A metric of the two-by-two table of decisions

The predictions are cut into presence and absence, and the table of decisions against observations is summarised. With H the hits, F the false alarms, M the misses and C the correct negatives:

Usage

table_metric(
  y,
  p,
  metric = names(.table_metrics),
  rule = c("youden", "kappa", "prevalence", "mpa"),
  threshold = NULL,
  perc = 0.9
)

Arguments

y: Observed presence-absence, 0/1 or logical.
p: Predicted scores for the same units, in the same order. Higher means presence.
metric: One of the names in the table.
rule: Threshold rule: "youden", "kappa", "prevalence" or "mpa". kappa_score() cuts at "prevalence" by default, the rule the registered kappa metric reads, and the other functions at "youden".
threshold: NULL for the maximum over every cut, or one cut, presence being predicted at p >= threshold.
perc: For rule = "mpa", the share of presences the cut must keep, 0.9 by default. Where a rule is named without a call to decision_threshold() it takes that default.

Value

One number, or NA where the cell defines none.

Details

`metric`	reads
`"pod"`	probability of detection, `H / (H + M)`
`"pofd"`	probability of false detection, `F / (F + C)`
`"far"`	false alarm ratio, `F / (H + F)`
`"sr"`	success ratio, `H / (H + F)`
`"accuracy"`	`(H + C) / n`
`"bias"`	`(H + F) / (H + M)`, the presences called against the presences there are
`"or"`	odds ratio, `H C / (M F)`
`"orss"`	odds ratio skill score, `(H C - M F) / (H C + M F)`
`"csi"`	critical success index, `H / (H + M + F)`
`"ets"`	equitable threat score, `(H - h) / (H + M + F - h)` with `h = (H + M)(H + F) / n`

These are biomod2's evaluation statistics. biomod2 reads each at the cut that brings that statistic closest to its own optimum on a grid of 100 cuts; here the cut is the one rule of decision_threshold() selects, "youden" by default, or a threshold learned elsewhere. Read at the cut that optimises it, some of these are trivial, so the cut is a separate choice and stays fixed while the statistic changes. Each is registered under its name at the default rule, so grain_ladder(metric = "csi") reads it. A registration at another rule is one line: register_metric("csi_kappa", function(y, p) table_metric(y, p, "csi", "kappa")).

A value the table does not define, a zero denominator, is NA, as is a cell of one class.

Examples

y <- c(0, 0, 0, 1, 1, 1, 0, 1)
p <- c(0.10, 0.20, 0.35, 0.40, 0.60, 0.90, 0.55, 0.70)
table_metric(y, p, "pod")
table_metric(y, p, "csi", threshold = 0.5)