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).
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'))
vector of knots used in the regression fit
vector of coefficients from the fit. If the length of coef is
length(knots), the
first coefficient must be for the linear term and remaining
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).
The default is to represent the cubic spline function corresponding
to the coefficients and knots. Set type = "integral" to
instead represent its anti-derivative.
a character string to use as the variable name in the LaTeX expression for the formula.
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.
normalization that was used in deriving the original nonlinear terms
used in the fit. See rcspline.eval for definitions.
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.
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".
text to place at the end of each line of output.
text with which to start the first line of output. Useful when adding LaTeX output to part of an existing formula
number of columns of printable text in begin
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 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.
# NOT RUN {
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
# }
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