Discrete and Smooth Scalar-on-Density Compositional Regression for Assessing the Impact of Climate Change on Rice Yield in Vietnam

Abstract

We compare several approaches to scalar-on-density regression. With a discrete point of view, the densities can be viewed as histograms whose frequency vectors belong to a simplex ${\cal S}^D$ and then classical compositional regression can be used. An alternative with a functional point of view is to consider density functions as infinite dimensional compositional objects, elements of the so-called Bayes space ${\cal B}^2$, and then compositional scalar-on-density regression can be performed. In the second approach, since the density covariate data is originally available as an histogram, these first need to be sent to ${\cal B}^2$ using a smoothing step performed by CB-splines smoothing. It is then interesting to investigate the potential advantage of the smooth approach with respect to the discrete one. We compare them through an application about the assessment of the impact of climate change on rice yield in Vietnam, where density covariates are the distributions of maximum daily temperatures during 30 years, from 1987 to 2016, in $63$ Vietnamese provinces. Additional covariates such as precipitation, regional dummies and a time trend are added to both models. Scenarios of climate change are modelled with perturbations of the initial density by a chosen change direction producing a shift of the densities towards higher temperatures. The impact on rice yield is then obtained in both models by computing a simple inner product, in ${\cal S}^D$ and respectively ${\cal B}^2,$ of the parameter of the density covariate with the change direction. The comparison shows that the smooth approach outperforms the discrete one by a better evaluation of the phenomenon scale which the discrete approach may fail to uncover.

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Reference

Thi-Huong Trinh, Michel Simioni, and Christine Thomas-Agnan, “Discrete and Smooth Scalar-on-Density Compositional Regression for Assessing the Impact of Climate Change on Rice Yield in Vietnam”, TSE Working Paper, n. 23-1410, February 2023.