Interaction models for functional regression

We consider a functional regression model with a scalar response and multiple functional predictors that accommodates two-way interactions in addition to their main effects. We develop an estimation procedure where the main effects are modeled using penalized regression splines, and the interaction effect by a tensor product basis. Extensions to generalized linear models and data observed on sparse grids or with error are presented. Additionally we describe hypothesis testing that the interaction effect is null. Our proposed method can be easily implemented through existing software. Through numerical study we find that fitting an additive model in the presence of interaction leads to both poor estimation performance and lost prediction power, while fitting an interaction model where there is in fact no interaction leads to negligible losses. We illustrate our methodology by analyzing the AneuRisk65 study data.

• Type: Journal
• Year: 2016
• Where: CSDA
• Authors: Joseph Usset, Ana-Maria Staicu, Arnab Maity
• Keywords: CSDA 2016, Social Sciences