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Population Stability Index

Source: R/obwoe_score.R
obwoe_psi.Rd

Compares how a variable, or a score, is distributed between two samples — typically the development window and a later vintage.

Usage

obwoe_psi(base, compare, levels = NULL, breaks = NULL, n_groups = 10L)

Arguments

base

Vector observed in the reference sample.

compare

Vector observed in the sample being monitored.

levels

Character vector of the categories or bin labels to compare over. Required when the inputs are not numeric; defaults to the union of the values seen.

breaks

Numeric vector of cut points used to band numeric inputs. NULL (default) bands them at the deciles of base.

n_groups

Integer. Number of bands when breaks is NULL. Default 10.

Value

A list with psi (the total), table (the contribution of each band) and flag, one of "stable", "watch" or "act" at the conventional 0.10 and 0.25 thresholds.

Details

$$\mathrm{PSI} = \sum_i (p_i - q_i)\,\ln\frac{p_i}{q_i}$$

which is the same symmetrised Kullback-Leibler divergence that defines Information Value, applied to two vintages of one variable instead of to two classes of one sample. The conventional reading is \(<0.10\) stable, \(0.10\)–\(0.25\) worth watching, \(>0.25\) act.

A band that is populated in one sample and empty in the other makes the divergence infinite. That is reported as Inf rather than smoothed away, because a segment that has vanished is exactly what monitoring exists to catch; the per-band table shows which one.

See also

obwoe_scorecard

Examples

set.seed(1)
obwoe_psi(rnorm(1000), rnorm(1000))
#> $psi
#> [1] 0.01130065
#> 
#> $flag
#> [1] "stable"
#> 
#> $table
#>                band pct_base pct_compare     psi_band
#> 1      [-Inf,-1.34]      0.1       0.103 8.867641e-05
#> 2    (-1.34,-0.882]      0.1       0.099 1.005034e-05
#> 3   (-0.882,-0.511]      0.1       0.111 1.147960e-03
#> 4   (-0.511,-0.296]      0.1       0.081 4.003700e-03
#> 5  (-0.296,-0.0353]      0.1       0.105 2.439508e-04
#> 6   (-0.0353,0.245]      0.1       0.112 1.359944e-03
#> 7     (0.245,0.536]      0.1       0.085 2.437784e-03
#> 8     (0.536,0.854]      0.1       0.096 1.632880e-04
#> 9      (0.854,1.32]      0.1       0.113 1.588829e-03
#> 10      (1.32, Inf]      0.1       0.095 2.564665e-04
#> 
obwoe_psi(rnorm(1000), rnorm(1000, mean = 0.6))
#> $psi
#> [1] 0.3198493
#> 
#> $flag
#> [1] "act"
#> 
#> $table
#>                band pct_base pct_compare     psi_band
#> 1      [-Inf,-1.29]      0.1       0.032 0.0774815313
#> 2    (-1.29,-0.836]      0.1       0.044 0.0459749109
#> 3   (-0.836,-0.483]      0.1       0.063 0.0170953120
#> 4   (-0.483,-0.245]      0.1       0.061 0.0192775566
#> 5  (-0.245,-0.0055]      0.1       0.075 0.0071920518
#> 6   (-0.0055,0.233]      0.1       0.089 0.0012818720
#> 7     (0.233,0.538]      0.1       0.108 0.0006156883
#> 8     (0.538,0.919]      0.1       0.144 0.0160442970
#> 9      (0.919,1.38]      0.1       0.149 0.0195400299
#> 10      (1.38, Inf]      0.1       0.235 0.1153460693
#>