Trinh, Thi Huong, Thomas-Agnan, Christine and Simioni, Michel (2023) 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, Toulouse

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Abstract

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 alterna-
tive models that respect the distributional nature of the temperature distribution
parameter. Replacing functional observations with the corresponding distribu-
tional 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 appro-
priate 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 repre-
sentation 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