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

Girault Gnanguenon Guesse (1) , Patrice Loisel (1) , Bénedicte Fontez (2) , Thierry Simonneau (1) , Nadine Hilgert (1)

1 INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
2 Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier

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.

Mots clés: joint distribution; penalized linear regression; information criteria; Generalized Fused Lasso; interpretable coefficient

Domaines: Statistiques [math.ST]

Girault Gnanguenon Guesse, Patrice Loisel, Bénedicte Fontez, Thierry Simonneau, Nadine Hilgert. An exploratory penalized regression to identify combined effects of functional variables -Application to agri-environmental issues. 2021. ⟨hal-03298977⟩