Functional response models. (English) Zbl 1073.62098

Chiou, Jeng-Min; Müller, Hans-Georg; Wang, Jane-Ling

Stat. Sin. 14, No. 3, 675-693 (2004).

Summary: 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 radom 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.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J02	General nonlinear regression
62M20	Inference from stochastic processes and prediction

Keywords:

dose response; eigenfunctions; functional data analysis; functional regression; multiplicative modeling; principal components; smoothing