Lecture Notes on Compositional Data Analysis

Preface These notes have been prepared as support to a short course on compositional data analysis. Their aim is to transmit the basic concepts and skills for simple applications, thus setting the premises for more advanced projects. One should be aware that frequent updates will be required in the near future, as the theory presented here is a field of active research. The notes are based both on the monograph by John Aitchison, Statistical analysis of compositional data (1986), and on recent developments that complement the theory developed there, mainly those by Aitchison constant references to mentioned documents, only complementary references will be given within the text. Readers should be aware that for a thorough understanding of composi-tional data analysis, a good knowledge in standard univariate statistics, basic linear algebra and calculus, complemented with an introduction to applied multivariate statistical analysis, is a must. The specific subjects of interest in multivariate statistics in real space can be learned in parallel from standard textbooks, like for instance Krzanowski (in Spanish). Thus, the intended audience goes from advanced students in applied sciences to practitioners. Concerning notation, it is important to note that, to conform to the standard praxis of registering samples as a matrix where each row is a sample and each column is a variate, vectors will be considered as row vectors to make the transfer from theoretical concepts to practical computations easier. Most chapters end with a list of exercises. They are formulated in such a way that they have to be solved using an appropriate software. A user friendly, MS-Excel based freeware to facilitate this task can be downloaded from the web at the following address: Details about this package can be found in Thió-Henestrosa and Martín-Fernández (2005) or Thió-Henestrosa et al. (2005). There is also available a whole library of subroutines for Matlab, developed mainly by John Aitchison, which can be obtained from John Aitchison himself or from anybody of the compositional data analysis group at the University of Girona. Finally, those interested in working with R (or S-plus) may either use the set of functions " mixeR " by Bren (2003), or the full-fledged package " compositions " by van den Boogaart and Tolosana-Delgado (2005). 1 Introduction The awareness of problems related to the statistical analysis of compositional data analysis dates back to a paper by Karl Pearson (1897) which title began significantly with the words " …