ABSTRACT
This chapter introduces inferential methods for function-on-function regression (FoFR), which is regression when the outcome is a function, and the predictors are scalars and functions. This is also referred to in the literature as the Functional Linear Model (FLM) with a functional outcome and a combination of scalar and functional predictors. Ideas introduced in Chapters 4 and 5 are further extended to FoFR, which can also be viewed as a mixed effects model. Methods are applied to the COVID-19 US mortality data, and the CONTENT child growth study. Goodness-of-fit analysis for FoFR is introduced based on the analysis of model residuals. Constructing correlation and multiplicity adjusted confidence intervals and p-values are discussed. Methods are implemented in the refund::pffr function and mgcv.
