aplus              package:compositions              R Documentation

_A_m_o_u_n_t_s _a_n_a_l_y_s_e_d _i_n _l_o_g-_s_c_a_l_e

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

     A class to analyse positive amounts in a logistic framework.

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

               aplus(X,parts=1:NCOL(oneOrDataset(X)),total=NA,warn.na=FALSE,detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL)
               

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

       X: vector or dataset of positive numbers

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

   total: a numeric vectors giving the total amounts of each dataset. 

 warn.na: should the user be warned in case of NA,NaN or 0 coding
          different types of missing values?

detectionlimit: a number, vector or matrix of positive numbers giving
          the detection limit of all values, all columns or each value,
          respectively

     BDL: the code for 'Below Detection Limit' in X

      SZ: the code for 'Structural Zero' in X

     MAR: the code for 'Missing At Random' in X

    MNAR: the code for 'Missing Not At Random' in X

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

     Many multivariate datasets essentially describe amounts of D
     different parts in a whole. When the whole is large in relation to
     the considered parts, such that they do not exclude each other, or
     when the total amount of each componenten is indeed determined by
     the phenomenon under investigation and not by sampling artifacts
     (such as dilution or sample preparation), then the parts can be
     treated as amounts rather than as a composition (cf. 'acomp',
     'rcomp'). 
      Like compositions, amounts have some important properties.
     Amounts are always positive. An amount of exactly zero essentially
     means that we have a substance of another quality. Different
     amounts - spanning different orders of magnitude  -  are often
     given in different units (ppm, ppb, g/l, vol.%, mass %, molar
     fraction). Often, these amounts are also taken as indicators of
     other non-measured components (e.g. K as indicator for potassium
     feldspar), which might be proportional to the measured amount. 
     However, in contrast to compositions, amounts themselves do
     matter. Amounts are typically heavily skewed and in many practical
     cases a log-transform makes their distribution roughly symmetric,
     even normal. 
      In full analogy to Aitchison's compositions, vector space
     operations are introduced for amounts: the perturbation
     'perturbe.aplus' as a vector space addition (corresponding to
     change of units), the power transformation 'power.aplus' as scalar
     multiplication describing the law of mass action, and a distance
     'dist' which is independent of the chosen units. The induced
     vector space is mapped isometrically to a classical R^D by a
     simple log-transformation called 'ilt', resembling classical log
     transform approaches.   
      The general approach in analysing aplus objects is thus to
     perform classical multivariate analysis on ilt-transformed
     coordinates (i.e., logs) and to backtransform or display the
     results in such a way that they can be interpreted in terms of the
     original amounts.    
      The class aplus is complemented by the 'rplus', allowing to
     analyse amounts directly as real numbers, and by the classes
     'acomp' and 'rcomp' to analyse the same data as compositions
     disregarding the total amounts, focusing on relative weights only. 
      The classes rcomp, acomp, aplus, and rplus are designed as
     similar as possible in order to allow direct comparison between
     results achieved   by the different approaches. Especially the
     acomp simplex transforms 'clr', 'alr', 'ilr' are mirrored in the
     aplus class by the single bijective isometric transform 'ilt'

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

     a vector of class '"aplus"' representing a vector of amounts or a
     matrix of class '"aplus"' representing multiple vectors of
     amounts, each vector in one row.

_M_i_s_s_i_n_g _P_o_l_i_c_y:

     The policy of treatment of zeroes, missing values and values 
     below detecion limit is explained in depth in
     compositions.missing.

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

     Raimon Tolosana-Delgado, K.Gerald v.d. Boogaart <URL:
     http://www.stat.boogaart.de>

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

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

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

     'ilt','acomp', 'rplus', 'princomp.aplus',  'plot.aplus',
     'boxplot.aplus', 'barplot.aplus', 'mean.aplus', 'var.aplus',
     'variation.aplus', 'cov.aplus', 'msd'

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

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

