Interaction models for functional regression

Joseph Usset, Ana-Maria Staicu and Arnab Maity

Computational Statistics & Data Analysis, 2016, vol. 94, issue C, 317-329

Abstract: A functional regression model with a scalar response and multiple functional predictors is proposed that accommodates two-way interactions in addition to their main effects. The proposed estimation procedure models the main effects 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 measurement error are presented. A hypothesis testing procedure for the functional interaction effect is described. The proposed method can be easily implemented through existing software. Numerical studies show 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. The methodology is illustrated on the AneuRisk65 study data.

Keywords: Functional regression; Hypothesis testing; Interaction; Spline smoothing (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:94:y:2016:i:c:p:317-329

DOI: 10.1016/j.csda.2015.08.020

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