Discrete and smooth scalar-on-density compositional regression for assessing the impact of climate change on rice yield in Vietnam

In econometrics, the impact of climate change on agricultural yield has often been modeled using linear functional regression, where crop yield, a scalar response, is regressed on the temperature distribution over a given time period, treated as an ordinary functional parameter, along with other covariates. We explore alternative models that respect the distributional nature of the temperature distribution parameter. Replacing functional observations with the corresponding distributional ones is appropriate for phenomena that are insensitive to the temporal order of events.Since classical addition and scalar multiplication are unsuitable for density functions, alternative operations and spaces are required. Moreover, compositional data analysis suggests that such covariates should undergo appropriate log-ratio transformations before inclusion in the model. We compare a discrete approach, where temperature histograms are treated as compositional vectors, with a smooth scalar-on-density regression using a Bayes space representation of temperature densities. We evaluate the strengths of each method in modeling rice yield in Vietnam, using data on daily temperature extremes.Additionally, we propose modeling climate change scenarios with perturbations of the initial density along a change direction curve informed by IPCC scenarios. The resulting rice yield impact is then quantified using a simple inner product between the density covariate parameter and the change direction curve. Our results indicate that while both approaches yield coherent findings, the smooth model outperforms the discrete one with an enhanced ability to accurately gauge the phenomenon's scale.