Constrained functional additive models for estimating interactions between a treatment and functional covariates
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A novel functional additive model is proposed which is uniquely modified and constrained to model nonlinear interactions between a treatment indicator and a potentially large number of functional/scalar covariates. We generalize functional additive regression models by incorporating treatment-specific components into additive effect components. A structural constraint is imposed on the treatment-specific components, to give a class of orthogonal main and interaction effect additive models. If primary interest is in interactions, we can avoid estimating main effects, obviating the need to specify their form and thereby avoiding the issue of model misspecification. The methods are illustrated with data from a clinical trial with imaging data as predictors.
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