| npreg {np} | R Documentation |
npreg computes a kernel regression estimate of a one
(1) dimensional dependent variable on p-variate explanatory
data, given a set of evaluation points, training points (consisting of
explanatory data and dependent data), and a bandwidth specification
using the method of Racine and Li (2004) and Li and Racine (2004). A
bandwidth specification can be a rbandwidth object, or a
bandwidth vector, bandwidth type and kernel type.
npreg(bws, ...)
## S3 method for class 'formula':
npreg(bws, data = NULL, newdata = NULL, ...)
## S3 method for class 'call':
npreg(bws, ...)
## Default S3 method:
npreg(bws, txdat, tydat, ...)
## S3 method for class 'rbandwidth':
npreg(bws,
txdat = stop("training data 'txdat' missing"),
tydat = stop("training data 'tydat' missing"),
exdat,
eydat,
gradients = FALSE,
residuals = FALSE,
...)
bws |
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 i corresponding
to the bandwidth for column i in 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. |
data |
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.
|
newdata |
An optional data frame in which to look for evaluation data. If omitted, the training data are used. |
txdat |
a p-variate data frame of explanatory data (training data) used to calculate the regression estimators. Defaults to the training data used to compute the bandwidth object. |
tydat |
a one (1) dimensional numeric or integer vector of dependent data, each
element i corresponding to each observation (row) i of
txdat. Defaults to the training data used to
compute the bandwidth object.
|
exdat |
a p-variate data frame of points on which the regression will be
estimated (evaluation data). By default,
evaluation takes place on the data provided by txdat.
|
eydat |
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. |
gradients |
a logical value indicating that you want gradients computed and
returned in the resulting npregression object. Defaults to
FALSE.
|
residuals |
a logical value indicating that you want residuals computed and
returned in the resulting npregression object. Defaults to
FALSE.
|
npreg implements a variety of methods for regression on
multivariate (p-variate) data, the types of which are possibly
continuous and/or discrete (unordered, ordered). 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 nearest-neighbor, and generalized nearest-neighbor. Adaptive nearest-neighbor bandwidths change with each sample realization in the set, x[i], when estimating the density at the point x. Generalized nearest-neighbor bandwidths change with the point at which the density is estimated, x. Fixed bandwidths are constant over the support of x.
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.
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:
eval |
evaluation points |
mean |
estimates of the regression function (conditional mean) at the evaluation points |
merr |
standard errors of the regression function estimates |
grad |
estimates of the gradients at each evaluation point |
gerr |
standard errors of the gradient estimates |
resid |
if residuals = TRUE, in-sample or out-of-sample
residuals where appropriate (or possible) |
R2 |
coefficient of determination |
MSE |
mean squared error |
MAE |
mean absolute error |
MAPE |
mean absolute percentage error |
CORR |
absolute value of Pearson's correlation coefficient |
SIGN |
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.
Tristen Hayfield hayfield@phys.ethz.ch, Jeffrey S. Racine racinej@mcmaster.ca
Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413-420.
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.
# 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). We override the default tolerances
# for the search method as the objective function is well-behaved (don't
# of course do this in general).
bw <- npregbw(formula=gdp~ordered(year), tol=.1, ftol=.1)
# Now take these bandwidths and fit the model and gradients
model <- npreg(bws = bw, gradients = TRUE)
summary(model)
## Not run:
# Use npplot() 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).
npplot(bws=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). We override the default tolerances
# for the search method as the objective function is well-behaved (don't
# of course do this in general).
bw <- npregbw(xdat=ordered(year), ydat=gdp, tol=.1, ftol=.1)
# Now take these bandwidths and fit the model and gradients
model <- npreg(bws = bw, gradients = TRUE)
summary(model)
# Use npplot() 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).
npplot(bws=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...
npplot(bws=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...
npplot(bws=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...
npplot(bws=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...
npplot(bws=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)
# We override the default tolerances for the search method as the
# objective function is well-behaved (don't of course do this in
# general).
bw <- npregbw(formula=growth~
factor(oecd)+
factor(year)+
initgdp+
popgro+
inv+
humancap,
tol=.1, ftol=.1)
npplot(bws=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)
# We override the default tolerances for the search method as the
# objective function is well-behaved (don't of course do this in
# general).
bw <- npregbw(xdat=X, ydat=y, tol=.1, ftol=.1)
npplot(bws=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
npplot(bws=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
npplot(bws=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",
tol=.01, ftol=.01)
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",
tol=.01, ftol=.01)
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")
## End(Not run)