Functional response models.

*(English)*Zbl 1073.62098Summary: 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.

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 |