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The R package smbinning (http://www.scoringmodeling.com/rpackage/smbinning) provides a very user-friendly interface for the WoE (Weight of Evidence) binning algorithm employed in the scorecard development. However, there are several improvement opportunities in my view:
1. First of all, the underlying algorithm in the smbinning() function utilizes the recursive partitioning, which does not necessarily guarantee the monotonicity.
2. Secondly, the density in each generated bin is not even. The frequency in some bins could be much higher than the one in others.
3. At last, the function might not provide the binning outcome for some variables due to the lack of statistical significance.
In light of the above, I wrote an enhanced version by utilizing the smbinning.custom() function, shown as below. The idea is very simple. Within the repeat loop, we would bin the variable iteratively until a certain criterion is met and then feed the list of cut points into the smbinning.custom() function. As a result, we are able to achieve a set of monotonic bins with similar frequencies regardless of the so-called “statistical significance”, which is a premature step for the variable transformation in my mind.
monobin <- function(data, y, x) {
d1 <- data[c(y, x)]
n <- min(20, nrow(unique(d1[x])))
repeat {
d1$bin <- Hmisc::cut2(d1[, x], g = n)
d2 <- aggregate(d1[-3], d1[3], mean)
c <- cor(d2[-1], method = "spearman")
if(abs(c[1, 2]) == 1 | n == 2) break
n <- n - 1
}
d3 <- aggregate(d1[-3], d1[3], max)
cuts <- d3[-length(d3[, 3]), 3]
return(smbinning::smbinning.custom(d1, y, x, cuts))
}
Below are a couple comparisons between the generic smbinning() and the home-brew monobin() functions with the use of a toy data.
In the first example, we applied the smbinning() function to a variable named “rev_util”. As shown in the highlighted rows in the column “BadRate”, the binning outcome is not monotonic.
Cutpoint CntRec CntGood CntBad CntCumRec CntCumGood CntCumBad PctRec GoodRate BadRate Odds LnOdds WoE IV 1 <= 0 965 716 249 965 716 249 0.1653 0.7420 0.2580 2.8755 1.0562 -0.2997 0.0162 2 <= 5 522 496 26 1487 1212 275 0.0894 0.9502 0.0498 19.0769 2.9485 1.5925 0.1356 3 <= 24 1166 1027 139 2653 2239 414 0.1998 0.8808 0.1192 7.3885 1.9999 0.6440 0.0677 4 <= 40 779 651 128 3432 2890 542 0.1335 0.8357 0.1643 5.0859 1.6265 0.2705 0.0090 5 <= 73 1188 932 256 4620 3822 798 0.2035 0.7845 0.2155 3.6406 1.2922 -0.0638 0.0008 6 <= 96 684 482 202 5304 4304 1000 0.1172 0.7047 0.2953 2.3861 0.8697 -0.4863 0.0316 7 > 96 533 337 196 5837 4641 1196 0.0913 0.6323 0.3677 1.7194 0.5420 -0.8140 0.0743 8 Missing 0 0 0 5837 4641 1196 0.0000 NaN NaN NaN NaN NaN NaN 9 Total 5837 4641 1196 NA NA NA 1.0000 0.7951 0.2049 3.8804 1.3559 0.0000 0.3352
Next, we did the same with the monobin() function. As shown below, the algorithm provided a monotonic binning at the cost of granularity. Albeit coarse, the result is directionally correct with no inversion.
Cutpoint CntRec CntGood CntBad CntCumRec CntCumGood CntCumBad PctRec GoodRate BadRate Odds LnOdds WoE IV 1 <= 30 2962 2495 467 2962 2495 467 0.5075 0.8423 0.1577 5.3426 1.6757 0.3198 0.0471 2 > 30 2875 2146 729 5837 4641 1196 0.4925 0.7464 0.2536 2.9438 1.0797 -0.2763 0.0407 3 Missing 0 0 0 5837 4641 1196 0.0000 NaN NaN NaN NaN NaN NaN 4 Total 5837 4641 1196 NA NA NA 1.0000 0.7951 0.2049 3.8804 1.3559 0.0000 0.0878
In the second example, we applied the smbinning() function to a variable named “bureau_score”. As shown in the highlighted rows, the frequencies in these two bins are much higher than the rest.
Cutpoint CntRec CntGood CntBad CntCumRec CntCumGood CntCumBad PctRec GoodRate BadRate Odds LnOdds WoE IV 1 <= 605 324 167 157 324 167 157 0.0555 0.5154 0.4846 1.0637 0.0617 -1.2942 0.1233 2 <= 632 468 279 189 792 446 346 0.0802 0.5962 0.4038 1.4762 0.3895 -0.9665 0.0946 3 <= 662 896 608 288 1688 1054 634 0.1535 0.6786 0.3214 2.1111 0.7472 -0.6087 0.0668 4 <= 699 1271 1016 255 2959 2070 889 0.2177 0.7994 0.2006 3.9843 1.3824 0.0264 0.0002 5 <= 717 680 586 94 3639 2656 983 0.1165 0.8618 0.1382 6.2340 1.8300 0.4741 0.0226 6 <= 761 1118 1033 85 4757 3689 1068 0.1915 0.9240 0.0760 12.1529 2.4976 1.1416 0.1730 7 > 761 765 742 23 5522 4431 1091 0.1311 0.9699 0.0301 32.2609 3.4739 2.1179 0.2979 8 Missing 315 210 105 5837 4641 1196 0.0540 0.6667 0.3333 2.0000 0.6931 -0.6628 0.0282 9 Total 5837 4641 1196 NA NA NA 1.0000 0.7951 0.2049 3.8804 1.3559 0.0000 0.8066
With the monobin() function applied to the same variable, we were able to get a set of more granular bins with similar frequencies.
Cutpoint CntRec CntGood CntBad CntCumRec CntCumGood CntCumBad PctRec GoodRate BadRate Odds LnOdds WoE IV 1 <= 617 513 284 229 513 284 229 0.0879 0.5536 0.4464 1.2402 0.2153 -1.1407 0.1486 2 <= 642 515 317 198 1028 601 427 0.0882 0.6155 0.3845 1.6010 0.4706 -0.8853 0.0861 3 <= 657 512 349 163 1540 950 590 0.0877 0.6816 0.3184 2.1411 0.7613 -0.5946 0.0363 4 <= 672 487 371 116 2027 1321 706 0.0834 0.7618 0.2382 3.1983 1.1626 -0.1933 0.0033 5 <= 685 494 396 98 2521 1717 804 0.0846 0.8016 0.1984 4.0408 1.3964 0.0405 0.0001 6 <= 701 521 428 93 3042 2145 897 0.0893 0.8215 0.1785 4.6022 1.5265 0.1706 0.0025 7 <= 714 487 418 69 3529 2563 966 0.0834 0.8583 0.1417 6.0580 1.8014 0.4454 0.0144 8 <= 730 489 441 48 4018 3004 1014 0.0838 0.9018 0.0982 9.1875 2.2178 0.8619 0.0473 9 <= 751 513 476 37 4531 3480 1051 0.0879 0.9279 0.0721 12.8649 2.5545 1.1986 0.0859 10 <= 775 492 465 27 5023 3945 1078 0.0843 0.9451 0.0549 17.2222 2.8462 1.4903 0.1157 11 > 775 499 486 13 5522 4431 1091 0.0855 0.9739 0.0261 37.3846 3.6213 2.2653 0.2126 12 Missing 315 210 105 5837 4641 1196 0.0540 0.6667 0.3333 2.0000 0.6931 -0.6628 0.0282 13 Total 5837 4641 1196 NA NA NA 1.0000 0.7951 0.2049 3.8804 1.3559 0.0000 0.7810
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