Compute the Value of a Function Over a Local Region Of An X-Y Plot

This function applies the specified function to the sets of y values that are defined by overlapping "windows" in the x-dimension. For example, setting fun=mean returns local means, while setting fun=function(x) sqrt(var(x)) returns local estimates of the standard deviation.

wapply(x, y, fun=mean, method="range", width, n=50, drop.na=TRUE,
       pts, ...)

Arguments

x

vector of x values for (x,y) pairs

y

vector of y values for (x,y) pairs

fun

function to be applied

method

method of defining an x-neighborhood. One of "width","nobs","range", or "fraction". See details.

width

width of an x-neighborhood. See details.

n

Number of equally spaced points at which to compute local estimates. See details.

drop.na

should points which result in missing values NA be omitted from the return value. Defaults to true.

pts

x locations at which to compute the local mean when using the "width" or "range" methods. Ignored otherwise.

...

arguments to be passed to fun

Details

Two basic techniques are available for determining what points fall within the same x-neighborhood. The first technique uses a window with a fixed width in the x-dimension and is is selected by setting method="width" or method="range". For method="width" the width argument is an absolute distance in the x-dimension. For method="range", the width is expressed as a fraction of the x-range. In both cases, pts specifies the points at which evaluation of fun occurs. When pts is omitted, n x values equally spaced along the x range are used.

The second technique uses windows containing k neighboring points. The (x,y) pairs are sorted by the x-values and the nearest k/2 points with higher x values and the k/2 nearest points with lower x values are included in the window. When method="nobs", k equals width (actually 2*floor(width/2) ). When method="fraction", width specifies what fraction of the total number of points should be included. The actual number of points included in each window will be floor(n*frac/2)*2. Regardless of the value of pts, the function fun will be evaluated at all x locations.

Value

Returns a list with components

x

x location'

y

Result of applying fun to the window about each x location

Author

Gregory R. Warnes greg@warnes.net

Examples

#show local mean and inner 2-sd interval to help diagnose changing mean
#or variance structure
x <- 1:1000
y <- rnorm(1000, mean=1, sd=1 + x/1000 )

plot(x,y)
lines(wapply(x,y,mean),col="red")

CL <- function(x,sd) mean(x)+sd*sqrt(var(x))

lines(wapply(x,y,CL,sd= 1),col="blue") 
lines(wapply(x,y,CL,sd=-1),col="blue") 
lines(wapply(x,y,CL,sd= 2),col="green")
lines(wapply(x,y,CL,sd=-2),col="green")


#show local mean and inner 2-sd interval to help diagnose changing mean
#or variance structure
x <- 1:1000
y <- rnorm(1000, mean=x/1000, sd=1)

plot(x,y)
lines(wapply(x,y,mean),col="red")

CL <- function(x,sd) mean(x)+sd*sqrt(var(x))

lines(wapply(x,y,CL,sd= 1,method="fraction",width=1/20),col="blue")
lines(wapply(x,y,CL,sd=-1,method="fraction",width=1/20),col="blue")
lines(wapply(x,y,CL,sd= 2,method="nobs",width=250),col="green")
lines(wapply(x,y,CL,sd=-2,method="nobs",width=250),col="green")