A General Framework for Multivariate Analysis with Optimal Scaling: The R Package aspect

Abstract

In a series of papers De Leeuw developed a general framework for multivariate analysis with optimal scaling. The basic idea of optimal scaling is to transform the observed variables (categories) in terms of quantifications. In the approach presented here the multivariate data are collected into a multivariable. An aspect of a multivariable is a function that is used to measure how well the multivariable satisfies some criterion. Basically we can think of two different families of aspects which unify many well-known multivariate methods: Correlational aspects based on sums of correlations, eigenvalues and determinants which unify multiple regression, path analysis, correspondence analysis, nonlinear PCA, etc. Non-correlational aspects which linearize bivariate regressions and can be used for SEM preprocessing with categorical data. Additionally, other aspects can be established that do not correspond to classical techniques at all. By means of the R package aspect we provide a unified majorization-based implementation of this methodology. Using various data examples we will show the flexibility of this approach and how the optimally scaled results can be represented using graphical tools provided by the package.