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

Within the econometrics literature, assessing the impact of climate change on agricultural yield has been approached with a linear functional regression model, wherein crop yield, a scalar response, is regressed against the temperature distribution, a functional parameter alongside with other covariates. However this treatment overlooks the specificity of the temperature density curve. In the realm of compositional data analysis, it is argued that such covariates should undergo appropriate log-ratio transformations before inclusion in the model. We compare a discrete version with temperature histograms treated as compositional vectors and a smooth scalar-on-density regression with temperature density treated as an object of the so-called Bayes space. In the latter approach, when density covariate data is initially available as histograms, a preprocessing smoothing step is performed involving CB-splines smoothing. We investigate the respective advantage of the smooth and discrete approaches by modelling the impact of maximum and minimum daily temperatures on rice yield in Vietnam. Moreover we advocate for the modelling of climate change scenarios through the introduction of perturbations of the initial density, determined by a change direction curve computed from the IPPC scenarios. The resulting impact on rice yield is then quantified by calculating a simple inner product between the parameter of the density covariate and the change direction curve. Our findings reveal that the smooth approach and the discrete counterpart yield coherent results, but the smooth seems to outperform the discrete one by an enhanced ability to accurately gauge the phenomenon scale.