Interaction models for functional regression

8 years 27 days ago

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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.

Joseph Usset, Ana-Maria Staicu, Arnab Maity

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