Calibration robustness and alternative sets

Calibration robustness needs a little more structure than the cutoff and case tests. qcaERT has to know which raw columns created the calibrated conditions, which calibration method was used, and which thresholds may be perturbed.

library(QCA)
library(qcaERT)

data(LR)

conditions <- c("DEV", "URB", "LIT", "IND", "STB")
outcome <- "SURV"
dir_exp <- rep("1", length(conditions))

thresholds <- list(
  DEV = findTh(LR$DEV, groups = 7),
  URB = findTh(LR$URB, groups = 4),
  LIT = findTh(LR$LIT, groups = 4),
  IND = findTh(LR$IND, groups = 4),
  STB = findTh(LR$STB, groups = 4),
  SURV = findTh(LR$SURV, groups = 4)
)

dat <- LR
dat$DEV <- calibrate(LR$DEV, type = "fuzzy", thresholds = thresholds$DEV)
dat$URB <- calibrate(LR$URB, type = "fuzzy", thresholds = thresholds$URB)
dat$LIT <- calibrate(LR$LIT, type = "fuzzy", thresholds = thresholds$LIT)
dat$IND <- calibrate(LR$IND, type = "fuzzy", thresholds = thresholds$IND)
dat$STB <- calibrate(LR$STB, type = "fuzzy", thresholds = thresholds$STB)
dat$SURV <- calibrate(LR$SURV, type = "fuzzy", thresholds = thresholds$SURV)

Use calibration specifications

Calibration-family functions use calib_spec: a named list with one entry per set you want qcaERT to be able to recalibrate. This structure keeps the raw source, calibration type, calibration method, thresholds, and extra QCA::calibrate() arguments together.

calib_spec <- list(
  DEV = list(
    raw = "DEV",
    type = "fuzzy",
    method = "direct",
    thresholds = thresholds$DEV
  ),
  URB = list(
    raw = "URB",
    type = "fuzzy",
    thresholds = thresholds$URB
  ),
  LIT = list(
    raw = "LIT",
    type = "fuzzy",
    thresholds = thresholds$LIT
  ),
  IND = list(
    raw = "IND",
    type = "fuzzy",
    thresholds = thresholds$IND
  ),
  STB = list(
    raw = "STB",
    type = "fuzzy",
    thresholds = thresholds$STB
  )
)

calib_spec_outcome <- calib_spec
calib_spec_outcome$SURV <- list(
  raw = "SURV",
  type = "fuzzy",
  thresholds = thresholds$SURV
)

Each entry contains:

raw: the raw column name in raw.data
type: "crisp" or "fuzzy"
thresholds: the baseline calibration thresholds
method: optional, passed to QCA::calibrate()
calibrate: optional list of extra QCA::calibrate() arguments

For condition-only runs, calib_spec must contain exactly one entry for every condition in conditions. When test.outcome = TRUE, it must contain the conditions plus one entry named by outcome. This keeps the recalibration structure the same across the calibration-family functions.

Conditions and test.conditions

conditions is the full condition set in the QCA model.

test.conditions is the subset whose thresholds should be perturbed.

calib.test(
  raw.data = LR,
  calib.data = dat,
  outcome = "SURV",
  conditions = c("DEV", "URB", "LIT", "IND", "STB"),
  calib_spec = calib_spec,
  test.conditions = c("DEV", "URB"),
  unit_step = NULL,
  unit_step_divisor = 10,
  max_steps = 5,
  incl.cut = 0.8,
  n.cut = 1,
  solution = "all",
  dir.exp = rep("1", 5),
  progress = TRUE
)

If test.conditions is not supplied, qcaERT tests all conditions in conditions.

Outcome calibration

The outcome is not a condition and should not be placed in conditions. To test outcome calibration, keep the QCA model unchanged and request the outcome explicitly with test.outcome = TRUE.

Use test.conditions = NULL when you want to test only the outcome calibration.

calib_outcome <- calib.test(
  raw.data = LR,
  calib.data = dat,
  outcome = outcome,
  conditions = conditions,
  calib_spec = calib_spec_outcome,
  test.conditions = NULL,
  test.outcome = TRUE,
  unit_step = NULL,
  unit_step_divisor = 10,
  max_steps = 5,
  incl.cut = 0.8,
  n.cut = 1,
  solution = "all",
  dir.exp = dir_exp,
  progress = TRUE
)

calib_outcome
as.data.frame(calib_outcome)

Anchors by calibration type

qcaERT uses anchor names that match the calibration method.

Calibration type	Thresholds	Anchor names
Crisp	one threshold	`T`
Fuzzy direct, three thresholds	`c(E, C, I)`	`E`, `C`, `I`
Fuzzy direct, six thresholds	`c(E1, C1, I1, I2, C2, E2)`	`E1`, `C1`, `I1`, `I2`, `C2`, `E2`
Fuzzy indirect	ordered cutpoints	`T1`, `T2`, …

By default, anchors_to_test = NULL means qcaERT uses all anchors implied by each tested condition.

calib.test(
  raw.data = LR,
  calib.data = dat,
  outcome = "SURV",
  conditions = conditions,
  calib_spec = calib_spec,
  test.conditions = "DEV",
  anchors_to_test = c("E1", "C1", "I1", "I2", "C2", "E2"),
  unit_step = NULL,
  unit_step_divisor = 10,
  max_steps = 5,
  incl.cut = 0.8,
  n.cut = 1,
  solution = "all",
  dir.exp = dir_exp,
  progress = TRUE
)

Scale-aware perturbations

Raw columns can live on very different scales. A one-unit move may be tiny for an economic measure and huge for an index. For that reason, qcaERT can compute the threshold step automatically.

calib_out <- calib.test(
  raw.data = LR,
  calib.data = dat,
  outcome = outcome,
  conditions = conditions,
  calib_spec = calib_spec,
  test.conditions = c("DEV", "URB"),
  unit_step = NULL,
  unit_step_divisor = 10,
  max_steps = 5,
  incl.cut = 0.8,
  n.cut = 1,
  solution = "all",
  dir.exp = dir_exp,
  progress = TRUE
)

With unit_step = NULL, qcaERT derives a step from the threshold geometry for each condition. unit_step_divisor = 10 means the function uses roughly one-tenth of the relevant threshold spacing as the move size.

Use a manually supplied unit_step only when you have a substantive reason to define the perturbation size yourself.

Direct, indirect, and six-threshold calibration

qcaERT supports the calibration-perturbation cases used in the ordinary QCA workflow:

crisp calibration
fuzzy direct calibration with three thresholds
fuzzy direct calibration with six thresholds
fuzzy indirect calibration with ordered cutpoints

For indirect calibration, qcaERT treats thresholds as ordered cutpoints. Anchor names are positional: T1, T2, and so on.

This scope is deliberate. calib.test() and altset.test() perturb explicit calibration thresholds; they are not general multi-value calibration robustness tools and they do not rediscover thresholds during the perturbation search.

calib_spec_indirect <- list(
  A = list(
    raw = "A_raw",
    type = "fuzzy",
    method = "indirect",
    thresholds = c(10, 20, 30, 40)
  )
)

The same output convention applies: results is the clean table, diagnostics keeps the path detail, and bounds summarizes the tested threshold bounds.

From calibration bounds to alternative sets

calib.test() asks: how far can one anchor move in one direction before the monitored solution changes?

altset.test() asks: what happens across sampled alternative analysis settings?

altset_out <- altset.test(
  raw.data = LR,
  calib.data = dat,
  outcome = outcome,
  conditions = conditions,
  calib_spec = calib_spec,
  test.conditions = c("DEV", "URB"),
  unit_step = NULL,
  unit_step_divisor = 10,
  calib_max_steps = 5,
  incl.cut = 0.8,
  incl_step = 0.02,
  incl_max_steps = 5,
  n.cut = 1,
  ncut_step = 1,
  ncut_max_steps = 2,
  n_draws = 50,
  seed = 123,
  solution = "all",
  dir.exp = dir_exp,
  progress = TRUE
)

altset_out
as.data.frame(altset_out)
altset_out$summary

The same calibration specification is used in both functions. This is intentional: the meaning of conditions, test.conditions, and test.outcome should not change from one sibling function to another.

altset_outcome <- altset.test(
  raw.data = LR,
  calib.data = dat,
  outcome = outcome,
  conditions = conditions,
  calib_spec = calib_spec_outcome,
  test.conditions = c("DEV", "URB"),
  test.outcome = TRUE,
  unit_step = NULL,
  unit_step_divisor = 10,
  calib_max_steps = 5,
  incl.cut = 0.8,
  incl_step = 0.02,
  incl_max_steps = 5,
  n.cut = 1,
  ncut_step = 1,
  ncut_max_steps = 2,
  n_draws = 50,
  seed = 456,
  solution = "all",
  dir.exp = dir_exp,
  progress = TRUE
)

as.data.frame(altset_outcome)

Plotting calibration results

If ggplot2 is installed, plot.calib_test() can show interval, heatmap, and trace views.

plot(calib_out, solution_type = "conservative")
plot(calib_out, solution_type = "conservative", type = "heatmap")
plot(calib_out, solution_type = "conservative", type = "trace", set = "DEV", anchor = "E1", direction = "lower")

Trace plots require an existing condition-anchor-direction path. If the requested path is unavailable, the error message lists the available paths.

See ?qcaERT_plots for the plotting API and ?qcaERT_conventions for the package-wide conventions.