| rcspline.restate {Hmisc} | R Documentation |
This function re-states a restricted cubic spline function in
the un-linearly-restricted form. Coefficients for that form are
returned, along with an S functional representation of this function
and a LaTeX character representation of the function.
rcsplineFunction is a fast function that creates a function to
compute a restricted cubic spline function with given coefficients and
knots, without reformatting the function to be pretty (i.e., into
unrestricted form).
rcspline.restate(knots, coef,
type=c("ordinary","integral"),
x="X", lx=nchar(x),
norm=2, columns=65, before="& &", after="\",
begin="", nbegin=0, digits=max(8, .Options$digits))
rcsplineFunction(knots, coef, norm=2)
knots |
vector of knots used in the regression fit |
coef |
vector of coefficients from the fit. If the length of coef is
k-1, where k=length(knots), the first coefficient must be
for the linear term and remaining k-2 coefficients
must be for the constructed terms (e.g., from rcspline.eval).
If the length of coef is k, an intercept is assumed to be in
the first element (or a zero is prepended to coef for
rcsplineFunction).
|
type |
The default is to represent the cubic spline function corresponding
to the coefficients and knots. Set type="integral" to instead represent
its anti-derivative.
|
x |
a character string to use as the variable name in the LaTeX expression for the formula. |
lx |
length of x to count with respect to columns. Default is length
of character string contained by x. You may want to set lx
smaller than this if it includes non-printable LaTeX commands.
|
norm |
normalization that was used in deriving the original nonlinear terms
used in the fit. See rcspline.eval for definitions.
|
columns |
maximum number of symbols in the LaTeX expression to allow before inserting a newline (\\) command. Set to a very large number to keep text all on one line. |
before |
text to place before each line of LaTeX output. Use "& &" for an equation
array environment in LaTeX where you want to have a left-hand prefix
e.g. f(X) & = & or using \lefteqn.
|
after |
text to place at the end of each line of output. |
begin |
text with which to start the first line of output. Useful when adding LaTeX output to part of an existing formula |
nbegin |
number of columns of printable text in begin
|
digits |
number of significant digits to write for coefficients and knots |
rcspline.restate returns a vector of coefficients. The
coefficients are un-normalized and two coefficients are added that are
linearly dependent on the other coefficients and knots. The vector of
coefficients has four attributes. knots is a vector of knots,
latex is a vector of text strings with the LaTeX representation
of the formula. columns.used is the number of columns used in the
output string since the last newline command. function is an S
function, which is also return in character string format as the
text attribute. rcsplineFunction returns an S function
with arguments x (a user-supplied numeric vector at which to
evaluate the function), and some automatically-supplied other arguments.
Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu
rcspline.eval, ns, rcs, latex, Function.transcan
set.seed(1)
x <- 1:100
y <- (x - 50)^2 + rnorm(100, 0, 50)
plot(x, y)
xx <- rcspline.eval(x, inclx=TRUE, nk=4)
knots <- attr(xx, "knots")
coef <- lsfit(xx, y)$coef
options(digits=4)
# rcspline.restate must ignore intercept
w <- rcspline.restate(knots, coef[-1], x="{\\rm BP}")
# could also have used coef instead of coef[-1], to include intercept
cat(attr(w,"latex"), sep="\n")
xtrans <- eval(attr(w, "function"))
# This is an S function of a single argument
lines(x, coef[1] + xtrans(x), type="l")
# Plots fitted transformation
xtrans <- rcsplineFunction(knots, coef)
xtrans
lines(x, xtrans(x), col='blue')
#x <- blood.pressure
xx.simple <- cbind(x, pmax(x-knots[1],0)^3, pmax(x-knots[2],0)^3,
pmax(x-knots[3],0)^3, pmax(x-knots[4],0)^3)
pred.value <- coef[1] + xx.simple %*% w
plot(x, pred.value, type='l') # same as above