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Non-parametric regression on compositional covariates using Bayesian P-splines

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  • Francesca Bruno

    (University of Bologna)

  • Fedele Greco

    (University of Bologna)

  • Massimo Ventrucci

    (University of Bologna)

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.

Suggested Citation

  • Francesca Bruno & Fedele Greco & Massimo Ventrucci, 2016. "Non-parametric regression on compositional covariates using Bayesian P-splines," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 75-88, March.
    • Handle: RePEc:spr:stmapp:v:25:y:2016:i:1:d:10.1007_s10260-015-0339-2
    DOI: 10.1007/s10260-015-0339-2
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    Cited by:

    1. Huiwen Wang & Zhichao Wang & Shanshan Wang, 2021. "Sliced inverse regression method for multivariate compositional data modeling," Statistical Papers, Springer, vol. 62(1), pages 361-393, February.

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