Modeling and Analysis of Compositional Data

Chapter 5Exploratory data analysis

5.1 General remarks

In this chapter, the first steps in any analysis of a compositional data set are addressed. The set is represented as a matrix with rows (observed compositions) and columns (parts). An exploratory analysis includes the following steps:

1. computing descriptive statistics, that is, the center and variation matrix of a data set, as well as its total variability;
2. looking at the biplot of the data set to discover patterns;
3. plotting patterns in ternary diagrams of subcompositions, possibly centered to enhance visualization;
4. defining an appropriate representation in orthonormal coordinates and computing the corresponding coordinates; and
5. computing classical summary statistics of the coordinates and representing the results in a balance-dendrogram.

In general, the last two steps will be based on a particular sequential binary partition, defined either a priori or as a result of the insights provided by the first three steps.

Before starting, some general considerations need to be made. The first step in a statistical analysis is to check the data set for errors. It can be done using standard procedures, for example, using the minimum ...