np.regression: Kernel Regression with Mixed Data Types
In np: Nonparametric Kernel Smoothing Methods for Mixed Data Types
npreg R Documentation
Kernel Regression with Mixed Data Types
Description
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.
Usage
npreg(bws, ...)
## S3 method for class 'formula'
npreg(bws, data = NULL, newdata = NULL, y.eval =
FALSE, ...)
## 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,
...)
Arguments
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.
y.eval
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.
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.
Details
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 (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.
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).
Value
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 (Doksum and Samarov (1995))
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
Usage Issues
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.
Author(s)
Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca
References
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.
See Also
loess
Examples
## 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")
## End(Not run)
np documentation built on March 31, 2023, 9:41 p.m.
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| npreg | R Documentation |
Kernel Regression with Mixed Data Types
Description
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.
Usage
npreg(bws, ...)
## S3 method for class 'formula'
npreg(bws, data = NULL, newdata = NULL, y.eval =
FALSE, ...)
## 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,
...)
Arguments
bws |
a bandwidth specification. This can be set as a |
... |
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 |
newdata |
An optional data frame in which to look for evaluation data. If omitted, the training data are used. |
y.eval |
If |
txdat |
a |
tydat |
a one (1) dimensional numeric or integer vector of dependent data, each
element |
exdat |
a |
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 |
residuals |
a logical value indicating that you want residuals computed and
returned in the resulting |
Details
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 (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.
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).
Value
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 |
R2 |
coefficient of determination (Doksum and Samarov (1995)) |
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 |
Usage Issues
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.
Author(s)
Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca
References
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.
See Also
loess
Examples
## 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")
## End(Not run)
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