Takes the raw score of any engine (the scorecard logit, the output of
a tree challenger, a legacy score) to the scale defined by base_score,
base_odds and pdo, recording odds_orientation on the object. This is
what makes two scorecards directly comparable. It runs automatically
inside scr_scorecard(); it is exposed to align other
scores to the same scale.
Arguments
- raw
Raw score: an event logit (or any score on which a higher value means a higher probability of the event).
- y
0/1 outcome vector (numeric or logical), same length as
raw.- base_score
Score at which the odds are
base_odds.- base_odds
Odds at
base_score, positive, in the orientation ofdirection.- pdo
Points that double the odds, positive.
- direction
"higher_is_safer"or"higher_is_riskier".- method
"regression"(default) or"direct".- n_bands
Bands of the calibration regression.
- laplace
Smoothing of the counts per band.
- weights
Optional non-negative weights per observation (sample reweighting), of the length of
raw.
Value
An scr_align object with base_score, base_odds, pdo,
direction, odds_orientation, factor, offset, sign,
calibration (method, intercept, slope, r2, n_bands, bands)
and the final coefficients a and b of score = a + b * raw. Use
predict.scr_align() to apply it.
Mechanism
With method = "regression" (default): the raw score is banded by
quantiles on the reference data, the empirical log-odds of every band is
computed with Laplace smoothing in the orientation direction implies,
and a regression weighted by band size fits
$$\ln(\mathrm{odds}) = I + S \cdot \mathrm{raw}.$$
This absorbs sample reweighting, miscalibration of the WOE fit and prior
shift. It then composes with the PDO map:
$$\mathrm{factor} = \mathrm{pdo}/\ln 2,\quad
\mathrm{offset} = \mathrm{base\_score} - \mathrm{factor}\cdot\ln(\mathrm{base\_odds}),$$
$$\mathrm{score} = \mathrm{offset} + \mathrm{factor}\,(I + S\cdot\mathrm{raw}) = a + b\cdot\mathrm{raw}.$$
With method = "direct", the model is assumed calibrated: I = 0 and
S is the sign of the direction (-1 under higher_is_safer, +1
under higher_is_riskier), that is, ln(odds) is raw itself in the
right orientation.
Odds orientation
base_odds is always expressed in the orientation direction implies:
non-event:event ("safe:event") under higher_is_safer, event:non-event
("event:safe") under higher_is_riskier. The same word, odds,
changes meaning between the two, and that is the most common sign trap in
the literature; hence the object records odds_orientation explicitly.
See also
Other stages:
scr_bin(),
scr_cutoff(),
scr_model(),
scr_reject(),
scr_scorecard(),
scr_select(),
scr_split(),
scr_strategy(),
scr_triage()
Examples
set.seed(3)
y <- stats::rbinom(4000, 1, 0.15)
raw <- stats::qlogis(0.15) + 1.3 * y + stats::rnorm(4000, sd = 1.2)
al <- scr_align(raw, y, base_score = 600, base_odds = 50, pdo = 20)
al
#> <scr_align> 600 points at odds 50:1 (safe:event), PDO 20 | higher_is_safer
#> factor = 28.853901 | offset = 487.122876
#> calibration: ln(odds) = 0.784416 + -0.827142 * raw (adj. R2 = 0.9900, 10 bands)
#> score = 509.756344 + -23.866273 * raw
head(predict(al, raw))
#> [1] 579.0785 545.5461 534.3009 575.8285 543.0500 562.7087
head(predict(al, raw, type = "prob"))
#> [1] 0.03966021 0.11662403 0.16313782 0.04417982 0.12583606 0.06788722
# propensity: more points = more event, odds event:non-event
scr_align(raw, y, base_score = 500, base_odds = 1/9, pdo = 40,
direction = "higher_is_riskier")
#> <scr_align> 500 points at odds 0.1111111:1 (event:safe), PDO 40 | higher_is_riskier
#> factor = 57.707802 | offset = 626.797000
#> calibration: ln(odds) = -0.784416 + 0.827142 * raw (adj. R2 = 0.9900, 10 bands)
#> score = 581.530064 + 47.732546 * raw