Find noteworthy (unusual) points in a 2D plot

This function extends the logic used by showLabels to provide a more general collection of methods to identify unusual or "noteworthy" points in a two-dimensional display. Standard methods include Mahalanobis and Euclidean distance from the centroid, absolute value of distance from the mean of X or Y, absolute value of Y and absolute value of the residual in a model Y ~ X.

Usage

noteworthy(x, y = NULL, n = length(x), method = "mahal", level = NULL, ...)

Arguments

x, y: The x and y coordinates of a set of points. Alternatively, a single argument x can be provided, since xy.coords(x, y) is used for construction of the coordinates.
n: Maximum number of points to identify. If set to 0, no points are identified.
method: Method of point identification. See Details.
level: Where appropriate, if supplied, the identified points are filtered so that only those for which the criterion is < level
...: Other arguments, silently ignored

Details

The `method` argument determines how the points to be identified are selected:

"mahal": Treat (x, y) as if it were a bivariate sample, and select cases according to their Mahalanobis distance from (mean(x), mean(y)).
"dsq": Similar to "mahal" but uses squared Euclidean distance.
"x": Select points according to their value of abs(x - mean(x)).
"y": Select points according to their value of abs(y - mean(y)).
"r": Select points according to their value of abs(y), as may be appropriate in residual plots, or others with a meaningful origin at 0, such as a chi-square QQ plot.
"ry": Fit the linear model, y ~ x and select points according to their absolute residuals.
case IDs: method can be an integer vector of case numbers in 1:length{x}, in which case those cases will be labeled.
numeric vector: method can be a vector of the same length as x consisting of values to determine the points to be labeled. For example, for a linear model mod, setting method=cooks.distance(mod) will label the n points corresponding to the largest values of Cook's distance. Warning: If missing data are present, points may be incorrectly selected.

In the case of method == "mahal" a value for level can be supplied. This is used as a filter to select cases whose criterion value exceeds level. In this case, the number of points identified will be less than or equal to n.

Examples

# example code
set.seed(47)
x <- c(runif(100), 1.5, 1.6, 0)
y <- c(2*x[1:100] + rnorm(100, sd = 1.2), -2, 6, 6 )
z <- y - x
mod <- lm(y ~ x)

# testing function to compare noteworthy with car::showLabels() 
testnote <- function(x, y, n, method=NULL, ...)  {
  plot(x, y)
  abline(lm(y ~ x))
  if (!is.null(method))
    car::showLabels(x, y, n=n, method = method) |> print()
  ids <- noteworthy(x, y, n=n, method = method, ...)
  text(x[ids], y[ids], labels = ids, col = "red")
  ids
  }

  # Mahalanobis distance 
testnote(x, y, n = 5, method = "mahal")

#> [1] 101 103 102  72  36
#> [1] 101 103 102  72  36
testnote(x, y, n = 5, method = "mahal", level = .99)

#> [1] 101 103 102  72  36
#> [1] 101 103 102
  # Euclidean distance 
testnote(x, y, n = 5, method = "dsq")

#> NULL
#> [1] 102 103  72 101  36

testnote(x, y, n = 5, method = "y")

#> [1] 102 103  72 101  36
#> [1] 102 103  72 101  36
testnote(x, y, n = 5, method = "ry")

#> NULL
#> [1] 103 101 102  72  36

  # a vector of criterion values
testnote(x, y, n = 5, method = Mahalanobis(data.frame(x,y)))

#> [1] 101 103 102  72  36
#> [1] 101 103 102  72  36
testnote(x, y, n = 5, method = z)

#> [1] 103 102   3  77  16
#> [1] 103 102   3  77  16
  # vector of case IDs
testnote(x, y, n = 4, method = seq(10, 60, 10))

#> [1] 10 20 30 40 50 60
#> [1] 10 20 30 40 50 60
testnote(x, y, n = 4, method = which(cooks.distance(mod) > .25))

#> [1] 101 102 103
#> 101 102 103 
#> 101 102 103 

  # test use of xy.coords  
noteworthy(data.frame(x,y), n=4)
#> [1] 101 103 102  72
noteworthy(y ~ x, n=4)
#> [1] 101 103 102  72