Statis

STATIS is a generalization of principal component analysis (PCA), and its goal is to analyze several sets of variables collected on the same set of observations. It is attributed to Escouffier and L'Hermier des Plantes. A related approach is known as procrustes matching by congruence coefficients in the English-speaking community. The goal of STATIS is (a) to compare and analyze the relationship between the different data sets, (b) to combine them into a common structure called a compromise, which is then analyzed via PCA to reveal the common structure between the observations, and finally (c) to project each of the original data sets onto the compromise to analyze communalities and discrepancies. STATIS is used in very different domains, such as sensory evaluation, molecular imaging, brain imaging, ecology, and chemometrics.

The number or nature of the variables used to describe the observations can vary from one data set to the other, but the observations should be the same in all the data sets.

For example, the data sets can be measurements taken on the same observations (individuals or objects) at different occasions. In this case, the first data set corresponds to the data collected at time t = 1, the second to the data collected at time t = 2, and so on. The goal of the analysis, then, is to evaluate whether the position of the observations is stable over time.

As another example, the data sets can be measurements taken on the same observations by different participants or groups of participants. In this case, the first data set corresponds to the first participant, the second to the second participant, and so on. The goal of the analysis, then, is to evaluate whether there is an agreement between the participants or groups of participants.

The general idea behind STATIS is to analyze the structure of the individual data sets (i.e., the relation between the individual data sets) and to derive from this structure an optimal set of weights for computing a common representation of the observations, called the compromise. The weights used to compute the compromise are chosen to make it as representative of [Page 956]all the data sets as possible. The PCA of the compromise gives, then, the position of the observations in the compromise space. The position of the observations for each data set can be represented in the compromise space as supplementary points. Finally, as a by-product of the weight computation, the data sets can be represented as points in a multidimensional space.