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\name{rcspline.eval}
\alias{rcspline.eval}
\title{
Restricted Cubic Spline Design Matrix
}
\description{
Computes matrix that expands a single variable into the terms needed
to fit a restricted cubic spline (natural spline) function using the
truncated power basis. Two normalization options are given for
somewhat reducing problems of ill-conditioning. The antiderivative
function can be optionally created. If knot locations are not given,
they will be estimated from the marginal distribution of \code{x}.
}
\usage{
rcspline.eval(x, knots, nk=5, inclx=FALSE, knots.only=FALSE,
type="ordinary", norm=2, rpm=NULL, pc=FALSE,
fractied=0.05)
}
\arguments{
\item{x}{
a vector representing a predictor variable
}
\item{knots}{
knot locations. If not given, knots will be estimated using default
quantiles of \code{x}. For 3 knots, the outer quantiles used are 0.10
and 0.90. For 4-6 knots, the outer quantiles used are 0.05 and
0.95. For \eqn{\code{nk}>6}, the outer quantiles are 0.025 and 0.975. The
knots are equally spaced between these on the quantile scale. For
fewer than 100 non-missing values of \code{x}, the outer knots are
the 5th smallest and largest \code{x}.
}
\item{nk}{
number of knots. Default is 5. The minimum value is 3.
}
\item{inclx}{
set to \code{TRUE} to add \code{x} as the first column of the
returned matrix
}
\item{knots.only}{
return the estimated knot locations but not the expanded matrix
}
\item{type}{
\samp{"ordinary"} to fit the function, \samp{"integral"} to fit its
anti-derivative.
}
\item{norm}{
\samp{0} to use the terms as originally given by \cite{Devlin and
Weeks (1986)}, \samp{1} to normalize non-linear terms by the cube
of the spacing between the last two knots, \samp{2} to normalize by
the square of the spacing between the first and last knots (the
default). \code{norm=2} has the advantage of making all nonlinear
terms beon the x-scale.
}
\item{rpm}{
If given, any \code{NA}s in \code{x} will be replaced with the value
\code{rpm} after estimating any knot locations.
}
\item{pc}{
Set to \code{TRUE} to replace the design matrix with orthogonal
(uncorrelated) principal components computed on the scaled, centered
design matrix
}
\item{fractied}{
If the fraction of observations tied at the lowest and/or highest
values of \code{x} is greater than or equal to \code{fractied}, the
algorithm attempts to use a different algorithm for knot finding
based on quantiles of \code{x} after excluding the one or two values
with excessive ties. And if the number of unique \code{x} values
excluding these values is small, the unique values will be used as
the knots. If the number of knots to use other than these exterior
values is only one, that knot will be at the median of the
non-extreme \code{x}. This algorithm is not used if any interior
values of \code{x} also have a proportion of ties equal to or
exceeding \code{fractied}.}
}
\value{
If \code{knots.only=TRUE}, returns a vector of knot
locations. Otherwise returns a matrix with \code{x} (if
\code{inclx=TRUE}) followed by \eqn{\code{nk}-2} nonlinear terms. The
matrix has an attribute \code{knots} which is the vector of knots
used. When \code{pc} is \code{TRUE}, an additional attribute is
stored: \code{pcparms}, which contains the \code{center} and
\code{scale} vectors and the \code{rotation} matrix.
}
\references{
Devlin TF and Weeks BJ (1986): Spline functions for logistic regression
modeling. Proc 11th Annual SAS Users Group Intnl Conf, p. 646--651.
Cary NC: SAS Institute, Inc.
}
\seealso{
\code{\link[splines]{ns}}, \code{\link{rcspline.restate}},
\code{\link[rms]{rcs}}
}
\examples{
x <- 1:100
rcspline.eval(x, nk=4, inclx=TRUE)
#lrm.fit(rcspline.eval(age,nk=4,inclx=TRUE), death)
x <- 1:1000
attributes(rcspline.eval(x))
x <- c(rep(0, 744),rep(1,6), rep(2,4), rep(3,10),rep(4,2),rep(6,6),
rep(7,3),rep(8,2),rep(9,4),rep(10,2),rep(11,9),rep(12,10),rep(13,13),
rep(14,5),rep(15,5),rep(16,10),rep(17,6),rep(18,3),rep(19,11),rep(20,16),
rep(21,6),rep(22,16),rep(23,17), 24, rep(25,8), rep(26,6),rep(27,3),
rep(28,7),rep(29,9),rep(30,10),rep(31,4),rep(32,4),rep(33,6),rep(34,6),
rep(35,4), rep(36,5), rep(38,6), 39, 39, 40, 40, 40, 41, 43, 44, 45)
attributes(rcspline.eval(x, nk=3))
attributes(rcspline.eval(x, nk=5))
u <- c(rep(0,30), 1:4, rep(5,30))
attributes(rcspline.eval(u))
}
\keyword{regression}
\keyword{smooth}
|
