rcspline.restate: Re-state Restricted Cubic Spline Function

Description

This function re-states a restricted cubic spline function in the un-linearly-restricted form. Coefficients for that form are returned, along with an R 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).

Usage

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, type=c('ordinary', 'integral'))

Value

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 R function, which is also return in character string format as the text attribute. rcsplineFunction

returns an R function with arguments x (a user-supplied numeric vector at which to evaluate the function), and some automatically-supplied other arguments.

Arguments

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 is equal to the 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

Author

Frank Harrell
Department of Biostatistics, Vanderbilt University
fh@fharrell.com

Examples

Run this code

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