Exploratory model analysis with R and GGobi

Why do we build models? There are two basic reasons: explanation or prediction [Ripley, 2004]. Using large ensembles of models for prediction is commonplace, but is rarely used for explanation, where we typically choose one “best” model. When there are several equally good models, it is common sense to look at them too, but can the “bad” models tell us something as well? This paper describes exploratory model analysis for ensembles of linear models, where we look at all possible main effects models for a given dataset (or a large subset of these models). This gives greater insight than looking at any small set of best models alone: an ensemble of many models can tell us more about the underlying data than any individual model alone. This paper builds heavily on exploratory modelling analysis as introduced by Unwin et al. [2003], but rather than describing different types of useful plots it is organised around different levels of data. We will assume we have m models describing a data set with n observations and p variables. If all possible main effects models are fit, there will be 2p − 1 models in the ensemble. After fitting the models, we compute summary statistics on four levels: