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(This article was first published on <strong><a href="https://statcompute.wordpress.com/2018/10/14/monotonic-binning-with-equal-sized-bads-for-scorecard-development/"> S+/R – Yet Another Blog in Statistical Computing</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p>In previous posts (<a rel="nofollow" href="https://statcompute.wordpress.com/2017/01/22/monotonic-binning-with-smbinning-package" target="_blank">https://statcompute.wordpress.com/2017/01/22/monotonic-binning-with-smbinning-package</a>) and (<a rel="nofollow" href="https://statcompute.wordpress.com/2017/06/15/finer-monotonic-binning-based-on-isotonic-regression" target="_blank">https://statcompute.wordpress.com/2017/06/15/finer-monotonic-binning-based-on-isotonic-regression</a>), I’ve developed 2 different algorithms for monotonic binning. While the first tends to generate bins with equal densities, the second would define finer bins based on the isotonic regression. </p>
<p>In the code snippet below, a third approach would be illustrated for the purpose to generate bins with roughly equal-sized bads. Once again, for the reporting layer, I leveraged the flexible smbinning::smbinning.custom() function with a small tweak. </p>
<pre>

df &lt;- sas7bdat::read.sas7bdat(&quot;Downloads/accepts.sas7bdat&quot;)

monobin &lt;- function(df, x, y) {
  yname &lt;- deparse(substitute(y))
  xname &lt;- deparse(substitute(x))
  d1 &lt;- df[c(yname, xname)]
  d2 &lt;- d1[which(d1[[yname]] == 1), ]
  nbin &lt;- round(1 / max(table(d2[[xname]]) / sum(table(d2[[xname]]))))
  repeat {
    cuts &lt;- Hmisc::cut2(d2[[xname]], g = nbin, onlycuts = T)
    d1$cut &lt;- cut(d1[[xname]], breaks = cuts, include.lowest = T)
    d3 &lt;- Reduce(rbind, Map(function(x) data.frame(xmean = mean(x[[xname]], na.rm = T), ymean = mean(x[[yname]])), split(d1, d1$cut)))
    if(abs(cor(d3$xmean, d3$ymean, method = &quot;spearman&quot;)) == 1 | nrow(d3) == 2) {
      break
    }
    nbin &lt;- nbin - 1
  }
  df$good &lt;- 1 -  d1[[yname]]
  return(smbinning::smbinning.custom(df, &quot;good&quot;, xname, cuts = cuts[c(-1, -length(cuts))]))
}
</pre>
<p>As shown in the output, the number of bads in each bin, with the exception for missings, is similar and varying within a small range. However, the number of records tends to increase to ensure the monotonicity of bad rates across all bins. </p>
<pre>
monobin(df, bureau_score, bad)
#   Cutpoint CntRec CntGood CntBad CntCumRec CntCumGood CntCumBad PctRec GoodRate BadRate    Odds LnOdds     WoE     IV
#1    &lt;= 602    268     136    132       268        136       132 0.0459   0.5075  0.4925  1.0303 0.0299 -1.3261 0.1075
#2    &lt;= 621    311     185    126       579        321       258 0.0533   0.5949  0.4051  1.4683 0.3841 -0.9719 0.0636
#3    &lt;= 636    302     186    116       881        507       374 0.0517   0.6159  0.3841  1.6034 0.4722 -0.8838 0.0503
#4    &lt;= 649    392     259    133      1273        766       507 0.0672   0.6607  0.3393  1.9474 0.6665 -0.6895 0.0382
#5    &lt;= 661    387     268    119      1660       1034       626 0.0663   0.6925  0.3075  2.2521 0.8119 -0.5441 0.0227
#6    &lt;= 676    529     415    114      2189       1449       740 0.0906   0.7845  0.2155  3.6404 1.2921 -0.0639 0.0004
#7    &lt;= 693    606     491    115      2795       1940       855 0.1038   0.8102  0.1898  4.2696 1.4515  0.0956 0.0009
#8     717   1883    1775    108      5522       4431      1091 0.3226   0.9426  0.0574 16.4352 2.7994  1.4435 0.4217
#10  Missing    315     210    105      5837       4641      1196 0.0540   0.6667  0.3333  2.0000 0.6931 -0.6628 0.0282
#11    Total   5837    4641   1196        NA         NA        NA 1.0000   0.7951  0.2049  3.8804 1.3559  0.0000 0.7508
</pre>
	<p>
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