npplreg  R Documentation 
npplreg
computes a partially linear kernel regression estimate
of a one (1) dimensional dependent variable on p+qvariate
explanatory data, using the model Y = XB + 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.
npplreg(bws, ...) ## S3 method for class 'formula' npplreg(bws, data = NULL, newdata = NULL, y.eval = FALSE, ...) ## S3 method for class 'call' npplreg(bws, ...) ## S3 method for class 'plbandwidth' npplreg(bws, txdat = stop("training data txdat missing"), tydat = stop("training data tydat missing"), tzdat = stop("training data tzdat missing"), exdat, eydat, ezdat, residuals = FALSE, ...)
bws 
a bandwidth specification. This can be set as a 
... 
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 
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 pvariate data frame of explanatory data (training data), corresponding to X in the model equation, whose linear relationship with the dependent data Y is posited. 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

tzdat 
a qvariate data frame of explanatory data (training data), corresponding to Z in the model equation, whose relationship to the dependent variable is unspecified (nonparametric). Defaults to the training data used to compute the bandwidth object. 
exdat 
a pvariate data frame of points on which the regression will be
estimated (evaluation data). By default,
evaluation takes place on the data provided by 
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. By default,
evaluation takes place on the data provided by 
ezdat 
a qvariate data frame of points on which the regression will
be estimated (evaluation data). By default,
evaluation takes place on the data provided by 
residuals 
a logical value indicating that you want residuals computed and
returned in the resulting 
npplreg
uses a combination of OLS and nonparametric
regression to estimate the parameter B in the model
Y = XB + theta(Z) + epsilon.
npplreg
implements a variety of methods for
nonparametric regression on multivariate (qvariate) 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.
Data contained in the data frame tzdat
may be a mix of
continuous (default), unordered discrete (to be specified in the data
frame tzdat
using factor
), and ordered discrete
(to be specified in the data frame tzdat
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.
npplreg
returns a plregression
object. The generic
accessor functions coef
, fitted
,
residuals
, predict
, and
vcov
, extract (or
estimate) coefficients, estimated values, residuals,
predictions, and variancecovariance matrices,
respectively, from
the returned object. Furthermore, the functions summary
and plot
support objects of this type. The returned object
has the following components:
evalx 
evaluation points 
evalz 
evaluation points 
mean 
estimation of the regression, or conditional mean, at the evaluation points 
xcoef 
coefficient(s) corresponding to the components B[i] in the model 
xcoeferr 
standard errors of the coefficients 
xcoefvcov 
covariance matrix of the coefficients 
bw 
the bandwidths, stored as a 
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 
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 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.
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 14431473.
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 compare the coefficient # estimates from the partially linear model with those from a correctly # specified parametric model... 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) # First, compute datadriven bandwidths. This may take a few minutes # depending on the speed of your computer... bw < npplregbw(formula=y~x1+factor(x2)factor(z1)+z2) # Next, compute the partially linear fit pl < npplreg(bws=bw) # Print a summary of the model... summary(pl) # Sleep for 5 seconds so that we can examine the output... Sys.sleep(5) # Retrieve the coefficient estimates and their standard errors... coef(pl) coef(pl, errors = TRUE) # Compare the partially linear results to those from a correctly # specified model's coefficients for x1 and x2 ols < lm(y~x1+factor(x2)+factor(z1)+I(sin(z2))) # The intercept is coef()[1], and those for x1 and x2 are coef()[2] and # coef()[3]. The standard errors are the square root of the diagonal of # the variancecovariance matrix (elements 2 and 3) coef(ols)[2:3] sqrt(diag(vcov(ols)))[2:3] # Sleep for 5 seconds so that we can examine the output... Sys.sleep(5) # Plot the regression surfaces via plot() (i.e., plot the `partial # regression surface plots'). plot(bw) # Note  to plot regression surfaces with variability bounds constructed # from bootstrapped standard errors, use the following (note that this # may take a minute or two depending on the speed of your computer as # the bootstrapping is done in real time, and note also that we override # the default number of bootstrap replications (399) reducing them to 25 # in order to quickly compute standard errors in this instance  don't # of course do this in general) plot(bw, plot.errors.boot.num=25, plot.errors.method="bootstrap") # EXAMPLE 1 (INTERFACE=DATA FRAME): For this example, we simulate an # example for a partially linear model and compare the coefficient # estimates from the partially linear model with those from a correctly # specified parametric model... 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) # First, compute datadriven bandwidths. This may take a few minutes # depending on the speed of your computer... bw < npplregbw(xdat=X, zdat=Z, ydat=y) # Next, compute the partially linear fit pl < npplreg(bws=bw) # Print a summary of the model... summary(pl) # Sleep for 5 seconds so that we can examine the output... Sys.sleep(5) # Retrieve the coefficient estimates and their standard errors... coef(pl) coef(pl, errors = TRUE) # Compare the partially linear results to those from a correctly # specified model's coefficients for x1 and x2 ols < lm(y~x1+factor(x2)+factor(z1)+I(sin(z2))) # The intercept is coef()[1], and those for x1 and x2 are coef()[2] and # coef()[3]. The standard errors are the square root of the diagonal of # the variancecovariance matrix (elements 2 and 3) coef(ols)[2:3] sqrt(diag(vcov(ols)))[2:3] # Sleep for 5 seconds so that we can examine the output... Sys.sleep(5) # Plot the regression surfaces via plot() (i.e., plot the `partial # regression surface plots'). plot(bw) # Note  to plot regression surfaces with variability bounds constructed # from bootstrapped standard errors, use the following (note that this # may take a minute or two depending on the speed of your computer as # the bootstrapping is done in real time, and note also that we override # the default number of bootstrap replications (399) reducing them to 25 # in order to quickly compute standard errors in this instance  don't # of course do this in general) plot(bw, plot.errors.boot.num=25, plot.errors.method="bootstrap") ## End(Not run)
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