smoothM: Smooth: wrapper function
In regr0: Building regression models

Description Usage Arguments Details Value Author(s) See Also Examples

Generate fits of a smoothing function for multiple y's. Smooths can be calculated within given groups.

  smoothM(x, y, weights = NULL, band = FALSE, group = NULL, power = 1,
          resid = "difference",
          par = 5 * length(x)^log10(1/2), parband = par*2^log10(2),
          iterations = 50, ...)

`x`	vector of x values.
`y`	vector or matrix of y values.
`weights`	vector of weights to be used for fitting.
`band`	logical: Should a band consisting of low and high smooth be calculated?
`group`	NULL or a factor that defines the groups for which the smooth is calculated.
`power`	`y` will be raised to `power` before smoothing. Results will be back-transformed. (Useful for smoothing absolute values for a 'scale plot', for which `power=0.5` is recommended.)
`resid`	Which residuals be calculated? `resid=1` or `="difference"` means usual residuals; `resid=2` or `="ratio"` means $y_i/\hat y_i$, which is useful to get scaled y's (regression residuals) according to a smooth fit in the scale plot.
`par, parband`	argument to be passed to the smoothing function, `parband` when calculating "band" smooths
`iterations`	argument passed on to the smoothing function.
`...`	Further arguments, passed to the smoothing function.

These functions are useful for generating the smooths enhancing residual plots. (smoothM) generates a smooth for a single x variable and multiple y's. It is used to draw smooths from simulated residuals. If argument group is specified, the smooths will be calculated within the specified groups.

NA's in either x or any column of y cause dropping the observation (equivalent to na.omit).

The smoothing function used to produce the smooth is smoothRegr, which relies loess by default. This may be changed via options(smoothFunction = func) where func is a smoothing function with the same arguments as smoothRegr.

smoothM: A list with components:

`x`	vector of x values, sorted, within levels of `group` if grouping is actif.
`y`	matrix with 1 or more columns of corresponding fitted values of the smoothing.
`group`	grouping factor, sorted, if actif. `NULL` otherwise.
`index`	vector of indices of the argument `x` used for sorting. This is useful to relate the results to the input. Use `ysmoothed[value$index,] <- value$y` to get values corresponding to input `y`.
`xorig`	original `x` values
`ysmorig`	corresponding fitted values
`residuals`	if required by the argument `resid`, residuals from the smooth fit are provided in the original order, i.e. `value$resid[i,j]` corresponds to the input `value$y[i,j]`.

If band==TRUE,

`yband`	vector of low and high smoothed values (for the first column of `y`)
`ybandindex`	Indicator if `yband` is a high value

Werner A. Stahel, ETH Zurich

smoothRegr

data(d.blast)
r.blast <-
  regr(log10(tremor)~location+log10(distance)+log10(charge), data=d.blast)
r.smooth <- smoothM( fitted(r.blast), residuals(r.blast))
showd(r.smooth$y)
plot(fitted(r.blast), resid(r.blast), main="Tukey-Anscombe Plot")
abline(h=0)
lines(r.smooth$x,r.smooth$y, col="red")

## grouped data
r.smx <- smoothM( d.blast$dist, residuals(r.blast), group=d.blast$location)
plot(d.blast$dist, resid(r.blast), main="Residuals against Regressor")
abline(h=0)
for (lg in 1:length(levels(r.smx$group))) {
  li <- as.numeric(r.smx$group)==lg 
  lines(r.smx$x[li],r.smx$y[li], col=lg+1, lwd=3)
}

## example with data from stats
data(swiss)
  plot(Fertility~Agriculture, swiss)

  r.sm <- smoothM( swiss$Agriculture, swiss$Fertility )
  lines(r.sm)

  r.sm <- smoothM( swiss$Agriculture, swiss$Fertility, band=TRUE )
  li <- r.sm$ybandind
  lines(r.sm$x[li], r.sm$yband[li], lty=2)
  lines(r.sm$x[!li], r.sm$yband[!li], lty=2)

## example with groups and band
  t.group <- swiss$Catholic>70
  plot(Fertility~Agriculture, swiss, pch=2+t.group, col=2+t.group)
  r.sm <- smoothM( swiss$Agriculture, swiss$Fertility,
                   group=t.group, band=TRUE )

  for (lg in c(FALSE,TRUE)) {
    lig <- which(r.sm$group==lg)
    lines(r.sm$x[lig], r.sm$y[lig], lty=1, col=2+lg)
    li <- r.sm$ybandind[lig]
    ligh <- lig[li]
    ligl <- lig[!li]
    lines(r.sm$x[ligh], r.sm$yband[ligh], lty=2+2*lg, col=2+lg)
    lines(r.sm$x[ligl], r.sm$yband[ligl], lty=2+2*lg, col=2+lg)
  }