pcaiv                  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 _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
     instrumental variables.

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

     pcaiv(dudi, df, scannf = TRUE, nf = 2)
     plot.pcaiv (x, xax = 1, yax = 2, ...) 
     print.pcaiv (x, ...) 

_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

       x: an object of class 'pcaiv'

     xax: the column number for the x-axis

     yax: the column number for the y-axis

     ...: further arguments passed to or from other methods

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

     returns an object of class 'pcaiv', 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 axes of 'dudi$tab' on PPA

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

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

      fa: a data frame with the loadings (Constraint Principal
          Components as linear combinations of X

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

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

     cor: a data frame with the correlations between the CPC and X 

_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.

      Obadia, J. (1978) L'analyse en composantes explicatives. _Revue
     de Statistique Applique_, *24*, 5-28.

      Lebreton, J. D., Sabatier, R., Banco G. and  Bacou A. M. (1991)
     Principal component and correspondence analyses with respect to
     instrumental variables : an overview of their role in studies of
     structure-activity and species- environment relationships. In J.
     Devillers and W. Karcher, editors. _Applied Multivariate Analysis
     in SAR and Environmental Studies_, Kluwer Academic Publishers,
     85-114

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

     data(rhone)
     pca1 <- dudi.pca(rhone$tab, scan = FALSE, nf = 3)
     iv1 <- pcaiv(pca1, rhone$disch, scan = FALSE)
     iv1
     # iner inercum inerC inercumC ratio R2    lambda
     # 6.27 6.27    5.52  5.52     0.879 0.671 3.7   
     # 4.14 10.4    4.74  10.3     0.984 0.747 3.54  
     plot(iv1)

