npplregbw  R Documentation 
npplregbw
computes a bandwidth object for a partially linear
kernel regression estimate of a one (1) dimensional dependent variable
on p+q
variate explanatory data, using the model Y = X\beta
+ \Theta (Z) + \epsilon
given a set of
estimation points, training points (consisting of explanatory data and
dependent data), and a bandwidth specification, which can be a
rbandwidth
object, or a bandwidth vector, bandwidth type and
kernel type.
npplregbw(...)
## S3 method for class 'formula'
npplregbw(formula, data, subset, na.action, call, ...)
## S3 method for class 'NULL'
npplregbw(xdat = stop("invoked without data `xdat'"),
ydat = stop("invoked without data `ydat'"),
zdat = stop("invoked without data `zdat'"),
bws,
...)
## Default S3 method:
npplregbw(xdat = stop("invoked without data `xdat'"),
ydat = stop("invoked without data `ydat'"),
zdat = stop("invoked without data `zdat'"),
bws,
...,
bandwidth.compute = TRUE,
nmulti,
remin,
itmax,
ftol,
tol,
small)
## S3 method for class 'plbandwidth'
npplregbw(xdat = stop("invoked without data `xdat'"),
ydat = stop("invoked without data `ydat'"),
zdat = stop("invoked without data `zdat'"),
bws,
nmulti,
...)
formula 
a symbolic description of variables on which bandwidth selection is to be performed. The details of constructing a formula are described below. 
data 
an optional data frame, list or environment (or object
coercible to a data frame by 
subset 
an optional vector specifying a subset of observations to be used in the fitting process. 
na.action 
a function which indicates what should happen when the data contain

call 
the original function call. This is passed internally by

xdat 
a 
ydat 
a one (1) dimensional numeric or integer vector of dependent data, each
element 
zdat 
a 
bws 
a bandwidth specification. This can be set as a If left unspecified, 
... 
additional arguments supplied to specify the regression type,
bandwidth type, kernel types, selection methods, and so on. To do
this, you may specify any of 
bandwidth.compute 
a logical value which specifies whether to do a numerical search for
bandwidths or not. If set to 
nmulti 
integer number of times to restart the process of finding extrema of
the crossvalidation function from different (random) initial
points. Defaults to 
remin 
a logical value which when set as 
itmax 
integer number of iterations before failure in the numerical
optimization routine. Defaults to 
ftol 
tolerance on the value of the crossvalidation function
evaluated at located minima. Defaults to 
tol 
tolerance on the position of located minima of the
crossvalidation function. Defaults to 
small 
a small number, at about the precision of the data type
used. Defaults to 
npplregbw
implements a variety of methods for nonparametric
regression on multivariate (q
variate) explanatory data defined
over a set of possibly continuous and/or discrete (unordered, ordered)
data. The approach is based on Li and Racine (2003), who employ
‘generalized product kernels’ that admit a mix of continuous and
discrete data types.
Three classes of kernel estimators for the continuous data types are
available: fixed, adaptive nearestneighbor, and generalized
nearestneighbor. Adaptive nearestneighbor bandwidths change with
each sample realization in the set, x_i
, when estimating the
density at the point x
. Generalized nearestneighbor bandwidths change
with the point at which the density is estimated, x
. Fixed bandwidths
are constant over the support of x
.
npplregbw
may be invoked either with a formulalike
symbolic
description of variables on which bandwidth selection is to be
performed or through a simpler interface whereby data is passed
directly to the function via the xdat
, ydat
, and
zdat
parameters. Use of these two interfaces is mutually exclusive.
Data contained in the data frame zdat
may be a mix of continuous
(default), unordered discrete (to be specified in the data frame
zdat
using factor
), and ordered discrete (to be
specified in the data frame zdat
using
ordered
). Data can be entered in an arbitrary order and
data types will be detected automatically by the routine (see
np
for details).
Data for which bandwidths are to be estimated may be specified
symbolically. A typical description has the form dependent
data
~
parametric
explanatory
data

nonparametric
explanatory
data
,
where dependent
data
is a univariate response, and
parametric
explanatory
data
and
nonparametric
explanatory
data
are both series of variables specified by name, separated by
the separation character '+'. For example, y1 ~ x1 + x2  z1
specifies that the bandwidth object for the partially linear model with
response y1
, linear parametric regressors x1
and
x2
, and
nonparametric regressor z1
is to be estimated. See below for
further examples.
A variety of kernels may be specified by the user. Kernels implemented for continuous data types include the second, fourth, sixth, and eighth order Gaussian and Epanechnikov kernels, and the uniform kernel. Unordered discrete data types use a variation on Aitchison and Aitken's (1976) kernel, while ordered data types use a variation of the Wang and van Ryzin (1981) kernel.
if bwtype
is set to fixed
, an object containing bandwidths
(or scale factors if bwscaling = TRUE
) is returned. If it is set to
generalized_nn
or adaptive_nn
, then instead the k
th nearest
neighbors are returned for the continuous variables while the discrete
kernel bandwidths are returned for the discrete variables. Bandwidths
are stored in a list under the component name bw
. Each element
is an rbandwidth
object. The first
element of the list corresponds to the regression of Y
on Z
.
Each subsequent element is the bandwidth object corresponding to the
regression of the i
th column of X
on Z
. See examples
for more information.
If you are using data of mixed types, then it is advisable to use the
data.frame
function to construct your input data and not
cbind
, since cbind
will typically not work as
intended on mixed data types and will coerce the data to the same
type.
Caution: multivariate datadriven bandwidth selection methods are, by
their nature, computationally intensive. Virtually all methods
require dropping the i
th observation from the data set, computing an
object, repeating this for all observations in the sample, then
averaging each of these leaveoneout estimates for a given
value of the bandwidth vector, and only then repeating this a large
number of times in order to conduct multivariate numerical
minimization/maximization. Furthermore, due to the potential for local
minima/maxima, restarting this procedure a large number of times may
often be necessary. This can be frustrating for users possessing
large datasets. For exploratory purposes, you may wish to override the
default search tolerances, say, setting ftol=.01 and tol=.01 and
conduct multistarting (the default is to restart min(5, ncol(zdat))
times) as is done for a number of examples. Once the procedure
terminates, you can restart search with default tolerances using those
bandwidths obtained from the less rigorous search (i.e., set
bws=bw
on subsequent calls to this routine where bw
is
the initial bandwidth object). A version of this package using the
Rmpi
wrapper is under development that allows one to deploy
this software in a clustered computing environment to facilitate
computation involving large datasets.
Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca
Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413420.
Gao, Q. and L. Liu and J.S. Racine (2015), “A partially linear kernel estimator for categorical data,” Econometric Reviews, 34 (610), 958977.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Li, Q. and J.S. Racine (2004), “Crossvalidated local linear nonparametric regression,” Statistica Sinica, 14, 485512.
Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.
Racine, J.S. and Q. Li (2004), “Nonparametric estimation of regression functions with both categorical and continuous data,” Journal of Econometrics, 119, 99130.
Robinson, P.M. (1988), “Rootnconsistent semiparametric regression,” Econometrica, 56, 931954.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301309.
npregbw
, npreg
## Not run:
# EXAMPLE 1 (INTERFACE=FORMULA): For this example, we simulate an
# example for a partially linear model and perform bandwidth selection
set.seed(42)
n < 250
x1 < rnorm(n)
x2 < rbinom(n, 1, .5)
z1 < rbinom(n, 1, .5)
z2 < rnorm(n)
y < 1 + x1 + x2 + z1 + sin(z2) + rnorm(n)
X < data.frame(x1, factor(x2))
Z < data.frame(factor(z1), z2)
# Compute datadriven bandwidths... this may take a minute or two
# depending on the speed of your computer...
bw < npplregbw(formula=y~x1+factor(x2)factor(z1)+z2)
summary(bw)
# Note  the default is to use the local constant estimator. If you wish
# to use instead a local linear estimator, this is accomplished via
# npplregbw(xdat=X, zdat=Z, ydat=y, regtype="ll")
# Note  see the example for npudensbw() for multiple illustrations
# of how to change the kernel function, kernel order, and so forth.
# You may want to manually specify your bandwidths
bw.mat < matrix(data = c(0.19, 0.34, # y on Z
0.00, 0.74, # X[,1] on Z
0.29, 0.23), # X[,2] on Z
ncol = ncol(Z), byrow=TRUE)
bw < npplregbw(formula=y~x1+factor(x2)factor(z1)+z2,
bws=bw.mat, bandwidth.compute=FALSE)
summary(bw)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# You may want to tweak some of the bandwidths
bw$bw[[1]] # y on Z, alternatively bw$bw$yzbw
bw$bw[[1]]$bw < c(0.17, 0.30)
bw$bw[[2]] # X[,1] on Z
bw$bw[[2]]$bw[1] < 0.00054
summary(bw)
# EXAMPLE 1 (INTERFACE=DATA FRAME): For this example, we simulate an
# example for a partially linear model and perform bandwidth selection
set.seed(42)
n < 250
x1 < rnorm(n)
x2 < rbinom(n, 1, .5)
z1 < rbinom(n, 1, .5)
z2 < rnorm(n)
y < 1 + x1 + x2 + z1 + sin(z2) + rnorm(n)
X < data.frame(x1, factor(x2))
Z < data.frame(factor(z1), z2)
# Compute datadriven bandwidths... this may take a minute or two
# depending on the speed of your computer...
bw < npplregbw(xdat=X, zdat=Z, ydat=y)
summary(bw)
# Note  the default is to use the local constant estimator. If you wish
# to use instead a local linear estimator, this is accomplished via
# npplregbw(xdat=X, zdat=Z, ydat=y, regtype="ll")
# Note  see the example for npudensbw() for multiple illustrations
# of how to change the kernel function, kernel order, and so forth.
# You may want to manually specify your bandwidths
bw.mat < matrix(data = c(0.19, 0.34, # y on Z
0.00, 0.74, # X[,1] on Z
0.29, 0.23), # X[,2] on Z
ncol = ncol(Z), byrow=TRUE)
bw < npplregbw(xdat=X, zdat=Z, ydat=y,
bws=bw.mat, bandwidth.compute=FALSE)
summary(bw)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# You may want to tweak some of the bandwidths
bw$bw[[1]] # y on Z, alternatively bw$bw$yzbw
bw$bw[[1]]$bw < c(0.17, 0.30)
bw$bw[[2]] # X[,1] on Z
bw$bw[[2]]$bw[1] < 0.00054
summary(bw)
## End(Not run)
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