modalreg               package:hdrcde               R Documentation

_N_o_n_p_a_r_a_m_e_t_r_i_c _M_u_l_t_i_m_o_d_a_l  _R_e_g_r_e_s_s_i_o_n

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

     Nonparametric multi-valued regression based on the modes of
     conditional density estimates.

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

     modalreg(x, y, xfix=seq(min(x),max(x),l=50), a, b, deg = 0, iter = 30, P = 2,
         start = "e", prun = TRUE, prun.const = 10, plot.type = c("p", 1),
         labels = c("", "x", "y"), pch=20, ...)

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

       x: Numerical vector: the conditioning variable.

       y: Numerical vector: the response variable.

    xfix: Numerical vector corresponding to the input values of which
          the fitted values shall be calculated.

       a: Optional bandwidth in x-direction.

       b: Optional bandwidth in y-direction. 

     deg: Degree of local polynomial used in estimation (0 or 1).

    iter: Positive integer giving the number of mean shift iterations
          per point and branch.

       P: Maximal number of branches.

   start: Character determining how the starting points are selected.
          '"q"': proportional to quantiles; '"e"': equidistant; '"r"':
          random. All, '"q"', '"e"', and '"r"', give starting points
          which are constant over 'x'. As an alternative, the choice
          '"v"' gives variable starting points, which are equal to
          '"q"' for the smallest 'x', and equal to the previously
          fitted values for all subsequent 'x'. 

    prun: Boolean. If TRUE, parts of branches are dismissed (in the
          plotted output) where their associated kernel density value
          falls below the threshold
          '1/(prun.const*(max(x)-min(x))*(max(y)-min(y)))'. 

prun.const: Numerical value giving the constant used above (the higher,
          the less pruning)

plot.type: Vector with two elements. The first one is character-valued,
          with possible values '"p"',  '"l"', and '"n"'.  If equal to
          '"n"', no plotted output is given at all. If equal to '"p"',
          fitted curves are symbolized as points in the graphical
          output, otherwise as lines.  The  second vector component is
          a numerical value either being 0 or 1. If 1, the position of
          the starting points is depicted in the plot, otherwise
          omitted.

  labels: Vector of three character strings. The first one is the
          "main" title of the graphical output, the second one is the
          label of the x axis, and the third one the label of the y
          axis.

     pch: Plotting character. The default corresponds to small bullets.

     ...: Other arguments passed to 'cde.bandwidths'.

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

     Computes multi-modal nonparametric regression curves based on the
     maxima of conditional density estimates. The tool for the
     estimation is the conditional mean shift as outlined in Einbeck
     and Tutz (2006). Estimates of the conditional modes might
     fluctuate highly if 'deg=1'. Hence, 'deg=0'  is  recommended. For
     bandwidth selection, the hybrid rule introduced by Bashtannyk and
     Hyndman (2001) is employed if 'deg=0'. This corresponds to the
     setting 'method=1' in function 'cde.bandwidths'. For 'deg=1'
     automatic  bandwidth selection is not supported.

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

     A list with the following components: 

    xfix: Grid of predictor values at which the fitted values are
          calculated.

fitted.values: A '[P x length(xfix)]'- matrix with fitted j-th branch
          in the j-th row (1 <=j <=P) 

bandwidths: A vector with bandwidths 'a' and 'b'.

 density: A '[P x length(xfix)]'- matrix with estimated kernel
          densities. This will only be computed if 'prun=TRUE'.

threshold: The pruning threshold.

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

     Jochen Einbeck (2007)

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

     Einbeck, J., and Tutz, G. (2006) "Modelling beyond regression
     functions: an application of multimodal regression to speed-flow
     data". _Journal of the Royal Statistical Society, Series C
     (Applied Statistics)_, *55*, 461-475.

     Bashtannyk, D.M., and Hyndman, R.J. (2001) "Bandwidth selection
     for kernel conditional density estimation". _Computational
     Statistics and Data Analysis_, *36*(3), 279-298.

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

     'cde.bandwidths'

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

       lane2.fit <- modalreg(lane2$flow, lane2$speed, xfix=(1:55)*40, a=100, b=4)

