STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling

STATIS is an extension of principal component analysis PCA tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, as in a variant called dual-STATIS, multiple data tables where the same variables are measured on different sets of observations. STATIS proceeds in two steps: First it analyzes the between data table similarity structure and derives from this analysis an optimal set of weights that are used to compute a linear combination of the data tables called the compromise that best represents the information common to the different data tables; Second, the PCA of this compromise gives an optimal map of the observations. Each of the data tables also provides a map of the observations that is in the same space as the optimum compromise map. In this article, we present STATIS, explain the criteria that it optimizes, review the recent inferential extensions to STATIS and illustrate it with a detailed example.