| npcmstest {np} | R Documentation |
npcmstest implements a consistent test for correct
specification of parametric regression models (linear or nonlinear) as
described in Hsiao, Li, and Racine (2007).
npcmstest(formula,
data = NULL,
subset,
xdat,
ydat,
model = stop(paste(sQuote("model")," has not been provided")),
distribution = c("bootstrap", "asymptotic"),
boot.method=c("iid","wild","wild-rademacher"),
boot.num = 399,
pivot = TRUE,
density.weighted = TRUE,
random.seed = 42,
...)
formula |
a symbolic description of variables on which the test is to be performed. The details of constructing a formula are described 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(formula), typically the environment from which the
function is called.
|
subset |
an optional vector specifying a subset of observations to be used. |
model |
a model object obtained from a call to lm (or
glm). Important: the
call to either glm or lm must have the arguments
x=TRUE and
y=TRUE or npcmstest will not work. Also, the test is
based on residual bootstrapping hence the outcome must be continuous
(which rules out Logit, Probit, and Count models).
|
xdat |
a p-variate data frame of explanatory data (training data) used to calculate the regression estimators. |
ydat |
a one (1) dimensional numeric or integer vector of dependent data, each
element i corresponding to each observation (row) i of
xdat.
|
distribution |
a character string used to specify the method of estimating the
distribution of the statistic to be calculated. bootstrap
will conduct bootstrapping. asymptotic will use the normal
distribution. Defaults to bootstrap.
|
boot.method |
a character string used to specify the bootstrap method.
iid will generate independent identically distributed
draws. wild will use a wild bootstrap. wild-rademacher
will use a wild bootstrap with Rademacher variables. Defaults to
iid.
|
boot.num |
an integer value specifying the number of bootstrap replications to
use. Defaults to 399.
|
pivot |
a logical value specifying whether the statistic should be
normalised such that it approaches N(0,1) in
distribution. Defaults to TRUE.
|
density.weighted |
a logical value specifying whether the statistic should be
weighted by the density of xdat. Defaults to TRUE.
|
random.seed |
an integer used to seed R's random number generator. This is to ensure replicability. Defaults to 42. |
... |
additional arguments supplied to control bandwidth selection on the
residuals. One can specify the bandwidth type,
kernel types, and so on. To do this, you may specify any of bwscaling,
bwtype, ckertype, ckerorder, ukertype,
okertype, as described in npregbw.
This is necessary if you specify bws as a p-vector and not
a bandwidth object, and you do not desire the default behaviours.
|
npcmstest returns an object of type cmstest with the
following components, components will contain information
related to Jn or In depending on the value of pivot:
Jn |
the statistic Jn |
In |
the statistic In |
Omega.hat |
as described in Hsiao, C. and Q. Li and J.S. Racine. |
q.* |
the various quantiles of the statistic Jn (or
In if
pivot=FALSE) are in
components q.90,
q.95, q.99 (one-sided 1%, 5%, 10% critical values) |
P |
the P-value of the statistic |
Jn.bootstrap |
if pivot=TRUE contains the bootstrap
replications of Jn |
In.bootstrap |
if pivot=FALSE contains the bootstrap
replications of In |
summary supports object of type cmstest.
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.
Hsiao, C. and Q. Li and J.S. Racine (2007), “A consistent model specification test with mixed categorical and continuous data,” Journal of Econometrics, 140, 802-826.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Maasoumi, E. and J.S. Racine and T. Stengos (2007), “Growth and convergence: a profile of distribution dynamics and mobility,” Journal of Econometrics, 136, 483-508.
Murphy, K. M. and F. Welch (1990), “Empirical age-earnings profiles,” Journal of Labor Economics, 8, 202-229.
Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301-309.
# EXAMPLE 1: For this example, we conduct a consistent model
# specification test for a parametric wage regression model that is
# quadratic in age. The work of Murphy and Welch (1990) would suggest
# that this parametric regression model is misspecified.
data("cps71")
attach(cps71)
model <- lm(logwage~age+I(age^2), x=TRUE, y=TRUE)
plot(age, logwage)
lines(age, fitted(model))
# Note - this may take a few minutes depending on the speed of your
# computer...
npcmstest(model = model, xdat = age, ydat = logwage)
## Not run:
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# Next try Murphy & Welch's (1990) suggested quintic specification.
model <- lm(logwage~age+I(age^2)+I(age^3)+I(age^4)+I(age^5), x=TRUE, y=TRUE)
plot(age, logwage)
lines(age, fitted(model))
X <- data.frame(age)
# Note - this may take a few minutes depending on the speed of your
# computer...
npcmstest(model = model, xdat = age, ydat = logwage)
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# Note - you can pass in multiple arguments to this function. For
# instance, to use local linear rather than local constant regression,
# you would use npcmstest(model, X, regtype="ll"), while you could also
# change the kernel type (default is second order Gaussian), numerical
# search tolerance, or feed in your own vector of bandwidths and so
# forth.
detach(cps71)
# EXAMPLE 2: For this example, we replicate the application in Maasoumi,
# Racine, and Stengos (2007) (see oecdpanel for details). We
# estimate a parametric model that is used in the literature, then
# subject it to the model specification test.
data("oecdpanel")
attach(oecdpanel)
model <- lm(growth ~ oecd +
factor(year) +
initgdp +
I(initgdp^2) +
I(initgdp^3) +
I(initgdp^4) +
popgro +
inv +
humancap +
I(humancap^2) +
I(humancap^3) - 1,
x=TRUE,
y=TRUE)
X <- data.frame(factor(oecd), factor(year), initgdp, popgro, inv, humancap)
# Note - we override the default tolerances for the sake of this example
# (don't of course do this in general). This example may take a few
# minutes depending on the speed of your computer (data-driven bandwidth
# selection is, by its nature, time consuming, while the bootstrapping
# also takes some time).
npcmstest(model = model, xdat = X, ydat = growth, tol=.1, ftol=.1)
detach(oecdpanel)
## End(Not run)