Finer Monotonic Binning Based on Isotonic Regression

This article is originally published at https://statcompute.wordpress.com

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 binned 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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