α$--regression for compositional data: a unified framework for standard, temporal and spatial regression models including compositional predictors Tsagris, Michail Pantazis, Yannis Methodology The paper revisits the $α$--regression framework for compositional data. The model 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, derive marginal effects for interpretation, and provide a visual inspection of the effect of each predictor. We further discuss robustified versions, the inclusion of natural splines, and the incorporation of compositional predictors which further facilitate the formulation of a simple time series model. The framework is extended to spatial settings through four models. a) The $α$--spatially--lagged X regression model, which incorporates spatial spillover effects via spatially--lagged covariates, with decomposition into direct and indirect effects. b) The $α$--spatial autoregressive model that allows for spatial autocorrelation. c) The geographically--weighted $α$--regression, which allows coefficients to vary spatially for capturing local relationships. d) The $α$--eigenvector spatial filtering that is computationally efficient and captures spatial dependence via the eigenvectors of the kernelized distance matrix. Applications to four real datasets illustrate that the models perform on par with or outperform existing models in the literature. The examples showcase that spatial extensions capture the dependence and improve the predictive performance. Overall, the examples provide evidence that the log--ratio methodology does not lead to the optimal results. |
| title | The $α$--regression for compositional data: a unified framework for standard, temporal and spatial regression models including compositional predictors |
| topic | Methodology |
| url | https://arxiv.org/abs/2510.12663 |