Calculate Generalized Discrimination Score 2AFC

This is the master routine for the calculation the Generalized Discrimination Score (aka Two-Alternatives Forced Choice Score - 2AFC) as described in the Paper of Mason and Weigel (2009). This routine requires, as input, datasets of forecasts and corresponding observations, as well as a specification of the verification context. The routine checks whether the input data are consistent with the verification context, then calls the appropriate function to calculate the 2AFC, and finally returns the 2AFC skill value.

Usage

afc(obsv, fcst, obsv.type, fcst.type, m = 0, m2 = 0, na.rm = FALSE)

Arguments

obsv: Vector of observations. The required format depends on the specific verification context. More details below.
fcst: Vector or two-dimensional array of forecasts. The required format depends on the specific verification context. More details below.
obsv.type: Character specifying the type of the observations. Possible values: "d" (dichotomous), "m" (polychotomous with ordinal categories), "n" (polychotomous with nominal categories), "c" (continuous).
fcst.type: Character specifying the type of the forecasts. Possible values: "d" (dichotomous), "m" (polychotomous with ordinal categories), "n" (polychotomous with nominal categories), "p" (probabilistic), "c" (continuous) and "e" (ensemble).
m: Number of observation or forecast categories (only required if obsv.type or fcst.type equals "m" or "n")
m2: Number of forecast categories (only required if both obsv.type and fcst.type equal "m"). The number of observation categories is then specified by the argument m above.
na.rm: logical; if TRUE pairs where obsv or fcst is NA are removed before scoring. Default FALSE returns NA if any input contains NA.

Value

p.afc: Value of Generalized Discrimination Score (2AFC)

Details

Depending on the specific verification context (i.e. the choice for obsv.type and fcst.type), this routine calls the appropriate function(s) to calculate the 2AFC score. The following combinations of obsv.type and fcst.type are possible: (1) "d-d"; (2) "d-m"; (3) "d-p"; (4) "d-c"; (5) "d-e"; (6) "m-m"; (7) "m-p"; (8) "m-c"; (9) "m-e"; (10) "n-n"; (11) "n-p"; (12) "c-c"; (13) "c-e". The required format of the input data obsv and fcst depends on the verification context:

(1) "d-d":
obsv: vector with dichotomous observations (values in {0,1})
fcst: vector of same length as obsv with dichotomous forecasts (values in {0,1})

(2) "d-m":
obsv: vector with dichotomous observations (values in {0,1})
fcst: vector of same length as obsv with polychotomous forecasts (values in {1,..,m})

(3) "d-p":
obsv: vector with dichotomous observations (values in {0,1})
fcst: vector of same length as obsv with forecast probabilities for the event to happen

(4) "d-c":
obsv: vector with dichotomous observations (values in {0,1})
fcst: vector of same length as obsv with real-valued forecasts

(5) "d-e":
obsv: vector with dichotomous observations (values in {0,1})
fcst: two-dimensional array with ensemble forecasts; dim(fcst)[1] = length(obsv); dim(fcst)[2] = ensemble size.

(6) "m-m":
obsv: vector with polychotomous observations (values in {1,..,m})
fcst: vector of same length as obsv with polychotomous forecasts (values in {1,..,m2})

(7) "m-p":
obsv: vector with polychotomous observations (values in {1,..,m})
fcst: two-dimensional array with forecast probabilities for the m categories; dim(fcst)[1] = length(obsv); dim(fcst)[2] = m

(8) "m-c":
obsv: vector with polychotomous observations (values in {1,..,m})
fcst: vector of same length as obsv with real-valued forecasts

(9) "m-e":
obsv: vector with polychotomous observations (values in {1,..,m})
fcst: two-dimensional array with ensemble forecasts; dim(fcst)[1] = length(obsv); dim(fcst)[2] = ensemble size.

(10) "n-n":
obsv: vector with polychotomous observations (values in {1,..,m})
fcst: vector of same length as obsv with polychotomous forecasts (values in {1,..,m})

(11) "n-p":
Same as "m-p".

(12) "c-c":
obsv: vector with real-valued observations
fcst: vector of same length as obsv with real-valued forecasts

(13) "c-e":
obsv: vector with real-valued observations
fcst: two-dimensional array with ensemble forecasts; dim(fcst)[1] = length(obsv); dim(fcst)[2] = ensemble size.

References

S.J. Mason and A.P. Weigel, 2009. A generic verification framework for administrative purposes. Mon. Wea. Rev., 137, 331-349

Author

Andreas Weigel, Federal Office of Meteorology and Climatology, MeteoSwiss, Zurich, Switzerland

Examples

  data(cnrm.nino34.dd)
  obsv = cnrm.nino34.dd$obsv
  fcst = cnrm.nino34.dd$fcst
  afc(obsv, fcst, obsv.type="d", fcst.type="d")
#> [1] 0.9266667

  data(cnrm.nino34.dm)
  obsv = cnrm.nino34.dm$obsv
  fcst = cnrm.nino34.dm$fcst
  afc(obsv, fcst, obsv.type="d", fcst.type="m", m=4)
#> [1] 0.952

  data(cnrm.nino34.dp)
  obsv = cnrm.nino34.dp$obsv
  fcst = cnrm.nino34.dp$fcst
  afc(obsv, fcst, obsv.type="d", fcst.type="p")
#> [1] 0.9826667

  data(cnrm.nino34.dc)
  obsv = cnrm.nino34.dc$obsv
  fcst = cnrm.nino34.dc$fcst
  afc(obsv, fcst, obsv.type="d", fcst.type="c")
#> [1] 0.9893333

  data(cnrm.nino34.de)
  obsv = cnrm.nino34.de$obsv
  fcst = cnrm.nino34.de$fcst
  afc(obsv, fcst, obsv.type="d", fcst.type="e")
#> [1] 0.984

  data(cnrm.nino34.mm)
  obsv = cnrm.nino34.mm$obsv
  fcst = cnrm.nino34.mm$fcst
  afc(obsv, fcst, obsv.type="m", fcst.type="m", m=4, m2=4)
#> [1] 0.9024605

  data(cnrm.nino34.mp)
  obsv = cnrm.nino34.mp$obsv
  fcst = cnrm.nino34.mp$fcst
  afc(obsv, fcst, obsv.type="m", fcst.type="p", m=4)
#> [1] 0.9200351

  data(cnrm.nino34.mc)
  obsv = cnrm.nino34.mc$obsv
  fcst = cnrm.nino34.mc$fcst
  afc(obsv, fcst, obsv.type="m", fcst.type="c", m=4)
#> [1] 0.9191564

  data(cnrm.nino34.me)
  obsv = cnrm.nino34.me$obsv
  fcst = cnrm.nino34.me$fcst
  afc(obsv, fcst, obsv.type="m", fcst.type="e", m=4)
#> [1] 0.9261863

  data(cnrm.nino34.mm)
  obsv = cnrm.nino34.mm$obsv
  fcst = cnrm.nino34.mm$fcst
  afc(obsv, fcst, obsv.type="n", fcst.type="n", m=4)
#> [1] 0.8049209

  data(cnrm.nino34.mp)
  obsv = cnrm.nino34.mp$obsv
  fcst = cnrm.nino34.mp$fcst
  afc(obsv, fcst, obsv.type="n", fcst.type="p", m=4)
#> [1] 0.8580844

  data(cnrm.nino34.cc)
  obsv = cnrm.nino34.cc$obsv
  fcst = cnrm.nino34.cc$fcst
  afc(obsv, fcst, obsv.type="c", fcst.type="c")
#> [1] 0.8717949

  data(cnrm.nino34.ce)
  obsv = cnrm.nino34.ce$obsv
  fcst = cnrm.nino34.ce$fcst
  afc(obsv, fcst, obsv.type="c", fcst.type="e")
#> [1] 0.8735561