  We extend the varying coefficient functional linear model to the nonlinear
model and propose a varying coefficient functional additive model. The proposed
method can represent the relationship between functional predictors and a
scalar response where the response depends on an exogenous variable.It captures
the nonlinear structure between variables and also provides interpretable
relationship of them. The model is estimated through basis expansions and
penalized likelihood method, and then the tuning parameters included at the
estimation procedure are selected by a model selection criterion. Simulation
studies are provided to show the effectiveness of the proposed method. We also
apply it to the analysis of crop yield data and then investigate how and when
the environmental factor relates to the amount of the crop yield.
