Abstract
Methods to perform regression on compositional covariates have recently been proposed using isometric log-ratios (ilr) representation of compositional parts. This approach consists of first applying standard regression on ilr coordinates and second, transforming the estimated ilr coefficients into their contrast log-ratio counterparts. This gives easy-to-interpret parameters indicating the relative effect of each compositional part. In this work we present an extension of this framework, where compositional covariate effects are allowed to be smooth in the ilr domain. This is achieved by fitting a smooth function over the multidimensional ilr space, using Bayesian P-splines. Smoothness is achieved by assuming random walk priors on spline coefficients in a hierarchical Bayesian framework. The proposed methodology is applied to spatial data from an ecological survey on a gypsum outcrop located in the Emilia Romagna Region, Italy.
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Acknowledgments
We wish to thank Carlo Ferrari, Giovanna Pezzi and Andrea Velli for introducing us to the problem, providing data and performing data pre-processing. The research work underlying this paper was funded by a FIRB 2012 Grant (Project No. RBFR12URQJ; title: Statistical modeling of environmental phenomena: pollution, meteorology, health and their interactions) for research projects by the Italian Ministry of Education, Universities and Research. We thank two anonymous referees for their suggestions and comments.
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Bruno, F., Greco, F. & Ventrucci, M. Non-parametric regression on compositional covariates using Bayesian P-splines. Stat Methods Appl 25, 75–88 (2016). https://doi.org/10.1007/s10260-015-0339-2
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DOI: https://doi.org/10.1007/s10260-015-0339-2