When several models are under
consideration, the standard approach is to select a single model based on some
principle. Classical principles are likelihood testing (which is the same as
backwards stepwise); AIC or alternatively forward stepwise. However, there may
be some value in using several models in parallel and averaging the results
(like the estimates of regression coefficients). Weights may depend on fit or
be chosen beforehand. This may give a better prediction. **Example 1:** Regression with several potential covariates. Suppose we
want to predict the body weight of a child and have information on sex, age and
height. Using all three covariates should in theory give the best prediction,
but could have extra uncertainty due to the high correlation between age and
height. So one could fit three models; sex and age; sex and height; sex, age
and height and then average the three predictions. **Example 2:** Dose finding with alternative dose-response models. In
this case, we may have alternative models, say as means f(x) at dose x, the
model could be of the Emax type (f(x)=α + β x /(x+γ)) or the exponential type
(f(x)= α + β (1- exp(-x γ)). Suppose conventional fit comparisons do not give a
clear conclusion as to which is best. Averaging the two predictions could be
better than either one. This research area has been pioneered by Claeskens and
Hjort.

The project:

The project consists of studying the statistical properties of the predictions. This includes how to weight two or more models to give the most meaningful prediction. A second question is to which extent this approach can be used for testing (that is, whether it satisfies the intended significance level).

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