Population stability index, with the fixed and the sample-size-adjusted threshold

PSI = sum((p - q) * ln(p / q)) over bins frozen on the base. Reports both thresholds side by side: the traditional fixed one (< 0.10 "stable", 0.10-0.25 "moderate", >= 0.25 "shift") and the sample-size-adjusted critical value of Yurdakul and Naranjo (2020), under which the PSI is asymptotically (1/n + 1/m) * chi-squared(B - 1). With n = m = 1000 and ten bins the 5% critical value is 0.034, not 0.10; on a monthly base of a hundred thousand rows, PSI = 0.01 is already significant. The fixed threshold remains what the market knows; the adjusted one is what the statistics support.

Usage

scr_psi(
  base,
  compare,
  levels = NULL,
  breaks = NULL,
  n_groups = 10L,
  alpha = 0.05,
  thresholds = c(0.1, 0.25)
)

Arguments

base: Reference vector (the "development" distribution).
compare: Vector to compare.
levels: For categorical vectors: the levels to consider. NULL uses the union of the observed ones.
breaks: For numeric vectors: frozen cut points. NULL derives n_groups quantiles of base.
n_groups: Number of bands when breaks = NULL.
alpha: Significance level of the adjusted threshold.
thresholds: The two fixed thresholds: below the first the flag is "stable", below the second "moderate", otherwise "shift".

Value

A list of class scr_psi with psi, flag_fixed, critical (adjusted critical value), flag_adjusted ("stable" or "shift"), n_base, n_compare, n_bins (bands declared; the degrees of freedom count only the populated ones) and table (per band: n_base, n_compare, pct_base, pct_compare, psi_band). The thresholds and alpha used are stored and printed.

Details

Rows where base or compare is NA, or that fall outside breaks or levels, are not counted. A band empty in both samples is left out of the index and of the degrees of freedom B - 1; when a populated band is empty on one side only, 0.5 is added to every populated band of both samples.

References

Yurdakul, B. and Naranjo, J. (2020). Statistical properties of the population stability index. Journal of Risk Model Validation, 14(4), 89-100.

Examples

set.seed(2)
base <- stats::rnorm(5000)
new  <- stats::rnorm(5000, mean = 0.15)
p <- scr_psi(base, new)
p
#> <scr_psi> PSI = 0.0143 | bands = 10 | n = 5,000 vs 5,000
#>   fixed threshold (0.1/0.25):       stable
#>   n-adjusted threshold (0.0068):     shift  [Yurdakul & Naranjo, alpha = 0.05]
p$table
#>               band n_base n_compare pct_base pct_compare     psi_band
#> 1     [-Inf,-1.25]    500       421      0.1      0.0842 2.717209e-03
#> 2   (-1.25,-0.822]    500       427      0.1      0.0854 2.304232e-03
#> 3  (-0.822,-0.495]    500       474      0.1      0.0948 2.776840e-04
#> 4  (-0.495,-0.214]    500       474      0.1      0.0948 2.776840e-04
#> 5  (-0.214,0.0465]    500       513      0.1      0.1026 6.673614e-05
#> 6   (0.0465,0.304]    500       509      0.1      0.1018 3.211185e-05
#> 7    (0.304,0.551]    500       444      0.1      0.0888 1.330376e-03
#> 8    (0.551,0.871]    500       575      0.1      0.1150 2.096429e-03
#> 9     (0.871,1.32]    500       603      0.1      0.1206 3.858567e-03
#> 10     (1.32, Inf]    500       560      0.1      0.1120 1.359944e-03