# Re-state Restricted Cubic Spline Function This function re-states a restricted cubic spline function in the un-linearly-restricted form. Coefficients for that form are returned, along with an 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). ```r 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')) ``` ## 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 ## Returns `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 function, which is also return in character string format as the `text` attribute. `rcsplineFunction` returns an function with arguments `x` (a user-supplied numeric vector at which to evaluate the function), and some automatically-supplied other arguments. ## Author(s) Frank Harrell Department of Biostatistics, Vanderbilt University fh@fharrell.com ## See Also `rcspline.eval`, `ns`, `rcs`, `latex`, `Function.transcan` ## Examples ```r 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 ```

rcspline.restate function