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'))

knots

vector of knots used in the regression fit

coef

vector of coefficients from the fit. If the length of `coef`

is
\(\var{k}-1\), 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

`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 # }