
npreg
computes a kernel regression estimate of a one
(1) dimensional dependent variable on rbandwidth
object, or a
bandwidth vector, bandwidth type and kernel type.
npreg(bws, …)# S3 method for formula
npreg(bws, data = NULL, newdata = NULL, y.eval =
FALSE, …)
# S3 method for call
npreg(bws, …)
# S3 method for default
npreg(bws, txdat, tydat, …)
# S3 method for rbandwidth
npreg(bws,
txdat = stop("training data 'txdat' missing"),
tydat = stop("training data 'tydat' missing"),
exdat,
eydat,
gradients = FALSE,
residuals = FALSE,
…)
a bandwidth specification. This can be set as a rbandwidth
object returned from an invocation of npregbw
, or
as a vector of bandwidths, with each element txdat
. If specified as
a vector, then additional arguments will need to be supplied as
necessary to specify the bandwidth type, kernel types, and so on.
additional arguments supplied to specify the regression type, bandwidth type, kernel types, training data, and so on, detailed below.
an optional data frame, list or environment (or object
coercible to a data frame by as.data.frame
) containing the variables
in the model. If not found in data, the variables are taken from
environment(bws)
, typically the environment from which
npregbw
was called.
An optional data frame in which to look for evaluation data. If omitted, the training data are used.
If newdata
contains dependent data and y.eval = TRUE
,
np
will compute goodness of fit statistics on these
data and return them. Defaults to FALSE
.
a
a one (1) dimensional numeric or integer vector of dependent data, each
element txdat
. Defaults to the training data used to
compute the bandwidth object.
a txdat
.
a one (1) dimensional numeric or integer vector of the true values of the dependent variable. Optional, and used only to calculate the true errors.
a logical value indicating that you want gradients computed and
returned in the resulting npregression
object. Defaults to
FALSE
.
a logical value indicating that you want residuals computed and
returned in the resulting npregression
object. Defaults to
FALSE
.
npreg
returns a npregression
object.
The generic
functions fitted
, residuals
,
se
, predict
, and
gradients
, extract (or generate) estimated values,
residuals, asymptotic standard
errors on estimates, predictions, and gradients, respectively, from
the returned object. Furthermore, the functions summary
and plot
support objects of this type. The returned object
has the following components:
evaluation points
estimates of the regression function (conditional mean) at the evaluation points
standard errors of the regression function estimates
estimates of the gradients at each evaluation point
standard errors of the gradient estimates
if residuals = TRUE
, in-sample or out-of-sample
residuals where appropriate (or possible)
coefficient of determination (Doksum and Samarov (1995))
mean squared error
mean absolute error
mean absolute percentage error
absolute value of Pearson's correlation coefficient
fraction of observations where fitted and observed values agree in sign
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.
Typical usages are (see below for a complete list of options and also the examples at the end of this help file)
Usage 1: first compute the bandwidth object via npregbw and then compute the conditional mean:bw <- npregbw(y~x) ghat <- npreg(bw)
Usage 2: alternatively, compute the bandwidth object indirectly:
ghat <- npreg(y~x)
Usage 3: modify the default kernel and order:
ghat <- npreg(y~x, ckertype="epanechnikov", ckerorder=4)
Usage 4: use the data frame interface rather than the formula interface:
ghat <- npreg(tydat=y, txdat=x, ckertype="epanechnikov", ckerorder=4)
npreg
implements a variety of methods for regression on
multivariate (
Three classes of kernel estimators for the continuous data types are
available: fixed, adaptive nearest-neighbor, and generalized
nearest-neighbor. Adaptive nearest-neighbor bandwidths change with
each sample realization in the set,
Data contained in the data frame txdat
may be a mix of
continuous (default), unordered discrete (to be specified in the data
frame txdat
using factor
), and ordered discrete
(to be specified in the data frame txdat
using
ordered
). Data can be entered in an arbitrary order and
data types will be detected automatically by the routine (see
np
for details).
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.
The use of compactly supported kernels or the occurrence of small bandwidths can lead to numerical problems for the local linear estimator when computing the locally weighted least squares solution. To overcome this problem we rely on a form or ‘ridging’ proposed by Cheng, Hall, and Titterington (1997), modified so that we solve the problem pointwise rather than globally (i.e. only when it is needed).
Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413-420.
Cheng, M.-Y. and P. Hall and D.M. Titterington (1997), “On the shrinkage of local linear curve estimators,” Statistics and Computing, 7, 11-17.
Doksum, K. and A. Samarov (1995), “Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression,” The Annals of Statistics, 23 1443-1473.
Hall, P. and Q. Li and J.S. Racine (2007), “Nonparametric estimation of regression functions in the presence of irrelevant regressors,” The Review of Economics and Statistics, 89, 784-789.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Li, Q. and J.S. Racine (2004), “Cross-validated local linear nonparametric regression,” Statistica Sinica, 14, 485-512.
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, 99-130.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301-309.
# NOT RUN {
# EXAMPLE 1 (INTERFACE=FORMULA): For this example, we compute a
# bivariate nonparametric regression estimate for Giovanni Baiocchi's
# Italian income panel (see Italy for details)
data("Italy")
attach(Italy)
# First, compute the least-squares cross-validated bandwidths for the
# local constant estimator (default).
bw <- npregbw(formula=gdp~ordered(year))
# Now take these bandwidths and fit the model and gradients
model <- npreg(bws = bw, gradients = TRUE)
summary(model)
# Use plot() to visualize the regression function, add bootstrap
# error bars, and overlay the data on the same plot.
# Note - this may take a minute or two depending on the speed of your
# computer due to bootstrapping being conducted (<ctrl>-C will
# interrupt). Note - nothing will appear in the graphics window until
# all computations are completed (if you use
# plot.errors.method="asymptotic" the figure will instantly appear).
plot(bw, plot.errors.method="bootstrap")
points(ordered(year), gdp, cex=.2, col="red")
detach(Italy)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# EXAMPLE 1 (INTERFACE=DATA FRAME): For this example, we compute a
# bivariate nonparametric regression estimate for Giovanni Baiocchi's
# Italian income panel (see Italy for details)
data("Italy")
attach(Italy)
# First, compute the least-squares cross-validated bandwidths for the
# local constant estimator (default).
bw <- npregbw(xdat=ordered(year), ydat=gdp)
# Now take these bandwidths and fit the model and gradients
model <- npreg(bws = bw, gradients = TRUE)
summary(model)
# Use plot() to visualize the regression function, add bootstrap
# error bars, and overlay the data on the same plot.
# Note - this may take a minute or two depending on the speed of your
# computer due to bootstrapping being conducted (<ctrl>-C will
# interrupt). Note - nothing will appear in the graphics window until
# all computations are completed (if you use
# plot.errors.method="asymptotic" the figure will instantly appear).
plot(bw, plot.errors.method="bootstrap")
points(ordered(year), gdp, cex=.2, col="red")
detach(Italy)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# EXAMPLE 2 (INTERFACE=FORMULA): For this example, we compute a local
# linear fit using the AIC_c bandwidth selection criterion. We then plot
# the estimator and its gradient using asymptotic standard errors.
data("cps71")
attach(cps71)
bw <- npregbw(logwage~age, regtype="ll", bwmethod="cv.aic")
# Next, plot the regression function...
plot(bw, plot.errors.method="asymptotic")
points(age, logwage, cex=.2, col="red")
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# Next, plot the derivative...
plot(bw, plot.errors.method="asymptotic", gradient=TRUE)
detach(cps71)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# EXAMPLE 2 (INTERFACE=DATA FRAME): For this example, we compute a local
# linear fit using the AIC_c bandwidth selection criterion. We then plot
# the estimator and its gradient using asymptotic standard errors.
data("cps71")
attach(cps71)
bw <- npregbw(xdat=age, ydat=logwage, regtype="ll", bwmethod="cv.aic")
# Next, plot the regression function...
plot(bw, plot.errors.method="asymptotic")
points(age, logwage, cex=.2, col="red")
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# Next, plot the derivative...
plot(bw, plot.errors.method="asymptotic", gradient=TRUE)
detach(cps71)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# EXAMPLE 3 (INTERFACE=FORMULA): For this example, we replicate the
# nonparametric regression in Maasoumi, Racine, and Stengos
# (2007) (see oecdpanel for details). Note that X is multivariate
# containing a mix of unordered, ordered, and continuous data types. Note
# - this may take a few minutes depending on the speed of your computer.
data("oecdpanel")
attach(oecdpanel)
bw <- npregbw(formula=growth~
factor(oecd)+
factor(year)+
initgdp+
popgro+
inv+
humancap)
plot(bw, plot.errors.method="asymptotic")
detach(oecdpanel)
# EXAMPLE 3 (INTERFACE=DATA FRAME): For this example, we replicate the
# nonparametric regression in Maasoumi, Racine, and Stengos
# (2007) (see oecdpanel for details). Note that X is multivariate
# containing a mix of unordered, ordered, and continuous data types. Note
# - this may take a few minutes depending on the speed of your computer.
data("oecdpanel")
attach(oecdpanel)
y <- growth
X <- data.frame(factor(oecd), factor(year), initgdp, popgro, inv, humancap)
bw <- npregbw(xdat=X, ydat=y)
plot(bw, plot.errors.method="asymptotic")
detach(oecdpanel)
# EXAMPLE 4 (INTERFACE=FORMULA): Experimental data - the effect of
# vitamin C on tooth growth in guinea pigs
#
# Description:
#
# The response is the length of odontoblasts (teeth) in each of 10
# guinea pigs at each of three dose levels of Vitamin C (0.5, 1, and
# 2 mg) with each of two delivery methods (orange juice or ascorbic
# acid).
#
# Usage:
#
# ToothGrowth
#
# Format:
#
# A data frame with 60 observations on 3 variables.
#
# [,1] len numeric Tooth length
# [,2] supp factor Supplement type (VC or OJ).
# [,3] dose numeric Dose in milligrams.
library("datasets")
attach(ToothGrowth)
# Note - in this example, there are six cells.
bw <- npregbw(formula=len~factor(supp)+ordered(dose))
# Now plot the partial regression surfaces with bootstrapped
# nonparametric confidence bounds
plot(bw, plot.errors.method="bootstrap", plot.errors.type="quantile")
detach(ToothGrowth)
# EXAMPLE 4 (INTERFACE=DATA FRAME): Experimental data - the effect of
# vitamin C on tooth growth in guinea pigs
#
# Description:
#
# The response is the length of odontoblasts (teeth) in each of 10
# guinea pigs at each of three dose levels of Vitamin C (0.5, 1, and
# 2 mg) with each of two delivery methods (orange juice or ascorbic
# acid).
#
# Usage:
#
# ToothGrowth
#
# Format:
#
# A data frame with 60 observations on 3 variables.
#
# [,1] len numeric Tooth length
# [,2] supp factor Supplement type (VC or OJ).
# [,3] dose numeric Dose in milligrams.
library("datasets")
attach(ToothGrowth)
# Note - in this example, there are six cells.
y <- len
X <- data.frame(supp=factor(supp), dose=ordered(dose))
bw <- npregbw(X, y)
# Now plot the partial regression surfaces with bootstrapped
# nonparametric confidence bounds
plot(bw, plot.errors.method="bootstrap", plot.errors.type="quantile")
detach(ToothGrowth)
# EXAMPLE 5 (INTERFACE=FORMULA): a pretty 2-d smoothing example adapted
# from the R mgcv library which was written by Simon N. Wood.
set.seed(12345)
# This function generates a smooth nonlinear DGP
dgp.func <- function(x, z, sx=0.3, sz=0.4)
{ (pi**sx*sz)*(1.2*exp(-(x-0.2)^2/sx^2-(z-0.3)^2/sz^2)+
0.8*exp(-(x-0.7)^2/sx^2-(z-0.8)^2/sz^2))
}
# Generate 500 observations, compute the true DGP (i.e., no noise),
# then a noisy sample
n <- 500
x <- runif(n)
z <- runif(n)
xs <- seq(0, 1, length=30)
zs <- seq(0, 1, length=30)
X.eval <- data.frame(x=rep(xs, 30), z=rep(zs, rep(30, 30)))
dgp <- matrix(dgp.func(X.eval$x, X.eval$z), 30, 30)
y <- dgp.func(x, z)+rnorm(n)*0.1
# Prepare the screen for output... first, plot the true DGP
split.screen(c(2, 1))
screen(1)
persp(xs, zs, dgp, xlab="x1", ylab="x2", zlab="y", main="True DGP")
# Next, compute a local linear fit and plot that
bw <- npregbw(formula=y~x+z, regtype="ll", bwmethod="cv.aic")
fit <- fitted(npreg(bws=bw, newdata=X.eval))
fit.mat <- matrix(fit, 30, 30)
screen(2)
persp(xs, zs, fit.mat, xlab="x1", ylab="x2", zlab="y",
main="Local linear estimate")
# EXAMPLE 5 (INTERFACE=DATA FRAME): a pretty 2-d smoothing example
# adapted from the R mgcv library which was written by Simon N. Wood.
set.seed(12345)
# This function generates a smooth nonlinear DGP
dgp.func <- function(x, z, sx=0.3, sz=0.4)
{ (pi**sx*sz)*(1.2*exp(-(x-0.2)^2/sx^2-(z-0.3)^2/sz^2)+
0.8*exp(-(x-0.7)^2/sx^2-(z-0.8)^2/sz^2))
}
# Generate 500 observations, compute the true DGP (i.e., no noise),
# then a noisy sample
n <- 500
x <- runif(n)
z <- runif(n)
xs <- seq(0, 1, length=30)
zs <- seq(0, 1, length=30)
X <- data.frame(x, z)
X.eval <- data.frame(x=rep(xs, 30), z=rep(zs, rep(30, 30)))
dgp <- matrix(dgp.func(X.eval$x, X.eval$z), 30, 30)
y <- dgp.func(x, z)+rnorm(n)*0.1
# Prepare the screen for output... first, plot the true DGP
split.screen(c(2, 1))
screen(1)
persp(xs, zs, dgp, xlab="x1", ylab="x2", zlab="y", main="True DGP")
# Next, compute a local linear fit and plot that
bw <- npregbw(xdat=X, ydat=y, regtype="ll", bwmethod="cv.aic")
fit <- fitted(npreg(exdat=X.eval, bws=bw))
fit.mat <- matrix(fit, 30, 30)
screen(2)
persp(xs, zs, fit.mat, xlab="x1", ylab="x2", zlab="y",
main="Local linear estimate")
# }
# NOT RUN {
# }
# NOT RUN {
<!-- % enddontrun -->
# }
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