homals                package:homals                R Documentation

_H_o_m_o_g_e_n_e_i_t_y _A_n_a_l_y_s_i_s

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

     This function performs a homogeneity analysis, aka a multiple
     correspondence analysis, but with many additional options.
     Variables can be grouped into sets, in order to emulate regression
     analysis and canonical analysis. For each variable there are, in
     addition, rank constraints on the category quantifications (or
     transformations) and level constraints (which allows one to treat
     a variable as nominal, ordinal, or numerical).

     The general idea of homogeneity analysis is to make a joint plot
     in p-space of all objects (or individuals) and the categories of
     all variables. In this plot we connect objects with the categories
     they are in, thus producing a graph plot. If there are m
     variables, then m lines depart from each object, and with n object
     the graph plot has nm lines. The technique, in its most simple
     form, makes the graph plot in such a way that the sum of squares
     of the length of the nm lines is a small as possible, subject to a
     normalization of the object scores (their n x p coordinate matrix
     must be orthonormal).

     Rank constraints require the category quantifications of the
     categories of a variable to lie in a subspace of p-space.
     Requiring rank equal to one for all variables reduces homogeneity
     analysis to principal component analysis (with optimal scaling of
     the variables). 

     Sets of variables are incorporated by using additivity
     restrictions on the category quantifications (i.e. we code the
     variables within a set interactively, but then use quantifications
     based on main effects only). 

     By combining the various types of restrictions we obtain
     far-reaching generalizations of principal component analysis,
     canonical analysis, discriminant analysis and regression analysis.

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

     homals(data, sets=0, ndim=2, active=T, rank=ndim, level="NO", starplots = FALSE,
     catplots =  FALSE, trfplots =  FALSE, lossplots =  FALSE, hullplots = FALSE, 
     spanplots = FALSE, graphplot =  FALSE, objplot =  FALSE, objscores =  FALSE,
     objlabel =  FALSE, offset =  1.20, eps1 =  -Inf, eps2 =  1e-6, itermax =  100,
     voronoi =  FALSE, saveMe =  FALSE, demo =  FALSE , timer =  FALSE , tk = FALSE,
     img1, img2, img3, name)

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

    data: data (in data-frame)

    sets: list of vectors of indices

    ndim: dimensionality (default 2)

  active: which variables are active (single T means all)

    rank: which quantification ranks (default all p)

   level: which quantification levels NO (nominal), OR (orthogonal)
          (default all nominal)

starplots: which starplots, default is none (FALSE)

catplots: which category plots, default is none (FALSE)

trfplots: which transformation plots, default is none (FALSE)

lossplots: which loss plots, default is none (FALSE)

hullplots: which hullplots, default is none (FALSE)

spanplots: which spanning tree plots, default is none (FALSE)

graphplot: graphplot, default is no (FALSE)

 objplot: object score plot, default is no (FALSE)

objscores: object scores written to file, default is no (FALSE)

objlabel: object score plot labeled, default is no (FALSE)

  offset: offset for labeled plots, default is 1.20

    eps1: iteration precision eigenvalues, default is -Inf

    eps2: iteration precision eigenvectors, default is 1e-6

 itermax: maximum number of iterations, default is 100

 voronoi: voronoi diagram, default is no (FALSE)

  saveMe: do we return the results, default is no (FALSE)

    demo: animated iteration demo, default is no (FALSE)

   timer: time the steps of program, default is no (FALSE)

      tk: create tk output, default is no (FALSE), used by 'tkhomals'

    img1: tkrplot image placeholder, used by 'tkhomals'

    img2: tkrplot image placeholder, used by 'tkhomals'

    img3: tkrplot image placeholder, used by 'tkhomals'

    name: dataframe name, used by 'tkhomals'

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

     This functions requires data to be stored in a data-frame. It can
     produce a variety of graphs which are stored in a pdf file.
     Results are stored in an ascii file.

_N_o_t_e:

     Needs to be executed from a writeable directory. File names are
     determined by the name of the data argument passed to the
     function.

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

     Jan de Leeuw

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

     ## produce graphplot and objplot for data set mammals,
     ## results are save into an ascii file "mammals.out"
     ## all graphs are is saved into a pdf file named "mammals.pdf"
     ## Don't run: data(mammals)
     ## Don't run: homals(mammals, graphplot = TRUE, objplot = TRUE)

