Abstract: We review functional regression models and discuss in more detail the situation where the predictor is a vector or scalar, such as a dose, and the response is a random trajectory. These models incorporate the influence of the predictor either through the mean response function, through the random components of a Karhunen-Loève or functional principal components expansion, or by means of a combination of both. In a case study, we analyze dose-response data with functional responses from an experiment on the age-specific reproduction of medflies. Daily egg-laying was recorded for a sample of 874 medflies in response to dietary dose provided to the flies. We compare several functional response models for these data. A useful criterion to evaluate models is a model's ability to predict the response at a new dose. We quantify this notion by means of a conditional prediction error that is obtained through a leave-one-dose-out technique.
Key words and phrases: Dose-response, eigenfunctions, functional data analysis, functional regression, multiplicative modeling, principal components, smoothing.