hatMat {sfsmisc} | R Documentation |
Compute the hat matrix or smoother matrix, of ‘any’ (linear) smoother, smoothing splines, by default.
hatMat(x, trace= FALSE, pred.sm = function(x, y, ...) predict(smooth.spline(x, y, ...), x = x)$y, ...)
x |
numeric vector or matrix. |
trace |
logical indicating if the whole hat matrix, or only its trace, i.e. the sum of the diagonal values should be computed. |
pred.sm |
a function of at least two arguments (x,y)
which returns fitted values, i.e. y.hat, of length
compatible to x (and y ). |
... |
optionally further arguments to the smoother function
pred.sm . |
The hat matrix H (if trace = FALSE
as per default) or
a number, tr(H), the trace of H, i.e.,
sum(i) H[i,i].
Note that dim(H) == c(n, n)
where n <- length(x)
also in
the case where some x values are duplicated (aka ties).
Martin Maechler maechler@stat.math.ethz.ch
Hastie and Tibshirani (1990). Generalized Additive Models. Chapman \& Hall.
smooth.spline
, etc
require(stats) # for smooth.spline() or loess() x1 <- c(1:4, 7:12) H1 <- hatMat(x1, spar = 0.5) matplot(x1, H1, type = "l", main = "columns of smoother hat matrix") ## Example `pred.sm' arguments for hatMat() : pspl <- function(x,y,...) predict(smooth.spline(x,y, ...), x = x)$y ploes <- function(x,y,...) predict(loess(y ~ x, ...)) pksm <- function(x,y,...) ksmooth(sort(x),y, "normal", x.points=x, ...)$y ## Rather than ksmooth(): if(require("sm")) pksm2 <- function(x,y,...) sm.regression(x,y, display="none", eval.points=x, ...)$estimate all.equal(sum(diag((hatMat(c(1:4, 7:12), df = 4)))), hatMat(c(1:4, 7:12), df = 4, trace = TRUE), tol = 1e-12) ## TRUE ## Loess() example: Hl <- hatMat(x1, pr = ploes) cat(sprintf("df = %.2f\n", sum(diag(Hl)))) image(Hl)