Fcat               package:exactmaxsel               R Documentation

_D_i_s_t_r_i_b_u_t_i_o_n _o_f _m_a_x_i_m_a_l_l_y _s_e_l_e_c_t_e_d _s_t_a_t_i_s_t_i_c_s _f_o_r _m_u_l_t_i_c_a_t_e_g_o_r_i_c_a_l _v_a_r_i_a_b_l_e_s

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

     The function 'Fcat' 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 unordered  categorical values, given 'n0', 'n1'
     and 'A'.

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

     Fcat(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.

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
     unordered categorical values (X=1,...,K). The criterion is
     maximized over all the binary splittings of the set {1,...,K}. 
     For example, if K=4, the criterion is thus maximized over the
     splittings {1}{2,3,4}, {1,2}{3,4},  {1,2,3}{4}, {1,2,4}{3},
     {1,4}{2,3}, {1,3,4}{2}, {1,3}{2,4}.

_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
     and binary splits of nominal variables, Biometrical Journal
     48:838-848.

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

     'Ford', 'Ford2', 'maxsel'.

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

     # load exactmaxsel library
     library(exactmaxsel)

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

