An exploratory penalized regression to identify combined effects of functional agri-environmental variables

Crop production is affected by a complex combination of agri-environmental dynamics, as temperature, irradiance, for example. To learn on these complex influences, the development of sensors in agriculture opens new avenues. This requires renewing statistical approaches to take into account the joint variations of these dynamic variables, which are considered here as functional variables. The objective of the paper is to infer an interpretable model to study the joint influence of two functional inputs on a scalar output. We propose a Sparse and Structured Procedure to Identify Combined Effects of Functional Predictors, denoted SPICEFP. It is based on a transformation of both functional variables into categorical variables by defining joint modalities, from which we derived a collection of multiple regression models, where the regressors are the frequencies associated to the joint class intervals. Selection of class intervals and related regression coefficients are performed through a Generalized Fused Lasso. SPICEFP is a generic and exploratory approach. Simulations performed show that it is flexible enough to select the true ranges of values. A use case in agronomy is also presented.