Isotonic regression, with or without tie groups

The non-decreasing sequence closest (least squares) to y – TDA's mmp, and with tie groups its mmp1/mmp2. Without groups this is plain pool-adjacent-violators and agrees with stats::isoreg exactly.

Usage

tda_isotonic(
  y,
  groups = NULL,
  ties = c("primary", "secondary"),
  dir = tempfile("tda"),
  ...
)

Arguments

y: a numeric vector, in the order to be respected.
groups: optional vector of the same length marking tie groups by consecutive runs of equal values.
ties: how tie groups are treated: "primary" or "secondary"; ignored without groups.
dir: working directory.
...: passed to tda_run.

Value

The fitted values, a numeric vector like y.

Details

groups marks observations whose order among themselves is not meaningful (ties in the ordering variable). Consecutive equal values form one group – the grouping follows runs, exactly as TDA reads its tie matrix, so c(1, 1, 2) is two groups but c(1, 2, 1) is three. How a group is treated is ties: "primary" (Kruskal's primary approach, mmp1) lets the fitted values untie freely – the group's values are sorted, fitted, and each observation receives its rank slot's value, so the result is monotone only up to reordering within groups; "secondary" (mmp2) forces one common value per group – the group mean is fitted and broadcast back.

Examples

tda_isotonic(c(5, 3, 4, 6, 2, 7))
#> [1] 4 4 4 4 4 7
# rows 1-2 tied, rows 4-6 tied:
tda_isotonic(c(5, 3, 4, 6, 2, 7), groups = c(1, 1, 2, 3, 3, 3),
             ties = "secondary")
#> [1] 4 4 4 5 5 5