linregEst          package:ffmanova          R Documentation(latin1)

_L_i_n_e_a_r _r_e_g_r_e_s_s_i_o_n _e_s_t_i_m_a_t_i_o_n

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

     Function that performs multivariate multiple linear regression 
     modelling (Y = XB + E) according to a principal component
     regression (PCR) approach where the number of components equals
     the number of nonzero  eigenvalues (generalised inverse).

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

     linregEst(X, Y)
     linregStart(X, rank_lim = 1e-9)
     linregEnd(Umodel, Y)

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

       X: regressor matrix

       Y: response matrix

rank_lim: tuning parameter for the rank. The default value corresponds
          to the rank function in Matlab.

  Umodel: this matrix is returned by 'linregStart'

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

     The function 'linregEst' performs the calculations in two steps by
     calling 'linregStart' and 'linregEnd'. The former functions
     function makes all calculations that can be done without knowing
     Y. The singular value decomposition (SVD) is an essential part of
     the calculations and some of the output variables are named
     according to SVD ('U', 'S' and 'V').

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

     'linregEst' returns a list with seven components. The first three
     components is returned by 'linregStart' - the rest by 'linregEnd'.

  Umodel: Matrix of score values according to the PCR model.

VmodelDivS: Matrix that can be used to calculate 'Umodel'  from 'X'.
          That is, 'Umodel' equals 'X %*% VmodelDivS'.

VextraDivS1: Matrix that can be used to check estimability. That is,
          predictions for a new X cannot be made if 'Xnew %*%
          VextraDivS1' is (close to) zero.

   BetaU: Matrix of regression parameters according to the PCR model.

 msError: Mean square error of each response

errorObs: Error observations that can be used in multivariate testing

    Yhat: Fitted values. Equals 'Umodel %*% BetaU' 

_N_o_t_e:

     When the number of error degrees of freedom exceeds the number of
     linearly independent responses, then the matrix of error
     observations is made so that several rows are zero. In this case
     the zero rows are omitted and a list with components 'errorObs'
     and 'df_error' is returned.

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

     yvind Langsrud and Bjrn-Helge Mevik

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

     'ffmanova'

