CHull: a generic convex-hull-based model selection method

When analyzing data, researchers are often confronted with a model selection problem (e.g., determining the number of components/factors in principal components analysis [PCA]/factor analysis or identifying the most important predictors in a regression analysis). To tackle such a problem, researchers may apply some objective procedure, like parallel analysis in PCA/factor analysis or stepwise selection methods in regression analysis. A drawback of these procedures is that they can only be applied to the model selection problem at hand. An interesting alternative is the CHull model selection procedure, which was originally developed for multiway analysis (e.g., multimode partitioning). However, the key idea behind the CHull procedure--identifying a model that optimally balances model goodness of fit/misfit and model complexity--is quite generic. Therefore, the procedure may also be used when applying many other analysis techniques. The aim of this article is twofold. First, we demonstrate the wide applicability of the CHull method by showing how it can be used to solve various model selection problems in the context of PCA, reduced K-means, best-subset regression, and partial least squares regression. Moreover, a comparison of CHull with standard model selection methods for these problems is performed. Second, we present the CHULL software, which may be downloaded from http://ppw.kuleuven.be/okp/software/CHULL/, to assist the user in applying the CHull procedure.