Nonparametric multi-valued regression based on the modes of conditional density estimates.
Usage
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, ...)
Arguments
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.
Details
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.
Value
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.
Author(s)
Jochen Einbeck (2007)
References
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.