Ford               package:exactmaxsel               R Documentation

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

     The function 'Ford' computes the distribution of the maximally
     selected association criterion of interest (either the chi-square
     statistic or the Gini-gain in the current version) when Y is
     binary and X has ordered  values, given 'n0', 'n1' and 'A'. Note
     that X must be AT LEAST ordinally scaled, i.e. continuous
     variables are also allowed as an extreme  special case.

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

     Ford(c, n0, n1, A, statistic)

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

       c: the value at which the distribution function has to be
          computed.

      n0: the number of observations in class Y=0.

      n1: the number of observations in class Y=1.

       A: a vector of length K giving the number of observations with
          X=1,...,X=K. In the special case of a continuous X variable
          taking distinct values in the available sample, 'A' takes the
          form 'A=rep(1,N)', where 'N=n0+n1'.

statistic: the association measure used as criterion to select the best
          split. Currently, only 'statistic="chi2"' (chi-square
          statistic) and 'statistic="gini"' (the Gini-gain from machine
          learning) are implemented.

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

     Suppose the response Y is binary (Y=0,1) and the predictor X has K
     ordered categorical values (X=1,...,K). The criterion is maximized
     over all the binary splittings of the set {1,...,K} that preserve
     the ordering.  For K=3, the criterion is thus maximized  over the
     splittings {1,2}{3} and {1}{2,3}. Note that X may also be a
     substantially continuous variable that is observed at a discrete
     scale and thus has ties.

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

     the value of the distribution function at 'c'.

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

     Anne-Laure Boulesteix (<URL:
     http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/>)

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

     A.-L. Boulesteix (2006), Maximally selected chi-square statistics
     for ordinal variables, Biometrical Journal 48:451-462.

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

     'Fcat', 'Ford2', 'maxsel'.

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

     # load exactmaxsel library
     library(exactmaxsel)

     Ford(c=4,n0=15,n1=10,A=c(6,10,9),statistic="chi2")
     Ford(c=0.02,n0=15,n1=15,A=c(5,8,7,10),statistic="gini")

