An exploratory penalized regression to identify combined effects of temporal variables-application to agri-environmental issues.

The development of sensors is opening new avenues in several fields of activity. Concerning agricultural crops, complex combinations of agri-environmental dynamics, such as soil and climate variables, are now commonly recorded. These new kinds of measurements are an opportunity to improve knowledge of the drivers of crop yield and crop quality at harvest. This involves renewing statistical approaches to account for the combined variations of these dynamic variables, here considered as temporal variables. The objective of the paper is to estimate an interpretable model to study the influence of the two combined inputs on a scalar output. A Sparse and Structured Procedure is proposed to Identify Combined Effects of Formatted temporal Predictors, hereafter denoted S piceFP. The method is based on the transformation of both temporal variables into categorical variables by defining joint modalities, from which a collection of multiple regression models is then derived. The regressors are the frequencies associated with joint class intervals. The class intervals and related regression coefficients are determined using a generalized fused lasso. S piceFP is a generic and exploratory approach. The simulations we performed show that it is flexible enough to select the non-null or influential modalities of values. A motivating example for grape quality is presented.