By K. Gerald van den Boogaart, Raimon Tolosana-Delgado
This booklet covers statistical research of compositional facts units from uncomplicated rules to purposes in descriptive exploratory research, strong linear types and complex multivariate statistical tools. deals many illustrated examples and code chunks.
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Extra resources for Analyzing Compositional Data with R (Use R!)
5) The distance between two compositions can be directly computed by norm(x-y). In “compositions”, the generic function dist automatically computes the Aitchison distances between all rows of an acomp data matrix. , as input to hierarchical cluster analysis, see Sect. 2). 5 The Centered Log-Ratio Transformation (clr) The set of compositions together with the operations perturbation ˚, powering ˇ and Aitchison scalar product . D 1/-dimensional Euclidean space structure on the simplex. This means that we can translate virtually anything defined for real vectors to compositions, as an Euclidean space is always equivalent to the real space.
The same applies to many other kinds of irregularities in compositional data, like measurements with errors, atypical values, or values below the detection limit: in all these cases, the total sum will either be unknown or affected by an error, which will propagate to all the variables by the closure. The solution comes by realizing that whichever this total value might be, the (log)ratios between any regular components are unaffected. The “compositions” package will thus close the non-missing parts as if the missing parts are 0, knowing that this value will not affect any proper analysis.
The multivariate normal distribution is its central statistical model. Most wellknown multivariate procedures were devised for this scale, such as cluster analysis, mean vector and variance–covariance matrix, principal component analysis, factor analysis, multivariate regression, and multivariate analysis of variance. Because it is the “conventional” scale, the package “compositions” only provides a limited functionality within it. It is mainly intended as a back-end for procedures based on treating the other scales through transformations.