ilrBase             package:compositions             R Documentation

_T_h_e _c_a_n_o_n_i_c_a_l _b_a_s_i_s _i_n _t_h_e _c_l_r _p_l_a_n_e _u_s_e_d _f_o_r _i_l_r _a_n_d _i_p_t _t_r_a_n_s_f_o_r_m_s.

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

     Compute the basis of a clr-plane, to use with isometric log-ratio
     or planar transform of a (dataset of) compositions.

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

               ilrBase( x=NULL , z=NULL , D = NULL, method = "basic" )
               gsi.ilrBase(D)
               

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

       x: optional dataset or vector of compositions

       z: optional dataset or vector containing ilr or ipt coordinates

       D: number of parts of the simplex

  method: method to build the basis, one of "basic", "balanced" and
          "optimal"

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

     Method "basic" computes a triangular Helmert matrix (corresponding
     to the original ilr transformation defined by Egozcue et al,
     2003). In this case, 'ilrBase' is a wrapper catching the answers
     of 'gsi.ilrBase' and is to be used as the more convenient
     function.

     Method "balanced" returns an ilr matrix associated with a balanced
     partition, splitting the parts in groups as equal as possible.
     Transforms 'ilr' and 'ipt' computed with this basis are less
     affected by any component (as happens with "basic").

     Method "optimal" is a wrapper to 'gsi.optimalilrBase', providing
     the ilr basis with less influence of missing values. It is
     computed as a hierarchical cluster of variables, with parts
     previously transformed to 1 (if the value is lost) or 0 (if it is
     recorded).

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

     All methods give a matrix containing by columns the basis elements
     for the canonical basis of the clr-plane used for the ilr and ipt
     transform. Only one of the arguments 'x', 'z' or 'D' is needed to
     determine the dimension of the simplex.

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

     Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C.
     Barcel'o-Vidal (2003) Isometric logratio transformations for
     compositional data analysis. _Mathematical Geology_, *35*(3)
     279-300

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

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

     'clr','ilr','ipt'

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

     ilr(c(1,2,3))
     ilrBase(D=2)
     ilrBase(c(1,2,3))
     ilrBase(z= ilr(c(1,2,3)) )
     round(ilrBase(D=7),digits= 3)
     ilrBase(D=7,method="basic")
     ilrBase(D=7,method="balanced")

