Detection of interactions in experiments on large numbers of factors

Lewis, S.M. and Dean, A.M. (2001) Detection of interactions in experiments on large numbers of factors. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63 (4), 633-672. (doi:10.1111/1467-9868.00304).

Abstract

One of the main advantages of factorial experiments is the information they can offer on interactions. When there are many factors to be studied, some or all of this information is often sacrificed in order to keep the size of the experiment economically feasible. Two strategies for group screening are presented for a large number of factors, over two stages of experimentation, with particular emphasis on the detection of interactions. One approach estimates only main effects at the first stage (classical group screening), whilst the other new method (interaction group screening) estimates both main effects and key two factor interactions at the first stage. Three criteria are used to guide the choice of screening technique, and also the size of the groups of factors for study in the first stage experiment. The criteria seek to minimise the expected total number of observations in the experiment, the probability that the experiment size exceeds a pre-specified target, and the proportion of active individual effects which are not detected. In order to implement these criteria, results are derived on the relationship between the grouped and individual factorial effects, and the probability distributions of the numbers of grouped factors whose main effects or interactions are declared active at the first stge. Examples are used to illustrate the methodology, and some issues and open questions for the practical implementation of the results are discussed.

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