ABSTRACT
This chapter introduces inferential methods for function-on-scalar regression (FoSR), which is regression when the outcome is a function, and the predictors are scalar. This is also referred to in the literature as the Functional Linear Model (FLM) with a functional outcome and scalar predictors. The chapter starts with an exploratory data analysis to build up the intuition about more complex FoSR models. Using ideas similar to those introduced in Chapter 4, it is shown that FoSr models can be viewed as mixed effects models that can be fit using existing software. Special attention is given to modeling the correlation of functional residuals and computational aspects of the problem. A scalable approach based on univariate regressions, followed by smoothing and bootstrap of study participants is discussed as a practical complementary approach. Methods are illustrated on the NHANES accelerometry data.
