Abstract:
|
We propose a functional additive model, uniquely modified and constrained to model nonlinear interactions between a treatment indicator and a potentially large number of functional/scalar regressors. We extend the functional additive regression of Fan et al. (2015), by incorporating treatment-specific link functions. A structural constraint is imposed on the treatment-specific components of the model, to give a class of orthogonal main and interaction effect additive models. Then the main effect components and the interaction effect components are estimated separately. If our interest is in interactions, we can estimate the interaction effects only, without having to model the main effect functionals, which side-steps the issue of potential misspecification of the main effects. Imposing a concave penalty in estimation, the method simultaneously selects functional/scalar treatment effect modifiers that exhibit possibly nonlinear interactions with the treatment indicator. We present theoretical properties of the proposed method. A set of simulation experiments and an application to a dataset from a depression clinical trial are presented to demonstrate this approach.
|