| npindex {np} | R Documentation |
npindex computes a semiparametric single index model
for a dependent variable and p-variate explanatory data using
the model Y = G(XB) + epsilon, given a
set of evaluation points, training points (consisting of explanatory
data and dependent data), and a npindexbw bandwidth
specification. Note that for this semiparametric estimator, the
bandwidth object contains parameters for the single index model and
the (scalar) bandwidth for the index function.
npindex(bws, ...)
## S3 method for class 'formula':
npindex(bws, data = NULL, newdata = NULL, ...)
## S3 method for class 'call':
npindex(bws, ...)
## Default S3 method:
npindex(bws, txdat, tydat, ...)
## S3 method for class 'sibandwidth':
npindex(bws,
txdat = stop("training data 'txdat' missing"),
tydat = stop("training data 'tydat' missing"),
exdat,
eydat,
gradients = FALSE,
residuals = FALSE,
errors = FALSE,
boot.num = 399,
...)
bws |
a bandwidth specification. This can be set as a
sibandwidth
object returned from an invocation of npindexbw, or
as a vector of parameters (beta) with each element i
corresponding to the coefficient for column i in txdat
where the first element is normalized to 1, and a scalar bandwidth
(h).
|
gradients |
a logical value indicating that you want gradients computed and
returned in the resulting singleindex object. Defaults to
FALSE.
|
residuals |
a logical value indicating that you want residuals computed and
returned in the resulting singleindex object. Defaults to
FALSE.
|
errors |
a logical value indicating that you want (bootstrapped)
standard errors for the conditional mean, gradients (when
gradients=TRUE is set), and average gradients (when
gradients=TRUE is set), computed and returned in the
resulting singleindex object. Defaults to FALSE.
|
boot.num |
an integer specifying the number of bootstrap replications to use
when performing standard error calculations. Defaults to
399.
|
... |
additional arguments supplied to specify the parameters to the
sibandwidth S3 method, which is called during estimation.
|
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
npindexbw 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. |
A matrix of gradients along with average derivatives are computed and
returned if gradients=TRUE is used.
npindex returns a npsingleindex object. The generic
functions fitted, residuals, coef,
se, predict, and
gradients, extract (or generate) estimated values,
residuals, coefficients, bootstrapped 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 |
beta |
the model coefficients |
merr |
standard errors of the regression function estimates |
grad |
estimates of the gradients at each evaluation point |
gerr |
standard errors of the gradient estimates |
mean.grad |
mean (average) gradient over the evaluation points |
mean.gerr |
bootstrapped standard error of the mean gradient estimates |
R2 |
if method="ichimura", coefficient of determination |
MSE |
if method="ichimura", mean squared error |
MAE |
if method="ichimura", mean absolute error |
MAPE |
if method="ichimura", mean absolute percentage error |
CORR |
if method="ichimura", absolute value of Pearson's correlation coefficient |
SIGN |
if method="ichimura", fraction of observations where fitted and observed values
agree in sign |
confusion.matrix |
if method="kleinspady", the confusion matrix or NA if outcomes
are not available |
CCR.overall |
if method="kleinspady", the overall correct
classification ratio, or NA if outcomes are not available |
CCR.byoutcome |
if method="kleinspady", a numeric vector containing the correct
classification ratio by outcome, or NA if outcomes are not
available |
fit.mcfadden |
if method="kleinspady", the McFadden-Puig-Kerschner performance measure
or NA if outcomes are not available |
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.
Ichimura, H., (1993), “Semiparametric least squares (SLS) and weighted SLS estimation of single-index models,” Journal of Econometrics, 58, 71-120.
Klein, R. W. and R. H. Spady (1993), “An efficient semiparametric estimator for binary response models,” Econometrica, 61, 387-421.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
McFadden, D. and C. Puig and D. Kerschner (1977), “Determinants of the long-run demand for electricity,” Proceedings of the American Statistical Association (Business and Economics Section), 109-117.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301-309.
# EXAMPLE 1 (INTERFACE=FORMULA): Generate a simple linear model then
# estimate it using a semiparametric single index specification and
# Ichimura's nonlinear least squares coefficients and bandwidth
# (default). Also compute the matrix of gradients and average derivative
# estimates.
set.seed(12345)
n <- 100
x1 <- runif(n, min=-1, max=1)
x2 <- runif(n, min=-1, max=1)
y <- x1 - x2 + rnorm(n)
# Note - this may take a minute or two depending on the speed of your
# computer. Note also that the first element of the vector beta is
# normalized to one for identification purposes, and that X must contain
# at least one continuous variable.
bw <- npindexbw(formula=y~x1+x2)
summary(bw)
model <- npindex(bws=bw, gradients=TRUE)
summary(model)
## Not run:
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# Or you can visualize the input with npplot.
npplot(bws=bw)
Sys.sleep(5)
# EXAMPLE 1 (INTERFACE=DATA FRAME): Generate a simple linear model then
# estimate it using a semiparametric single index specification and
# Ichimura's nonlinear least squares coefficients and bandwidth
# (default). Also compute the matrix of gradients and average derivative
# estimates.
set.seed(12345)
n <- 100
x1 <- runif(n, min=-1, max=1)
x2 <- runif(n, min=-1, max=1)
y <- x1 - x2 + rnorm(n)
X <- cbind(x1, x2)
# Note - this may take a minute or two depending on the speed of your
# computer. Note also that the first element of the vector beta is
# normalized to one for identification purposes, and that X must contain
# at least one continuous variable.
bw <- npindexbw(xdat=X, ydat=y)
summary(bw)
model <- npindex(bws=bw, gradients=TRUE)
summary(model)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# Or you can visualize the input with npplot.
npplot(bws=bw)
Sys.sleep(5)
# EXAMPLE 2 (INTERFACE=FORMULA): Generate a simple binary outcome linear
# model then estimate it using a semiparametric single index
# specification and Klein and Spady's likelihood-based coefficients and
# bandwidth (default). Also compute the matrix of gradients and average
# derivative estimates.
n <- 100
x1 <- runif(n, min=-1, max=1)
x2 <- runif(n, min=-1, max=1)
y <- ifelse(x1 + x2 + rnorm(n) > 0, 1, 0)
# Note that the first element of the vector beta is normalized to one
# for identification purposes, and that X must contain at least one
# continuous variable.
bw <- npindexbw(formula=y~x1+x2, method="kleinspady")
summary(bw)
model <- npindex(bws=bw, gradients=TRUE)
# Note that, since the outcome is binary, we can assess model
# performance using methods appropriate for binary outcomes. We look at
# the confusion matrix, various classification ratios, and McFadden et
# al's measure of predictive performance.
summary(model)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# EXAMPLE 2 (INTERFACE=DATA FRAME): Generate a simple binary outcome
# linear model then estimate it using a semiparametric single index
# specification and Klein and Spady's likelihood-based coefficients and
# bandwidth (default). Also compute the matrix of gradients and average
# derivative estimates.
n <- 100
x1 <- runif(n, min=-1, max=1)
x2 <- runif(n, min=-1, max=1)
y <- ifelse(x1 + x2 + rnorm(n) > 0, 1, 0)
X <- cbind(x1, x2)
# Note that the first element of the vector beta is normalized to one
# for identification purposes, and that X must contain at least one
# continuous variable.
bw <- npindexbw(xdat=X, ydat=y, method="kleinspady")
summary(bw)
model <- npindex(bws=bw, gradients=TRUE)
# Note that, since the outcome is binary, we can assess model
# performance using methods appropriate for binary outcomes. We look at
# the confusion matrix, various classification ratios, and McFadden et
# al's measure of predictive performance.
summary(model)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# EXAMPLE 3 (INTERFACE=FORMULA): Replicate the DGP of Klein & Spady
# (1993) (see their description on page 405, pay careful attention to
# footnote 6 on page 405).
set.seed(123)
n <- 1000
# x1 is chi-squared having 3 df truncated at 6 standardized by
# subtracting 2.348 and dividing by 1.511
x <- rchisq(n, df=3)
x1 <- (ifelse(x < 6, x, 6) - 2.348)/1.511
# x2 is normal (0, 1) truncated at +- 2 divided by 0.8796
x <- rnorm(n)
x2 <- ifelse(abs(x) < 2 , x, 2) / 0.8796
# y is 1 if y* > 0, 0 otherwise.
y <- ifelse(x1 + x2 + rnorm(n) > 0, 1, 0)
# Compute the parameter vector and bandwidth. Note that the first
# element of the vector beta is normalized to one for identification
# purposes, and that X must contain at least one continuous variable.
bw <- npindexbw(formula=y~x1+x2, method="kleinspady")
# Next, create the evaluation data in order to generate a perspective
# plot
# Create an evaluation data matrix
x1.seq <- seq(min(x1), max(x1), length=50)
x2.seq <- seq(min(x2), max(x2), length=50)
X.eval <- expand.grid(x1=x1.seq, x2=x2.seq)
# Now evaluate the single index model on the evaluation data
fit <- fitted(npindex(exdat=X.eval,
eydat=rep(1, nrow(X.eval)),
bws=bw))
# Finally, coerce the fitted model into a matrix suitable for 3D
# plotting via persp()
fit.mat <- matrix(fit, 50, 50)
# Generate a perspective plot similar to Figure 2 b of Klein and Spady
# (1993)
persp(x1.seq,
x2.seq,
fit.mat,
col="white",
ticktype="detailed",
expand=0.5,
axes=FALSE,
box=FALSE,
main="Estimated Semiparametric Probability Perspective",
theta=310,
phi=25)
# EXAMPLE 3 (INTERFACE=DATA FRAME): Replicate the DGP of Klein & Spady
# (1993) (see their description on page 405, pay careful attention to
# footnote 6 on page 405).
set.seed(123)
n <- 1000
# x1 is chi-squared having 3 df truncated at 6 standardized by
# subtracting 2.348 and dividing by 1.511
x <- rchisq(n, df=3)
x1 <- (ifelse(x < 6, x, 6) - 2.348)/1.511
# x2 is normal (0, 1) truncated at +- 2 divided by 0.8796
x <- rnorm(n)
x2 <- ifelse(abs(x) < 2 , x, 2) / 0.8796
# y is 1 if y* > 0, 0 otherwise.
y <- ifelse(x1 + x2 + rnorm(n) > 0, 1, 0)
# Create the X matrix
X <- cbind(x1, x2)
# Compute the parameter vector and bandwidth. Note that the first
# element of the vector beta is normalized to one for identification
# purposes, and that X must contain at least one continuous variable.
bw <- npindexbw(xdat=X, ydat=y, method="kleinspady")
# Next, create the evaluation data in order to generate a perspective
# plot
# Create an evaluation data matrix
x1.seq <- seq(min(x1), max(x1), length=50)
x2.seq <- seq(min(x2), max(x2), length=50)
X.eval <- expand.grid(x1=x1.seq, x2=x2.seq)
# Now evaluate the single index model on the evaluation data
fit <- fitted(npindex(exdat=X.eval,
eydat=rep(1, nrow(X.eval)),
bws=bw))
# Finally, coerce the fitted model into a matrix suitable for 3D
# plotting via persp()
fit.mat <- matrix(fit, 50, 50)
# Generate a perspective plot similar to Figure 2 b of Klein and Spady
# (1993)
persp(x1.seq,
x2.seq,
fit.mat,
col="white",
ticktype="detailed",
expand=0.5,
axes=FALSE,
box=FALSE,
main="Estimated Semiparametric Probability Perspective",
theta=310,
phi=25)
## End(Not run)