clr               package:compositions               R Documentation

_C_e_n_t_e_r_e_d _l_o_g _r_a_t_i_o _t_r_a_n_s_f_o_r_m

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

     Compute the centered log ratio transform of a (dataset of)
     composition(s) and its inverse.

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

               clr( x,... )
               clr.inv( z,... )
               

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

       x: a composition or a data matrix of compositions, not
          necessarily closed

       z: the clr-transform of a composition or a data matrix of
          clr-transforms of compositions, not necessarily centered
          (i.e. summing up to zero)

     ...: for generic use only

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

     The clr-transform maps a composition in the D-part
     Aitchison-simplex isometrically to a D-dimensonal euclidian vector
     subspace: consequently, the transformation is not injective. Thus
     resulting covariance matrices are always singular.  
       The data can then be analysed in this transformation by all
     classical multivariate analysis tools not relying on a full rank
     of the covariance. See 'ilr' and 'alr' for alternatives. The
     interpretation of the results is relatively easy since the
     relation between each original part and a transformed variable is
     preserved. 
        The centered logratio transform is given by

 clr(x) := (_ln_ *x* - mean(_ln_ *x]) ) * The image of the 'clr' is a vector with entries summing to 0. This hyperplane is also called the clr-plane.

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

     'clr' gives the centered log ratio transform, 'clr.inv' gives
     closed compositions with the given clr-transform

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

     K.Gerald v.d. Boogaart <URL: http://www.stat.boogaart.de>

_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.

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

     'ilr','alr','apt'

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

     (tmp <- clr(c(1,2,3)))
     clr.inv(tmp)
     clr.inv(tmp) - clo(c(1,2,3)) # 0
     data(Hydrochem)
     cdata <- Hydrochem[,6:19]
     pairs(clr(cdata)) 

