slda                  package:ipred                  R Documentation

_S_t_a_b_i_l_i_s_e_d _L_i_n_e_a_r _D_i_s_c_r_i_m_i_n_a_n_t _A_n_a_l_y_s_i_s

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

     Linear discriminant analysis based on left-spherically 
     distributed linear scores.

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

     ## S3 method for class 'formula':
     slda(formula, data, subset, na.action=na.rpart, ...)
     ## S3 method for class 'factor':
     slda(y, X, q=NULL, ...)

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

       y: the response variable: a factor vector of class labels.

       X: a data frame of predictor variables.

       q: the number of positive eigenvalues the scores are derived
          from, see below.

 formula: a formula of the form 'lhs ~ rhs' where 'lhs'  is the
          response variable and 'rhs' a set of predictors.

    data: optional data frame containing the variables in the model
          formula.

  subset: optional vector specifying a subset of observations to be
          used.

na.action: function which indicates what should happen when the data
          contain 'NA's.  Defaults to 'na.rpart'.

     ...: additional parameters passed to 'lda'.

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

     This function implements the LDA for q-dimensional linear scores
     of the original p predictors derived from the PC_q rule by Laeuter
     et al. (1998). Based on the product sum matrix 

                   W = (X - bar{X})^top(X - bar{X})

     the eigenvalue problem WD = diag(W)DL is solved. The first q
     columns D_q of D are used as a weight matrix for the  original p
     predictors: XD_q. By default, q is the number of eigenvalues
     greater one. The q-dimensional linear scores are left-spherically
     distributed and are used as predictors for a classical  LDA. 

     This form of reduction of the dimensionality was  developed for
     discriminant analysis problems by Laeuter (1992) and was used for
     multivariate tests by Laeuter et al. (1998), Kropf (2000) gives an
     overview. For details on left-spherically distributions see Fang
     and  Zhang (1990).

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

     An object of class 'slda', a list with components 

  scores: the weight matrix.

   mylda: an object of class 'lda'.

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

     Torsten.Hothorn <Torsten.Hothorn@rzmail.uni-erlangen.de>

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

     Fang Kai-Tai and Zhang Yao-Ting (1990), _Generalized Multivariate
     Analysis_, Springer, Berlin.

     Siegfried Kropf (2000), _Hochdimensionale multivariate Verfahren
     in der medizinischen Statistik_, Shaker Verlag, Aachen (in
     german).

     Juergen Laeuter (1992), _Stabile multivariate Verfahren_, Akademie
     Verlag, Berlin (in german).

     Juergen Laeuter, Ekkehard Glimm and Siegfried Kropf (1998),
     Multivariate Tests Based on Left-Spherically Distributed Linear
     Scores. _The Annals of Statistics_, *26*(5) 1972-1988.

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

     'predict.slda'

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

     learn <- as.data.frame(mlbench.twonorm(100))
     test <- as.data.frame(mlbench.twonorm(1000))

     mlda <- lda(classes ~ ., data=learn)
     mslda <- slda(classes ~ ., data=learn)

     print(mean(predict(mlda, newdata=test)$class != test$classes))
     print(mean(predict(mslda, newdata=test)$class != test$classes))

