Finer Monotonic Binning Based on Isotonic Regression
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In my early post (https://statcompute.wordpress.com/2017/01/22/monotonic-binning-with-smbinning-package/), I wrote a monobin() function based on the smbinning package by Herman Jopia to improve the monotonic binning algorithm. The function works well and provides robust binning outcomes. However, there are a couple potential drawbacks due to the coarse binning. First of all, the derived Information Value for each binned variable might tend to be low. Secondly, the binning variable might not be granular enough to reflect the data nature.
In light of the aforementioned, I drafted an improved function isobin() based on the isotonic regression (https://en.wikipedia.org/wiki/Isotonic_regression), as shown below.
isobin <- function(data, y, x) {
d1 <- data[c(y, x)]
d2 <- d1[!is.na(d1[x]), ]
c <- cor(d2[, 2], d2[, 1], method = "spearman", use = "complete.obs")
reg <- isoreg(d2[, 2], c / abs(c) * d2[, 1])
k <- knots(as.stepfun(reg))
sm1 <-smbinning.custom(d1, y, x, k)
c1 <- subset(sm1$ivtable, subset = CntGood * CntBad > 0, select = Cutpoint)
c2 <- suppressWarnings(as.numeric(unlist(strsplit(c1$Cutpoint, " "))))
c3 <- c2[!is.na(c2)]
return(smbinning.custom(d1, y, x, c3[-length(c3)]))
}
Compared with the legacy monobin(), the isobin() function is able to significantly increase the binning granularity as well as moderately improve the Information Value.
LTV Binning with isobin() Function
Cutpoint CntRec CntGood CntBad CntCumRec CntCumGood CntCumBad PctRec GoodRate BadRate Odds LnOdds WoE IV 1 <= 46 81 78 3 81 78 3 0.0139 0.9630 0.0370 26.0000 3.2581 1.9021 0.0272 2 <= 71 312 284 28 393 362 31 0.0535 0.9103 0.0897 10.1429 2.3168 0.9608 0.0363 3 <= 72 22 20 2 415 382 33 0.0038 0.9091 0.0909 10.0000 2.3026 0.9466 0.0025 4 <= 73 27 24 3 442 406 36 0.0046 0.8889 0.1111 8.0000 2.0794 0.7235 0.0019 5 <= 81 303 268 35 745 674 71 0.0519 0.8845 0.1155 7.6571 2.0356 0.6797 0.0194 6 <= 83 139 122 17 884 796 88 0.0238 0.8777 0.1223 7.1765 1.9708 0.6149 0.0074 7 <= 90 631 546 85 1515 1342 173 0.1081 0.8653 0.1347 6.4235 1.8600 0.5040 0.0235 8 <= 94 529 440 89 2044 1782 262 0.0906 0.8318 0.1682 4.9438 1.5981 0.2422 0.0049 9 <= 95 145 119 26 2189 1901 288 0.0248 0.8207 0.1793 4.5769 1.5210 0.1651 0.0006 10 <= 100 907 709 198 3096 2610 486 0.1554 0.7817 0.2183 3.5808 1.2756 -0.0804 0.0010 11 <= 101 195 151 44 3291 2761 530 0.0334 0.7744 0.2256 3.4318 1.2331 -0.1229 0.0005 12 <= 110 1217 934 283 4508 3695 813 0.2085 0.7675 0.2325 3.3004 1.1940 -0.1619 0.0057 13 <= 112 208 158 50 4716 3853 863 0.0356 0.7596 0.2404 3.1600 1.1506 -0.2054 0.0016 14 <= 115 253 183 70 4969 4036 933 0.0433 0.7233 0.2767 2.6143 0.9610 -0.3950 0.0075 15 <= 136 774 548 226 5743 4584 1159 0.1326 0.7080 0.2920 2.4248 0.8857 -0.4702 0.0333 16 <= 138 27 18 9 5770 4602 1168 0.0046 0.6667 0.3333 2.0000 0.6931 -0.6628 0.0024 17 > 138 66 39 27 5836 4641 1195 0.0113 0.5909 0.4091 1.4444 0.3677 -0.9882 0.0140 18 Missing 1 0 1 5837 4641 1196 0.0002 0.0000 1.0000 0.0000 -Inf -Inf Inf 19 Total 5837 4641 1196 NA NA NA 1.0000 0.7951 0.2049 3.8804 1.3559 0.0000 0.1897
LTV Binning with monobin() Function
Cutpoint CntRec CntGood CntBad CntCumRec CntCumGood CntCumBad PctRec GoodRate BadRate Odds LnOdds WoE IV 1 <= 85 1025 916 109 1025 916 109 0.1756 0.8937 0.1063 8.4037 2.1287 0.7727 0.0821 2 <= 94 1019 866 153 2044 1782 262 0.1746 0.8499 0.1501 5.6601 1.7334 0.3775 0.0221 3 <= 100 1052 828 224 3096 2610 486 0.1802 0.7871 0.2129 3.6964 1.3074 -0.0486 0.0004 4 <= 105 808 618 190 3904 3228 676 0.1384 0.7649 0.2351 3.2526 1.1795 -0.1765 0.0045 5 <= 114 985 748 237 4889 3976 913 0.1688 0.7594 0.2406 3.1561 1.1493 -0.2066 0.0076 6 > 114 947 665 282 5836 4641 1195 0.1622 0.7022 0.2978 2.3582 0.8579 -0.4981 0.0461 7 Missing 1 0 1 5837 4641 1196 0.0002 0.0000 1.0000 0.0000 -Inf -Inf Inf 8 Total 5837 4641 1196 NA NA NA 1.0000 0.7951 0.2049 3.8804 1.3559 0.0000 0.1628
Bureau_Score Binning with isobin() Function
Cutpoint CntRec CntGood CntBad CntCumRec CntCumGood CntCumBad PctRec GoodRate BadRate Odds LnOdds WoE IV 1 <= 491 4 1 3 4 1 3 0.0007 0.2500 0.7500 0.3333 -1.0986 -2.4546 0.0056 2 <= 532 24 9 15 28 10 18 0.0041 0.3750 0.6250 0.6000 -0.5108 -1.8668 0.0198 3 <= 559 51 24 27 79 34 45 0.0087 0.4706 0.5294 0.8889 -0.1178 -1.4737 0.0256 4 <= 560 2 1 1 81 35 46 0.0003 0.5000 0.5000 1.0000 0.0000 -1.3559 0.0008 5 <= 572 34 17 17 115 52 63 0.0058 0.5000 0.5000 1.0000 0.0000 -1.3559 0.0143 6 <= 602 153 84 69 268 136 132 0.0262 0.5490 0.4510 1.2174 0.1967 -1.1592 0.0459 7 <= 605 56 31 25 324 167 157 0.0096 0.5536 0.4464 1.2400 0.2151 -1.1408 0.0162 8 <= 606 14 8 6 338 175 163 0.0024 0.5714 0.4286 1.3333 0.2877 -1.0683 0.0035 9 <= 607 17 10 7 355 185 170 0.0029 0.5882 0.4118 1.4286 0.3567 -0.9993 0.0037 10 <= 632 437 261 176 792 446 346 0.0749 0.5973 0.4027 1.4830 0.3940 -0.9619 0.0875 11 <= 639 150 95 55 942 541 401 0.0257 0.6333 0.3667 1.7273 0.5465 -0.8094 0.0207 12 <= 653 451 300 151 1393 841 552 0.0773 0.6652 0.3348 1.9868 0.6865 -0.6694 0.0412 13 <= 662 295 213 82 1688 1054 634 0.0505 0.7220 0.2780 2.5976 0.9546 -0.4014 0.0091 14 <= 665 100 77 23 1788 1131 657 0.0171 0.7700 0.2300 3.3478 1.2083 -0.1476 0.0004 15 <= 667 57 44 13 1845 1175 670 0.0098 0.7719 0.2281 3.3846 1.2192 -0.1367 0.0002 16 <= 677 381 300 81 2226 1475 751 0.0653 0.7874 0.2126 3.7037 1.3093 -0.0466 0.0001 17 <= 679 66 53 13 2292 1528 764 0.0113 0.8030 0.1970 4.0769 1.4053 0.0494 0.0000 18 <= 683 160 129 31 2452 1657 795 0.0274 0.8062 0.1938 4.1613 1.4258 0.0699 0.0001 19 <= 689 203 164 39 2655 1821 834 0.0348 0.8079 0.1921 4.2051 1.4363 0.0804 0.0002 20 <= 699 304 249 55 2959 2070 889 0.0521 0.8191 0.1809 4.5273 1.5101 0.1542 0.0012 21 <= 707 312 268 44 3271 2338 933 0.0535 0.8590 0.1410 6.0909 1.8068 0.4509 0.0094 22 <= 717 368 318 50 3639 2656 983 0.0630 0.8641 0.1359 6.3600 1.8500 0.4941 0.0132 23 <= 721 134 119 15 3773 2775 998 0.0230 0.8881 0.1119 7.9333 2.0711 0.7151 0.0094 24 <= 723 49 44 5 3822 2819 1003 0.0084 0.8980 0.1020 8.8000 2.1748 0.8188 0.0043 25 <= 739 425 394 31 4247 3213 1034 0.0728 0.9271 0.0729 12.7097 2.5424 1.1864 0.0700 26 <= 746 166 154 12 4413 3367 1046 0.0284 0.9277 0.0723 12.8333 2.5520 1.1961 0.0277 27 <= 756 234 218 16 4647 3585 1062 0.0401 0.9316 0.0684 13.6250 2.6119 1.2560 0.0422 28 <= 761 110 104 6 4757 3689 1068 0.0188 0.9455 0.0545 17.3333 2.8526 1.4967 0.0260 29 <= 763 46 44 2 4803 3733 1070 0.0079 0.9565 0.0435 22.0000 3.0910 1.7351 0.0135 30 <= 767 96 92 4 4899 3825 1074 0.0164 0.9583 0.0417 23.0000 3.1355 1.7795 0.0293 31 <= 772 77 74 3 4976 3899 1077 0.0132 0.9610 0.0390 24.6667 3.2055 1.8495 0.0249 32 <= 787 269 260 9 5245 4159 1086 0.0461 0.9665 0.0335 28.8889 3.3635 2.0075 0.0974 33 <= 794 95 93 2 5340 4252 1088 0.0163 0.9789 0.0211 46.5000 3.8395 2.4835 0.0456 34 > 794 182 179 3 5522 4431 1091 0.0312 0.9835 0.0165 59.6667 4.0888 2.7328 0.0985 35 Missing 315 210 105 5837 4641 1196 0.0540 0.6667 0.3333 2.0000 0.6931 -0.6628 0.0282 36 Total 5837 4641 1196 NA NA NA 1.0000 0.7951 0.2049 3.8804 1.3559 0.0000 0.8357
Bureau_Score Binning with monobin() Function
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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