acomp              package:compositions              R Documentation

_A_i_t_c_h_i_s_o_n _c_o_m_p_o_s_i_t_i_o_n_s

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

     A class providing the means to analyse compositions in the
     philosophical framework of the Aitchison Simplex.

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

               acomp(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 for its own, called a
     composition. This scale  was in-depth analysed by Aitchison (1986)
     and the functions around the class '"acomp"' follow his approach.
      Compositions have some important properties: Amounts are always
     positive. The amount of every part is limited to the whole. The
     absolute amount of the whole is noninformative since it is
     typically due to artifacts on the measurement procedure. Thus only
     relative changes are relevant. If the relative amount of one part
     increases, the amounts of other parts must decrease, introducing
     spurious anticorrelation (Chayes 1960), when analysed directly.
     Often parts (e.g H2O, Si) are missing in the dataset leaving the
     total amount unreported and longing for analysis procedures
     avoiding spurious effects when applied to such subcompositions.
     Furthermore,  the result of an analysis should be indepent of the
     units (ppm, g/l, vol.%, mass.%, molar fraction) of the dataset. 
      From these properties Aitchison showed that the analysis should
     be based on ratios or log-ratios only. He introduced  several
     transformations (e.g. 'clr','alr'), operations (e.g. 'perturbe',
     'power.acomp'), and a distance ('dist') which are compatible with
     these properties. Later it was found that the set of compostions
     equiped with perturbations as addition and powertransform as
     scalar multiplication and the 'dist' as distance form a D-1
     dimensional euclidean vector space (Billheimer, Fagan and Guttorp,
     2001), which  can be mapped isometrically to a usual real vector
     space by 'ilr'  (Pawlowsky-Glahn and Egozcue, 2001). 
      The general approach in analysing acomp objects is thus to
     performe classical multivariate analysis on
     clr/alr/ilr-transformed coordinates and to backtransform or
     display the results in such a way that they can be interpreted in
     terms of the original compositional parts.    
      A side effect of the procedure is to force the compositions to
     sum up to a total, which is done by the closure operation 'clo' .

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

     a vector of class '"acomp"' representing one closed composition or
     a matrix of class '"acomp"' representing multiple closed
     compositions each in one row.

_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.

     Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn
     (2002) A consise guide to the algebraic geometric structure of the
     simplex, the sample space for compositional data analysis, _Terra
     Nostra_, Schriften der Alfred Wegener-Stiftung, 03/2003

     Billheimer, D., P. Guttorp, W.F. and Fagan (2001) Statistical
     interpretation of species composition, _Journal of the American
     Statistical Association_, *96* (456), 1205-1214

     Pawlowsky-Glahn, V. and J.J. Egozcue (2001) Geometric approach to
     statistical analysis on the simplex. _SERRA_ *15*(5), 384-398

     Pawlowsky-Glahn, V. and ??? (2003) ???

     <URL: http://ima.udg.es/Activitats/CoDaWork03>

     <URL: http://ima.udg.es/Activitats/CoDaWork05>

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

     'clr','rcomp', 'aplus', 'princomp.acomp',  'plot.acomp',
     'boxplot.acomp', 'barplot.acomp', 'mean.acomp', 'var.acomp',
     'variation.acomp', 'cov.acomp', 'msd'

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

     data(SimulatedAmounts)
     plot(acomp(sa.lognormals))

