pcaivortho               package:ade4               R Documentation

_P_r_i_n_c_i_p_a_l _C_o_m_p_o_n_e_n_t _A_n_a_l_y_s_i_s _w_i_t_h _r_e_s_p_e_c_t _t_o _o_r_t_h_o_g_o_n_a_l _i_n_s_t_r_u_m_e_n_t_a_l _v_a_r_i_a_b_l_e_s

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

     performs a Principal Component Analysis with respect to orthogonal
     instrumental variables.

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

     pcaivortho(dudi, df, scannf = TRUE, nf = 2)

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

    dudi: a duality diagram, object of class 'dudi'

      df: a data frame with the same rows

  scannf: a logical value indicating whether the eigenvalues bar plot
          should be displayed

      nf: if scannf FALSE, an integer indicating the number of kept
          axes

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

     an object of class 'pcaivortho' sub-class of class 'dudi' 

    rank: an integer indicating the rank of the studied matrix

      nf: an integer indicating the number of kept axes

     eig: a vector with the all eigenvalues

      lw: a numeric vector with the row weigths (from 'dudi')

      cw: a numeric vector with the column weigths (from 'dudi')

       Y: a data frame with the dependant variables

       X: a data frame with the explanatory variables

     tab: a data frame with the modified array (projected variables)

      c1: a data frame with the Pseudo Principal Axes (PPA)

      as: a data frame with the Principal axis of 'dudi$tab' on PAP

      ls: a data frame with the projection of lines of 'dudi$tab' on
          PPA

      li: a data frame 'dudi$ls' with the predicted values by X

      l1: a data frame with the Constraint Principal Components (CPC)

      co: a data frame with the inner product between the CPC and Y

   param: a data frame containing a summary

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

     Daniel Chessel chessel@biomserv.univ-lyon1.fr

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

     Rao, C. R. (1964) The use and interpretation of principal
     component analysis in applied research. _Sankhya_, *A 26*,
     329-359.

      Sabatier, R., Lebreton J. D. and Chessel D. (1989) Principal
     component analysis with instrumental variables as a tool for
     modelling composition data. In R. Coppi and S. Bolasco, editors.
     _Multiway data analysis_, Elsevier Science Publishers B.V.,
     North-Holland, 341-352

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

     ## Not run: 
     par(mfrow = c(2,2))
     data(avimedi)
     cla <- avimedi$plan$reg:avimedi$plan$str

     # simple ordination
     coa1 <- dudi.coa(avimedi$fau, scan = FALSE, nf = 3)
     s.class(coa1$li, cla, sub = "Sans contrainte")

     # within region
     w1 <- within(coa1, avimedi$plan$reg, scan = FALSE)
     s.match(w1$li, w1$ls, clab = 0, sub = "Intra Rgion")
     s.class(w1$li, cla, add.plot = TRUE)

     # no region the same result
     pcaivnonA <- pcaivortho(coa1, avimedi$plan$reg, scan = FALSE)
     s.match(pcaivnonA$li, pcaivnonA$ls, clab = 0, 
         sub = "Contrainte Non A")
     s.class(pcaivnonA$li, cla, add.plot = TRUE)

     # region + strate
     interAplusB <- pcaiv(coa1, avimedi$plan, scan = FALSE)
     s.match(interAplusB$li, interAplusB$ls, clab = 0, 
         sub = "Contrainte A + B")
     s.class(interAplusB$li, cla, add.plot = TRUE)

     par(mfrow = c(1,1))## End(Not run)

