krscv
computes exhaustive crossvalidation directed search for
a regression spline estimate of a one (1) dimensional dependent
variable on an r
dimensional vector of continuous and
nominal/ordinal (factor
/ordered
)
predictors.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  krscv(xz,
y,
degree.max = 10,
segments.max = 10,
degree.min = 0,
segments.min = 1,
restarts = 0,
complexity = c("degreeknots","degree","knots"),
knots = c("quantiles","uniform","auto"),
basis = c("additive","tensor","glp","auto"),
cv.func = c("cv.ls","cv.gcv","cv.aic"),
degree = degree,
segments = segments,
tau = NULL,
weights = NULL,
singular.ok = FALSE)

y 
continuous univariate vector 
xz 
continuous and/or nominal/ordinal
( 
degree.max 
the maximum degree of the Bspline basis for
each of the continuous predictors (default 
segments.max 
the maximum segments of the Bspline basis for
each of the continuous predictors (default 
degree.min 
the minimum degree of the Bspline basis for
each of the continuous predictors (default 
segments.min 
the minimum segments of the Bspline basis for
each of the continuous predictors (default 
restarts 
number of times to restart 
complexity 
a character string (default

knots 
a character string (default 
basis 
a character string (default 
cv.func 
a character string (default 
degree 
integer/vector specifying the degree of the Bspline
basis for each dimension of the continuous 
segments 
integer/vector specifying the number of segments of
the Bspline basis for each dimension of the continuous 
tau 
if nonnull a number in (0,1) denoting the quantile for which a quantile
regression spline is to be estimated rather than estimating the
conditional mean (default 
weights 
an optional vector of weights to be used in the fitting process. Should be ‘NULL’ or a numeric vector. If nonNULL, weighted least squares is used with weights ‘weights’ (that is, minimizing ‘sum(w*e^2)’); otherwise ordinary least squares is used. 
singular.ok 
a logical value (default 
krscv
computes exhaustive crossvalidation for a regression
spline estimate of a one (1) dimensional dependent variable on an
r
dimensional vector of continuous and nominal/ordinal
(factor
/ordered
) predictors. The optimal
K
/lambda
combination is returned along with other
results (see below for return values). The method uses kernel
functions appropriate for categorical (ordinal/nominal) predictors
which avoids the loss in efficiency associated with samplesplitting
procedures that are typically used when faced with a mix of continuous
and nominal/ordinal (factor
/ordered
)
predictors.
For the continuous predictors the regression spline model employs
either the additive or tensor product Bspline basis matrix for a
multivariate polynomial spline via the Bspline routines in the GNU
Scientific Library (http://www.gnu.org/software/gsl/) and the
tensor.prod.model.matrix
function.
For the discrete predictors the product kernel function is of the ‘LiRacine’ type (see Li and Racine (2007) for details).
For each unique combination of degree
and segment
,
numerical search for the bandwidth vector lambda
is undertaken
using optim
and the boxconstrained LBFGSB
method (see optim
for details). The user may restart the
optim
algorithm as many times as desired via the
restarts
argument. The approach ascends from K=0
through
degree.max
/segments.max
and for each value of K
searches for the optimal bandwidths for this value of K
. After
the most complex model has been searched then the optimal
K
/lambda
combination is selected. If any element of the
optimal K
vector coincides with
degree.max
/segments.max
a warning is produced and the
user ought to restart their search with a larger value of
degree.max
/segments.max
.
krscv
returns a crscv
object. Furthermore, the
function summary
supports objects of this type. The
returned objects have the following components:
K 
scalar/vector containing optimal degree(s) of spline or number of segments 
K.mat 
vector/matrix of values of 
restarts 
number of restarts during search, if any 
lambda 
optimal bandwidths for categorical predictors 
lambda.mat 
vector/matrix of optimal bandwidths for each degree of spline 
cv.func 
objective function value at optimum 
cv.func.vec 
vector of objective function values at each degree
of spline or number of segments in 
Jeffrey S. Racine racinej@mcmaster.ca
Craven, P. and G. Wahba (1979), “Smoothing Noisy Data With Spline Functions,” Numerische Mathematik, 13, 377403.
Hurvich, C.M. and J.S. Simonoff and C.L. Tsai (1998), “Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion,” Journal of the Royal Statistical Society B, 60, 271293.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Ma, S. and J.S. Racine and L. Yang (under revision), “Spline Regression in the Presence of Categorical Predictors,” Journal of Applied Econometrics.
Ma, S. and J.S. Racine (2013), “Additive Regression Splines with Irrelevant Categorical and Continuous Regressors,” Statistica Sinica, Volume 23, 515541.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  set.seed(42)
## Simulated data
n < 1000
x < runif(n)
z < round(runif(n,min=0.5,max=1.5))
z.unique < uniquecombs(as.matrix(z))
ind < attr(z.unique,"index")
ind.vals < sort(unique(ind))
dgp < numeric(length=n)
for(i in 1:nrow(z.unique)) {
zz < ind == ind.vals[i]
dgp[zz] < z[zz]+cos(2*pi*x[zz])
}
y < dgp + rnorm(n,sd=.1)
xdata < data.frame(x,z=factor(z))
## Compute the optimal K and lambda, determine optimal number of knots, set
## spline degree for x to 3
cv < krscv(x=xdata,y=y,complexity="knots",degree=c(3))
summary(cv)

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