rcomp              package:compositions              R Documentation

_C_o_m_p_o_s_i_t_i_o_n_s _a_s _e_l_e_m_e_n_t_s _o_f _t_h_e _S_i_m_p_l_e_x _e_m_b_e_d_d_e_d _i_n _t_h_e _D-_d_i_m_e_n_s_i_o_n_a_l _r_e_a_l _s_p_a_c_e

_D_e_s_c_r_i_p_t_i_o_n:

     A class providing a way to analyse compositions in the
     philosophical framework of the Simplex as subset of the R^D.

_U_s_a_g_e:

               rcomp(X,parts=1:NCOL(oneOrDataset(X)),total=1)
               

_A_r_g_u_m_e_n_t_s:

       X: composition or dataset of compositions

   parts: vector containing the indices xor names of the columns to be
          used

   total: the total amount to be used, typically 1 or 100

_D_e_t_a_i_l_s:

     Many multivariate datasets essentially describe amounts of D
     different parts in a whole. This has some important implications
     justifying to regard them as a scale on its own, called a
     composition. The functions around the class '"rcomp"' follow the
     traditional (but statistically inconsistent) approach regarding
     compositions simply as a multivariate vector of positive numbers
     summing up to 1. This space of D positive numbers summing to 1 is
     traditionally called the D-1-dimensional simplex.

     The compositional scale was in-depth analysed by Aitchison (1986)
     and he found serious reasons why compositional data should be
     analysed with a different geometry.  The functions around the
     class '"acomp"' follow his approach. However the Aitchison
     approach based on log-ratios is  sometimes criticized (e.g. Rehder
     and Zier, 2002). It cannot deal with  absent parts (i.e. zeros).
     It is sensitive to large measurement errors in small amounts. The
     Aitchison operations cannot represent simple mixture of different
     chemical compositions. The used transformations are not uniformly
     continuous. Straight lines and ellipses in Aitchison space look
     strangely in ternary diagrams. As all uncritical statistical
     analysis, blind application of logratio-based analysis is
     sometimes misleading. Therefore it is sometimes usefull to analyse
     compositional data directly as a multivariate dataset of portions
     summing to 1. However a clear warning must be given that the
     utilisation of almost any kind of classical multivariate analysis
     introduce some kinds of artifacts (e.g. Chayes 1960) when applied
     to compositional data. So extra care and considerable expert
     knowlegde is needed for the proper interpretation of results
     achieved in this non-Aitchison approach. The package tries to lead
     the user around these artifacts as much as possible and gives
     hints to major pitfalls in the help. However meaningless results
     cannot be fully avoided in this (rather inconsistent) approach.  
      A side effect of the procedure is to force the compositions to
     sum to one, which is done by the closure operation 'clo' .  
      The classes rcomp, acomp, aplus, and rplus are designed in a
     fashion as similar as possible, in order to allow direct
     comparison between results achieved   by the different approaches.
     Especially the acomp logistic transforms 'clr', 'alr', 'ilr' are
     mirrored by analogous linear transforms 'cpt', 'apt', 'ipt' in the
     rcomp class framework.

_V_a_l_u_e:

     a vector of class '"rcomp"' representing a closed composition or a
     matrix of class '"rcomp"' representing multiple closed
     compositions, by rows.

_R_e_f_e_r_e_n_c_e_s:

     Aitchison, J. (1986) _The Statistical Analysis of Compositional
     Data_ Monographs on Statistics and Applied Probability. Chapman &
     Hall Ltd., London (UK). 416p.

     Rehder, S. and U. Zier (2001) Letter to the Editor: Comment on 
     ``Logratio Analysis and Compositional Distance'' by {J}.
     {A}itchison, {C}.  {B}arcel\'o-{V}idal, {J.A.}
     {M}art{\'\i}n-{F}ern\'andez and {V}. Pawlowsky-Glahn,
     _Mathematical Geology_, *33* (7), 845-848.

     Zier, U. and S. Rehder (2002) Some comments on log-ratio
     transformation and compositional distance, _Terra Nostra_,
     Schriften der Alfred Wegener-Stiftung, 03/2003

_S_e_e _A_l_s_o:

     'cpt', 'apt', 'ipt', 'acomp', 'rplus', 'princomp.rcomp',
     'plot.rcomp', 'boxplot.rcomp', 'barplot.rcomp', 'mean.rcomp',
     'var.rcomp', 'variation.rcomp', 'cov.rcomp', 'msd',
     'convex.rcomp', '+.rcomp'

_E_x_a_m_p_l_e_s:

     data(SimulatedAmounts)
     plot(rcomp(sa.tnormals))

