compositions-package      package:compositions      R Documentation

_l_i_b_r_a_r_y(_c_o_m_p_o_s_i_t_i_o_n_s)

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

     "compositions" is a package for the analysis of compositional and
     multivariate positive data (generally called "amounts"), based on
     several alternative approaches.

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

     To get detailed "getting started" introduction use 'help.start()'
     or 'help.start(browser="myfavouritebrowser")' Go to "Packages"
     then "compositions" and then "overview" and then launch the file
     "UsingCompositions.pdf" from there. 
      The package is devoted to the analysis of multiple amounts.
     Amounts have typically non-negative values, and often sum up to
     100% or one. These constraints lead to spurious effects on the
     covariance structure,  as pointed out by Chayes (1960). The
     problem is treated rigorously  in the monography by Aitchison
     (1986),  who characterizes compositions as vectors having a
     relative scale, and identifies its sample space with the D-part
     simplex.  However still (i.e. 2005) most statistical packages do
     not provided any support for this scale. 
      The grounding idea of the package exploits the class concept: 
     the analyst gives the data a compositional or amount class, and
     then all further analysis are (should be) automatically  done in a
     consistent way, e.g. 'x <- acomp(X); plot(x)'  should plot the
     data as a composition (in a ternary diagram)  directly without any
     further interaction of the user.  
      The package provides four different approaches to analyse
     amounts. These approaches are associated to four R-classes,
     representing four different geometries of the sampling space of
     amounts. These geometries depend on two questions: whether the
     total sum of the amounts is a relevant information, and which is
     the meaningful measure of difference of the data. 

     'rplus' : (Real Plus) The total amount matters, and amounts should
     be compared on an absolute basis. i.e. the difference between 1g
     and 2g is the same as the difference between 1kg and 1001g, one
     gram. 
      'aplus' : (Aitchison Plus) The total amount matters, but amounts
     should be compared relatively, i.e. the difference between 1mg and
     2mg is the same as that of 1g and 2g: the double. 
      'acomp' : (Aitchison composition) the total amount is constant 
     (or an artifact of the sampling/measurement procedure), and the
     meaningful  difference is a relative one. This class follows the
     original proposals of Aitchison. 
      'rcomp' : (Real composition) the sum is a constant, and the
     difference in amount from 0% to 1% and from 10% to 11% is regarded
     as equal. This class represents the raw/naive treatment of
     compositions as elements of the real simplex based on an absolute
     geometry. This treatment is implicitly used  in most amalgamation
     problems. However the whole approach suffers from the drawbacks
     and problems discussed in Chayes (1960) and Aitchison (1986). 
      The aim of the package is to provide all the functionality to do
     a consistent analysis in all of these approaches and to make the
     results obtained with different geometries as easy to compare as
     possible.

_A_u_t_h_o_r(_s):

     K.Gerald v.d. Boogaart <URL: http://www.stat.boogaart.de>, Raimon
     Tolosana Delgado, with contributions of Matev Bren

_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

     Chayes, F. (1960). On correlation between variables of constant
     sum. Journal of Geophysical Research 65~(12), 4185-4193.

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

     Pawlowsky-Glahn, V. (2003) Statistical modelling on coordinates.
     In:  Thi{\'o}-Henestrosa, S. and Mart{\'\i}n-Fern{\'a}ndez, J.A.
     (Eds.) _Proceedings of the 1st International Workshop on
     Compositional Data Analysis_, Universitat de Girona, {ISBN}
     84-8458-111-X, <URL: http://ima.udg.es/Activitats/CoDaWork03>

     Mateu-Figueras, G. and Barcel\'o-Vidal, C. (Eds.) _Proceedings of
     the 2nd International Workshop on Compositional Data Analysis_,
     Universitat de Girona, {ISBN} 84-8458-222-1, <URL:
     http://ima.udg.es/Activitats/CoDaWork05>

     van den Boogaart, K.G. and R. Tolosana-Delgado (2007)
     "compositions": a unified  R package to analyze Compositional
     Data, _Computers & Geosciences_.  (in press).

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

     library(compositions)      # load library
     data(SimulatedAmounts)     # load data sa.lognormals
     x <- acomp(sa.lognormals)  # Declare the dataset to be compositional
                                # and use relative geometry
     plot(x)                    # plot.acomp : ternary diagram
     ellipses(mean(x),var(x),r=2,col="red")  # Simplex 2sigma predictive region
     pr <- princomp(x)
     straight(mean(x),pr$Loadings) 

     x <- rcomp(sa.lognormals)  # Declare the dataset to be compositional
                                # and use absolute geometry
     plot(x)                    # plot.acomp : ternary diagram
     ellipses(mean(x),var(x),r=2,col="red")  # Real 2sigma predictive region
     pr <- princomp(x)          
     straight(mean(x),pr$Loadings) 

