# autobinning

Perform automatic binning of given predictors

## Description

performs automatic binning of all predictors.`sc`

= autobinning(`sc`

)

Automatic binning finds binning maps or rules to bin numeric data and to group
categories of categorical data. The binning rules are stored in the
`creditscorecard`

object. To apply the binning rules to the
`creditscorecard`

object data, or to a new dataset, use
`bindata`

.

performs automatic binning of the predictors given in
`sc`

= autobinning(`sc`

,`PredictorNames`

)`PredictorNames`

.

Automatic binning finds binning maps or rules to bin numeric data and to group
categories of categorical data. The binning rules are stored in the
`creditscorecard`

object. To apply the binning rules to the
`creditscorecard`

object data, or to a new dataset, use
`bindata`

.

performs automatic binning of the predictors given in
`sc`

= autobinning(___,`Name,Value`

)`PredictorNames`

using optional name-value pair
arguments. See the name-value argument `Algorithm`

for a
description of the supported binning algorithms.

Automatic binning finds binning maps or rules to bin numeric data and to group
categories of categorical data. The binning rules are stored in the
`creditscorecard`

object. To apply the binning rules to the
`creditscorecard`

object data, or to a new dataset, use
`bindata`

.

## Examples

### Perform Automatic Binning Using the Defaults

Create a `creditscorecard`

object using the `CreditCardData.mat`

file to load the data (using a dataset from Refaat 2011).

load CreditCardData sc = creditscorecard(data,'IDVar','CustID');

Perform automatic binning using the default options. By default, `autobinning`

bins all predictors and uses the `Monotone`

algorithm.

sc = autobinning(sc);

Use `bininfo`

to display the binned data for the predictor `CustAge`

.

`bi = bininfo(sc, 'CustAge')`

`bi=`*8×6 table*
Bin Good Bad Odds WOE InfoValue
_____________ ____ ___ ______ _________ _________
{'[-Inf,33)'} 70 53 1.3208 -0.42622 0.019746
{'[33,37)' } 64 47 1.3617 -0.39568 0.015308
{'[37,40)' } 73 47 1.5532 -0.26411 0.0072573
{'[40,46)' } 174 94 1.8511 -0.088658 0.001781
{'[46,48)' } 61 25 2.44 0.18758 0.0024372
{'[48,58)' } 263 105 2.5048 0.21378 0.013476
{'[58,Inf]' } 98 26 3.7692 0.62245 0.0352
{'Totals' } 803 397 2.0227 NaN 0.095205

Use `plotbins`

to display the histogram and WOE curve for the predictor `CustAge`

.

`plotbins(sc,'CustAge')`

### Perform Automatic Binning with a Named Predictor Using the Defaults

Create a `creditscorecard`

object using the `CreditCardData.mat`

file to load the `data`

(using a dataset from Refaat 2011).

```
load CreditCardData
sc = creditscorecard(data);
```

Perform automatic binning for the predictor `CustIncome`

using the default options. By default, `autobinning`

uses the `Monotone`

algorithm.

`sc = autobinning(sc,'CustIncome');`

Use `bininfo`

to display the binned data.

`bi = bininfo(sc, 'CustIncome')`

`bi=`*8×6 table*
Bin Good Bad Odds WOE InfoValue
_________________ ____ ___ _______ _________ __________
{'[-Inf,29000)' } 53 58 0.91379 -0.79457 0.06364
{'[29000,33000)'} 74 49 1.5102 -0.29217 0.0091366
{'[33000,35000)'} 68 36 1.8889 -0.06843 0.00041042
{'[35000,40000)'} 193 98 1.9694 -0.026696 0.00017359
{'[40000,42000)'} 68 34 2 -0.011271 1.0819e-05
{'[42000,47000)'} 164 66 2.4848 0.20579 0.0078175
{'[47000,Inf]' } 183 56 3.2679 0.47972 0.041657
{'Totals' } 803 397 2.0227 NaN 0.12285

### Perform Automatic Binning Using Two Name-Value Pair Arguments

Create a `creditscorecard`

object using the `CreditCardData.mat`

file to load the `data`

(using a dataset from Refaat 2011).

```
load CreditCardData
sc = creditscorecard(data);
```

Perform automatic binning for the predictor `CustIncome`

using the `Monotone`

algorithm with the initial number of bins set to 20. This example explicitly sets both the `Algorithm`

and the `AlgorithmOptions`

name-value arguments.

AlgoOptions = {'InitialNumBins',20}; sc = autobinning(sc,'CustIncome','Algorithm','Monotone','AlgorithmOptions',... AlgoOptions);

Use `bininfo`

to display the binned data. Here, the cut points, which delimit the bins, are also displayed.

`[bi,cp] = bininfo(sc,'CustIncome')`

`bi=`*11×6 table*
Bin Good Bad Odds WOE InfoValue
_________________ ____ ___ _______ _________ __________
{'[-Inf,19000)' } 2 3 0.66667 -1.1099 0.0056227
{'[19000,29000)'} 51 55 0.92727 -0.77993 0.058516
{'[29000,31000)'} 29 26 1.1154 -0.59522 0.017486
{'[31000,34000)'} 80 42 1.9048 -0.060061 0.0003704
{'[34000,35000)'} 33 17 1.9412 -0.041124 7.095e-05
{'[35000,40000)'} 193 98 1.9694 -0.026696 0.00017359
{'[40000,42000)'} 68 34 2 -0.011271 1.0819e-05
{'[42000,43000)'} 39 16 2.4375 0.18655 0.001542
{'[43000,47000)'} 125 50 2.5 0.21187 0.0062972
{'[47000,Inf]' } 183 56 3.2679 0.47972 0.041657
{'Totals' } 803 397 2.0227 NaN 0.13175

`cp = `*9×1*
19000
29000
31000
34000
35000
40000
42000
43000
47000

### Perform Automatic Binning Using Multiple Name-Value Pair Arguments

This example shows how to use the `autobinning`

default `Monotone`

algorithm and the `AlgorithmOptions`

name-value pair arguments associated with the `Monotone`

algorithm. The `AlgorithmOptions`

for the `Monotone`

algorithm are three name-value pair parameters: `‘InitialNumBins'`

, `'Trend'`

, and `'SortCategories'`

. `'InitialNumBins'`

and `'Trend'`

are applicable for numeric predictors and `'Trend'`

and `'SortCategories'`

are applicable for categorical predictors.

`creditscorecard`

object using the `CreditCardData.mat`

file to load the data (using a dataset from Refaat 2011).

load CreditCardData sc = creditscorecard(data,'IDVar','CustID');

Perform automatic binning for the numeric predictor `CustIncome`

using the `Monotone`

algorithm with 20 bins. This example explicitly sets both the `Algorithm`

argument and the `AlgorithmOptions`

name-value arguments for `'InitialNumBins'`

and `'Trend'`

.

AlgoOptions = {'InitialNumBins',20,'Trend','Increasing'}; sc = autobinning(sc,'CustIncome','Algorithm','Monotone',... 'AlgorithmOptions',AlgoOptions);

Use `bininfo`

to display the binned data.

`bi = bininfo(sc,'CustIncome')`

`bi=`*11×6 table*
Bin Good Bad Odds WOE InfoValue
_________________ ____ ___ _______ _________ __________
{'[-Inf,19000)' } 2 3 0.66667 -1.1099 0.0056227
{'[19000,29000)'} 51 55 0.92727 -0.77993 0.058516
{'[29000,31000)'} 29 26 1.1154 -0.59522 0.017486
{'[31000,34000)'} 80 42 1.9048 -0.060061 0.0003704
{'[34000,35000)'} 33 17 1.9412 -0.041124 7.095e-05
{'[35000,40000)'} 193 98 1.9694 -0.026696 0.00017359
{'[40000,42000)'} 68 34 2 -0.011271 1.0819e-05
{'[42000,43000)'} 39 16 2.4375 0.18655 0.001542
{'[43000,47000)'} 125 50 2.5 0.21187 0.0062972
{'[47000,Inf]' } 183 56 3.2679 0.47972 0.041657
{'Totals' } 803 397 2.0227 NaN 0.13175

### Perform Automatic Binning for Multiple Predictors

`creditscorecard`

object using the `CreditCardData.mat`

file to load the `data`

(using a dataset from Refaat 2011).

load CreditCardData sc = creditscorecard(data,'IDVar','CustID');

Perform automatic binning for the predictor `CustIncome`

and `CustAge`

using the default `Monotone`

algorithm with `AlgorithmOptions`

for `InitialNumBins`

and `Trend`

.

AlgoOptions = {'InitialNumBins',20,'Trend','Increasing'}; sc = autobinning(sc,{'CustAge','CustIncome'},'Algorithm','Monotone',... 'AlgorithmOptions',AlgoOptions);

Use `bininfo`

to display the binned data.

`bi1 = bininfo(sc, 'CustIncome')`

`bi1=`*11×6 table*
Bin Good Bad Odds WOE InfoValue
_________________ ____ ___ _______ _________ __________
{'[-Inf,19000)' } 2 3 0.66667 -1.1099 0.0056227
{'[19000,29000)'} 51 55 0.92727 -0.77993 0.058516
{'[29000,31000)'} 29 26 1.1154 -0.59522 0.017486
{'[31000,34000)'} 80 42 1.9048 -0.060061 0.0003704
{'[34000,35000)'} 33 17 1.9412 -0.041124 7.095e-05
{'[35000,40000)'} 193 98 1.9694 -0.026696 0.00017359
{'[40000,42000)'} 68 34 2 -0.011271 1.0819e-05
{'[42000,43000)'} 39 16 2.4375 0.18655 0.001542
{'[43000,47000)'} 125 50 2.5 0.21187 0.0062972
{'[47000,Inf]' } 183 56 3.2679 0.47972 0.041657
{'Totals' } 803 397 2.0227 NaN 0.13175

`bi2 = bininfo(sc, 'CustAge')`

`bi2=`*8×6 table*
Bin Good Bad Odds WOE InfoValue
_____________ ____ ___ ______ _________ __________
{'[-Inf,35)'} 93 76 1.2237 -0.50255 0.038003
{'[35,40)' } 114 71 1.6056 -0.2309 0.0085141
{'[40,42)' } 52 30 1.7333 -0.15437 0.0016687
{'[42,44)' } 58 32 1.8125 -0.10971 0.00091888
{'[44,47)' } 97 51 1.902 -0.061533 0.00047174
{'[47,62)' } 333 130 2.5615 0.23619 0.020605
{'[62,Inf]' } 56 7 8 1.375 0.071647
{'Totals' } 803 397 2.0227 NaN 0.14183

### Perform Automatic Binning for a Categorical Predictor Using the Defaults

`creditscorecard`

object using the `CreditCardData.mat`

file to load the `data`

(using a dataset from Refaat 2011).

```
load CreditCardData
sc = creditscorecard(data);
```

Perform automatic binning for the predictor that is a categorical predictor called `ResStatus`

using the default options. By default, `autobinning`

uses the `Monotone`

algorithm.

`sc = autobinning(sc,'ResStatus');`

Use `bininfo`

to display the binned data.

`bi = bininfo(sc, 'ResStatus')`

`bi=`*4×6 table*
Bin Good Bad Odds WOE InfoValue
______________ ____ ___ ______ _________ _________
{'Tenant' } 307 167 1.8383 -0.095564 0.0036638
{'Home Owner'} 365 177 2.0621 0.019329 0.0001682
{'Other' } 131 53 2.4717 0.20049 0.0059418
{'Totals' } 803 397 2.0227 NaN 0.0097738

### Perform Automatic Binning for a Categorical Predictor Using Name-Value Pair Arguments

This example shows how to modify the data (for this example only) to illustrate binning categorical predictors using the `Monotone`

algorithm.

`creditscorecard`

object using the `CreditCardData.mat`

file to load the `data`

(using a dataset from Refaat 2011).

`load CreditCardData`

Add two new categories and updating the response variable.

newdata = data; rng('default'); %for reproducibility Predictor = 'ResStatus'; Status = newdata.status; NumObs = length(newdata.(Predictor)); Ind1 = randi(NumObs,100,1); Ind2 = randi(NumObs,100,1); newdata.(Predictor)(Ind1) = 'Subtenant'; newdata.(Predictor)(Ind2) = 'CoOwner'; Status(Ind1) = randi(2,100,1)-1; Status(Ind2) = randi(2,100,1)-1; newdata.status = Status;

Update the `creditscorecard`

object using the `newdata`

and plot the bins for a later comparison.

scnew = creditscorecard(newdata,'IDVar','CustID'); [bi,cg] = bininfo(scnew,Predictor)

`bi=`*6×6 table*
Bin Good Bad Odds WOE InfoValue
______________ ____ ___ ______ ________ _________
{'Home Owner'} 308 154 2 0.092373 0.0032392
{'Tenant' } 264 136 1.9412 0.06252 0.0012907
{'Other' } 109 49 2.2245 0.19875 0.0050386
{'Subtenant' } 42 42 1 -0.60077 0.026813
{'CoOwner' } 52 44 1.1818 -0.43372 0.015802
{'Totals' } 775 425 1.8235 NaN 0.052183

`cg=`*5×2 table*
Category BinNumber
______________ _________
{'Home Owner'} 1
{'Tenant' } 2
{'Other' } 3
{'Subtenant' } 4
{'CoOwner' } 5

plotbins(scnew,Predictor)

Perform automatic binning for the categorical `Predictor`

using the default `Monotone`

algorithm with the `AlgorithmOptions`

name-value pair arguments for `'SortCategories'`

and `'Trend'`

.

AlgoOptions = {'SortCategories','Goods','Trend','Increasing'}; scnew = autobinning(scnew,Predictor,'Algorithm','Monotone',... 'AlgorithmOptions',AlgoOptions);

Use `bininfo`

to display the bin information. The second output parameter `'cg'`

captures the bin membership, which is the bin number that each group belongs to.

[bi,cg] = bininfo(scnew,Predictor)

`bi=`*4×6 table*
Bin Good Bad Odds WOE InfoValue
__________ ____ ___ ______ ________ _________
{'Group1'} 42 42 1 -0.60077 0.026813
{'Group2'} 52 44 1.1818 -0.43372 0.015802
{'Group3'} 681 339 2.0088 0.096788 0.0078459
{'Totals'} 775 425 1.8235 NaN 0.05046

`cg=`*5×2 table*
Category BinNumber
______________ _________
{'Subtenant' } 1
{'CoOwner' } 2
{'Other' } 3
{'Tenant' } 3
{'Home Owner'} 3

Plot bins and compare with the histogram plotted pre-binning.

plotbins(scnew,Predictor)

### Perform Automatic Binning When** **Using Missing Data

Create a `creditscorecard`

object using the `CreditCardData.mat`

file to load the `dataMissing`

with missing values.

```
load CreditCardData.mat
head(dataMissing,5)
```

`ans=`*5×11 table*
CustID CustAge TmAtAddress ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance UtilRate status
______ _______ ___________ ___________ _________ __________ _______ _______ _________ ________ ______
1 53 62 <undefined> Unknown 50000 55 Yes 1055.9 0.22 0
2 61 22 Home Owner Employed 52000 25 Yes 1161.6 0.24 0
3 47 30 Tenant Employed 37000 61 No 877.23 0.29 0
4 NaN 75 Home Owner Employed 53000 20 Yes 157.37 0.08 0
5 68 56 Home Owner Employed 53000 14 Yes 561.84 0.11 0

`fprintf('Number of rows: %d\n',height(dataMissing))`

Number of rows: 1200

`fprintf('Number of missing values CustAge: %d\n',sum(ismissing(dataMissing.CustAge)))`

Number of missing values CustAge: 30

`fprintf('Number of missing values ResStatus: %d\n',sum(ismissing(dataMissing.ResStatus)))`

Number of missing values ResStatus: 40

Use `creditscorecard`

with the name-value argument `'BinMissingData'`

set to `true`

to bin the missing numeric and categorical data in a separate bin.

```
sc = creditscorecard(dataMissing,'BinMissingData',true);
disp(sc)
```

creditscorecard with properties: GoodLabel: 0 ResponseVar: 'status' WeightsVar: '' VarNames: {1x11 cell} NumericPredictors: {1x7 cell} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 1 IDVar: '' PredictorVars: {1x10 cell} Data: [1200x11 table]

Perform automatic binning using the `Merge`

algorithm.

sc = autobinning(sc,'Algorithm','Merge');

Display bin information for numeric data for `'CustAge'`

that includes missing data in a separate bin labelled `<missing> `

and this is the last bin. No matter what binning algorithm is used in `autobinning`

, the algorithm operates on the non-missing data and the bin for the `<missing>`

numeric values for a predictor is always the last bin.

```
[bi,cp] = bininfo(sc,'CustAge');
disp(bi)
```

Bin Good Bad Odds WOE InfoValue _____________ ____ ___ _______ ________ __________ {'[-Inf,32)'} 56 39 1.4359 -0.34263 0.0097643 {'[32,33)' } 13 13 1 -0.70442 0.011663 {'[33,34)' } 9 11 0.81818 -0.90509 0.014934 {'[34,65)' } 677 317 2.1356 0.054351 0.002424 {'[65,Inf]' } 29 6 4.8333 0.87112 0.018295 {'<missing>'} 19 11 1.7273 -0.15787 0.00063885 {'Totals' } 803 397 2.0227 NaN 0.057718

`plotbins(sc,'CustAge')`

Display bin information for categorical data for `'ResStatus'`

that includes missing data in a separate bin labelled `<missing> `

and this is the last bin. No matter what binning algorithm is used in `autobinning`

, the algorithm operates on the non-missing data and the bin for the `<missing>`

categorical values for a predictor is always the last bin.

```
[bi,cg] = bininfo(sc,'ResStatus');
disp(bi)
```

Bin Good Bad Odds WOE InfoValue _____________ ____ ___ ______ _________ __________ {'Group1' } 648 332 1.9518 -0.035663 0.0010449 {'Group2' } 128 52 2.4615 0.19637 0.0055808 {'<missing>'} 27 13 2.0769 0.026469 2.3248e-05 {'Totals' } 803 397 2.0227 NaN 0.0066489

`plotbins(sc,'ResStatus')`

### Perform Automatic Binning Using the Split Algorithm

This example demonstrates using the `'Split'`

algorithm with categorical and numeric predictors. Load the `CreditCardData.mat`

dataset and modify so that it contains four categories for the predictor '`ResStatus'`

to demonstrate how the split algorithm works.

load CreditCardData.mat x = data.ResStatus; Ind = find(x == 'Tenant'); Nx = length(Ind); x(Ind(1:floor(Nx/3))) = 'Subletter'; data.ResStatus = x;

Create a `creditscorecard`

and use `bininfo`

to display the `'Statistics'`

.

sc = creditscorecard(data,'IDVar','CustID'); [bi1,cg1] = bininfo(sc,'ResStatus','Statistics',{'Odds','WOE','InfoValue'}); disp(bi1)

Bin Good Bad Odds WOE InfoValue ______________ ____ ___ ______ _________ __________ {'Home Owner'} 365 177 2.0621 0.019329 0.0001682 {'Tenant' } 204 112 1.8214 -0.1048 0.0029415 {'Other' } 131 53 2.4717 0.20049 0.0059418 {'Subletter' } 103 55 1.8727 -0.077023 0.00079103 {'Totals' } 803 397 2.0227 NaN 0.0098426

disp(cg1)

Category BinNumber ______________ _________ {'Home Owner'} 1 {'Tenant' } 2 {'Other' } 3 {'Subletter' } 4

**Using the Split Algorithm with a Categorical Predictor**

Apply presorting to the `'ResStatus'`

category using the default sorting by `'Odds'`

and specify the `'Split'`

algorithm.

sc = autobinning(sc,'ResStatus', 'Algorithm', 'split','AlgorithmOptions',... {'Measure','gini','SortCategories','odds','Tolerance',1e-4}); [bi2,cg2] = bininfo(sc,'ResStatus','Statistics',{'Odds','WOE','InfoValue'}); disp(bi2)

Bin Good Bad Odds WOE InfoValue __________ ____ ___ ______ _________ _________ {'Group1'} 307 167 1.8383 -0.095564 0.0036638 {'Group2'} 365 177 2.0621 0.019329 0.0001682 {'Group3'} 131 53 2.4717 0.20049 0.0059418 {'Totals'} 803 397 2.0227 NaN 0.0097738

disp(cg2)

Category BinNumber ______________ _________ {'Tenant' } 1 {'Subletter' } 1 {'Home Owner'} 2 {'Other' } 3

**Using the Split Algorithm with a Numeric Predictor**

To demonstrate a split for the numeric predictor, 'T`mAtAddress'`

, first use `autobinning`

with the default `'Monotone'`

algorithm.

sc = autobinning(sc,'TmAtAddress'); bi3 = bininfo(sc,'TmAtAddress','Statistics',{'Odds','WOE','InfoValue'}); disp(bi3)

Bin Good Bad Odds WOE InfoValue _____________ ____ ___ ______ _________ __________ {'[-Inf,23)'} 239 129 1.8527 -0.087767 0.0023963 {'[23,83)' } 480 232 2.069 0.02263 0.00030269 {'[83,Inf]' } 84 36 2.3333 0.14288 0.00199 {'Totals' } 803 397 2.0227 NaN 0.004689

Then use `autobinning`

with the `'Split'`

algorithm.

sc = autobinning(sc,'TmAtAddress','Algorithm', 'Split'); bi4 = bininfo(sc,'TmAtAddress','Statistics',{'Odds','WOE','InfoValue'}); disp(bi4)

Bin Good Bad Odds WOE InfoValue ____________ ____ ___ _______ _________ __________ {'[-Inf,4)'} 20 12 1.6667 -0.19359 0.0010299 {'[4,5)' } 4 7 0.57143 -1.264 0.015991 {'[5,23)' } 215 110 1.9545 -0.034261 0.00031973 {'[23,33)' } 130 39 3.3333 0.49955 0.0318 {'[33,Inf]'} 434 229 1.8952 -0.065096 0.0023664 {'Totals' } 803 397 2.0227 NaN 0.051507

### Perform Automatic Binning Using the Merge Algorithm

Load the `CreditCardData.mat`

dataset. This example demonstrates using the `'Merge'`

algorithm with categorical and numeric predictors.

`load CreditCardData.mat`

**Using the Merge Algorithm with a Categorical Predictor**

To merge a categorical predictor, create a `creditscorecard`

using default sorting by `'Odds' `

and then use `bininfo`

on the categorical predictor `'ResStatus'`

.

sc = creditscorecard(data,'IDVar','CustID'); [bi1,cg1] = bininfo(sc,'ResStatus','Statistics',{'Odds','WOE','InfoValue'}); disp(bi1);

Bin Good Bad Odds WOE InfoValue ______________ ____ ___ ______ _________ _________ {'Home Owner'} 365 177 2.0621 0.019329 0.0001682 {'Tenant' } 307 167 1.8383 -0.095564 0.0036638 {'Other' } 131 53 2.4717 0.20049 0.0059418 {'Totals' } 803 397 2.0227 NaN 0.0097738

disp(cg1);

Category BinNumber ______________ _________ {'Home Owner'} 1 {'Tenant' } 2 {'Other' } 3

Use `autobinning`

and specify the `'Merge'`

algorithm.

sc = autobinning(sc,'ResStatus','Algorithm', 'Merge'); [bi2,cg2] = bininfo(sc,'ResStatus','Statistics',{'Odds','WOE','InfoValue'}); disp(bi2)

Bin Good Bad Odds WOE InfoValue __________ ____ ___ ______ _________ _________ {'Group1'} 672 344 1.9535 -0.034802 0.0010314 {'Group2'} 131 53 2.4717 0.20049 0.0059418 {'Totals'} 803 397 2.0227 NaN 0.0069732

disp(cg2)

Category BinNumber ______________ _________ {'Tenant' } 1 {'Home Owner'} 1 {'Other' } 2

**Using the Merge Algorithm with a Numeric Predictor**

To demonstrate a merge for the numeric predictor, 'T`mAtAddress'`

, first use `autobinning`

with the default `'Monotone'`

algorithm.

sc = autobinning(sc,'TmAtAddress'); bi3 = bininfo(sc,'TmAtAddress','Statistics',{'Odds','WOE','InfoValue'}); disp(bi3)

Bin Good Bad Odds WOE InfoValue _____________ ____ ___ ______ _________ __________ {'[-Inf,23)'} 239 129 1.8527 -0.087767 0.0023963 {'[23,83)' } 480 232 2.069 0.02263 0.00030269 {'[83,Inf]' } 84 36 2.3333 0.14288 0.00199 {'Totals' } 803 397 2.0227 NaN 0.004689

Then use `autobinning`

with the `'Merge'`

algorithm.

sc = autobinning(sc,'TmAtAddress','Algorithm', 'Merge'); bi4 = bininfo(sc,'TmAtAddress','Statistics',{'Odds','WOE','InfoValue'}); disp(bi4)

Bin Good Bad Odds WOE InfoValue _____________ ____ ___ _______ _________ __________ {'[-Inf,28)'} 303 152 1.9934 -0.014566 8.0646e-05 {'[28,30)' } 27 2 13.5 1.8983 0.054264 {'[30,98)' } 428 216 1.9815 -0.020574 0.00022794 {'[98,106)' } 11 13 0.84615 -0.87147 0.016599 {'[106,Inf]'} 34 14 2.4286 0.18288 0.0012942 {'Totals' } 803 397 2.0227 NaN 0.072466

## Input Arguments

`sc`

— Credit scorecard model

`creditscorecard`

object

Credit scorecard model, specified as a
`creditscorecard`

object. Use `creditscorecard`

to create
a `creditscorecard`

object.

`PredictorNames`

— Predictor or predictors names to automatically bin

character vector | cell array of character vectors

Predictor or predictors names to automatically bin, specified as a
character vector or a cell array of character vectors containing the
name of the predictor or predictors. `PredictorNames`

are case-sensitive and when no `PredictorNames`

are
defined, all predictors in the `PredictorVars`

property
of the `creditscorecard`

object are binned.

**Data Types: **`char`

| `cell`

### Name-Value Arguments

Specify optional
comma-separated pairs of `Name,Value`

arguments. `Name`

is
the argument name and `Value`

is the corresponding value.
`Name`

must appear inside quotes. You can specify several name and value
pair arguments in any order as
`Name1,Value1,...,NameN,ValueN`

.

**Example:**

```
sc =
autobinning(sc,'Algorithm','EqualFrequency')
```

`Algorithm`

— Algorithm selection

`'Monotone'`

(default) | character vector with values `'Monotone'`

,
`'Split'`

, `'Merge'`

,
`'EqualFrequency'`

,
`'EqualWidth'`

Algorithm selection, specified as the comma-separated pair
consisting of `'Algorithm'`

and a character vector
indicating which algorithm to use. The same algorithm is used for all
predictors in `PredictorNames`

. Possible values are:

`'Monotone'`

— (default) Monotone Adjacent Pooling Algorithm (MAPA), also known as Maximum Likelihood Monotone Coarse Classifier (MLMCC). Supervised optimal binning algorithm that aims to find bins with a monotone Weight-Of-Evidence (WOE) trend. This algorithm assumes that only neighboring attributes can be grouped. Thus, for categorical predictors, categories are sorted before applying the algorithm (see`'SortCategories'`

option for`AlgorithmOptions`

). For more information, see Monotone.`'Split'`

— Supervised binning algorithm, where a measure is used to split the data into bins. The measures supported by`'Split'`

are`gini`

,`chi2`

,`infovalue`

, and`entropy`

. The resulting split must be such that the gain in the information function is maximized. For more information on these measures, see`AlgorithmOptions`

and Split.`'Merge'`

— Supervised automatic binning algorithm, where a measure is used to merge bins into buckets. The measures supported by`'Merge'`

are`chi2`

,`gini`

,`infovalue`

, and`entropy`

. The resulting merging must be such that any pair of adjacent bins is statistically different from each other, according to the chosen measure. For more information on these measures, see`AlgorithmOptions`

and Merge.`'EqualFrequency'`

— Unsupervised algorithm that divides the data into a predetermined number of bins that contain approximately the same number of observations. This algorithm is also known as “equal height” or “equal depth.” For categorical predictors, categories are sorted before applying the algorithm (see`'SortCategories'`

option for`AlgorithmOptions`

). For more information, see Equal Frequency.`'EqualWidth'`

— Unsupervised algorithm that divides the range of values in the domain of the predictor variable into a predetermined number of bins of “equal width.” For numeric data, the width is measured as the distance between bin edges. For categorical data, width is measured as the number of categories within a bin. For categorical predictors, categories are sorted before applying the algorithm (see`'SortCategories'`

option for`AlgorithmOptions`

). For more information, see Equal Width.

**Data Types: **`char`

`AlgorithmOptions`

— Algorithm options for selected `Algorithm`

`{'InitialNumBins',10,'Trend','Auto','SortCategories','Odds'}`

for `Monotone`

(default) | cell array with
`{`

`'OptionName'`

,*OptionValue*`}`

for `Algorithm`

options

Algorithm options for the selected `Algorithm`

,
specified as the comma-separated pair consisting of
`'AlgorithmOptions'`

and a cell array. Possible
values are:

For

`Monotone`

algorithm:`{`

`'InitialNumBins',`

*n*`}`

— Initial number (*n*) of bins (default is 10).`'InitialNumBins'`

must be an integer >`2`

. Used for numeric predictors only.`{'Trend','TrendOption'}`

— Determines whether the Weight-Of-Evidence (WOE) monotonic trend is expected to be increasing or decreasing. The values for`'TrendOption'`

are:`'Auto'`

— (Default) Automatically determines if the WOE trend is increasing or decreasing.`'Increasing'`

— Look for an increasing WOE trend.`'Decreasing'`

— Look for a decreasing WOE trend.

The value of the optional input parameter

`'Trend'`

does not necessarily reflect that of the resulting WOE curve. The parameter`'Trend'`

tells the algorithm to “look for” an increasing or decreasing trend, but the outcome may not show the desired trend. For example, the algorithm cannot find a decreasing trend when the data actually has an increasing WOE trend. For more information on the`'Trend'`

option, see Monotone.`{'SortCategories','SortOption'}`

— Used for categorical predictors only. Used to determine how the predictor categories are sorted as a preprocessing step before applying the algorithm. The values of`'SortOption'`

are:`'Odds'`

— (default) The categories are sorted by order of increasing values of odds, defined as the ratio of “Good” to “Bad” observations, for the given category.`'Goods'`

— The categories are sorted by order of increasing values of “Good.”`'Bads'`

— The categories are sorted by order of increasing values of “Bad.”`'Totals'`

— The categories are sorted by order of increasing values of total number of observations (“Good” plus “Bad”).`'None'`

— No sorting is applied. The existing order of the categories is unchanged before applying the algorithm. (The existing order of the categories can be seen in the category grouping optional output from`bininfo`

.)

For more information, see Sort Categories

For

`Split`

algorithm:`{'InitialNumBins',`

— Specifies an integer that determines the number (*n*}*n*>0) of bins that the predictor is initially binned into before splitting. Valid for numeric predictors only. Default is`50`

.`{'Measure',`

— Specifies the measure where*MeasureName*}*'MeasureName'*is one of the following:`'Gini'`

(default),`'Chi2'`

,`'InfoValue'`

, or`'Entropy'`

.`{'MinBad',`

— Specifies the minimum number*n*}*n*(*n*>=`0`

) of Bads per bin. The default value is`1`

, to avoid pure bins.`{'MaxBad',`

— Specifies the maximum number*n*}*n*(*n*>=`0`

) of Bads per bin. The default value is`Inf`

.`{'MinGood',`

— Specifies the minimum number*n*}*n*(*n*>=`0`

) of Goods per bin. The default value is`1`

, to avoid pure bins.`{'MaxGood',`

— Specifies the maximum number*n*}*n*(*n*>=`0`

) of Goods per bin. The default value is`Inf`

.`{'MinCount',`

— Specifies the minimum number*n*}*n*(*n*>=`0`

) of observations per bin. The default value is`1`

, to avoid empty bins.`{'MaxCount',`

— Specifies the maximum number*n*}*n*(*n*>=`0`

) of observations per bin. The default value is`Inf`

.`{'MaxNumBins',`

— Specifies the maximum number*n*}*n*(*n*>=`2`

) of bins resulting from the splitting. The default value is`5`

.`{'Tolerance',`

— Specifies the minimum gain (>0) in the information function, during the iteration scheme, to select the cut-point that maximizes the gain. The default is*Tol*}`1e-4`

.`{'Significance',`

— Significance level threshold for the chi-square statistic, above which splitting happens. Values are in the interval*n*}`[0,1]`

. Default is`0.9`

(90% significance level).`{'SortCategories','SortOption'}`

— Used for categorical predictors only. Used to determine how the predictor categories are sorted as a preprocessing step before applying the algorithm. The values of`'SortOption'`

are:`'Goods'`

— The categories are sorted by order of increasing values of “Good.”`'Bads'`

— The categories are sorted by order of increasing values of “Bad.”`'Odds'`

— (default) The categories are sorted by order of increasing values of odds, defined as the ratio of “Good” to “Bad” observations, for the given category.`'Totals'`

— The categories are sorted by order of increasing values of total number of observations (“Good” plus “Bad”).`'None'`

— No sorting is applied. The existing order of the categories is unchanged before applying the algorithm. (The existing order of the categories can be seen in the category grouping optional output from`bininfo`

.)

For more information, see Sort Categories

For

`Merge`

algorithm:`{'InitialNumBins',`

— Specifies an integer that determines the number (*n*}*n*>0) of bins that the predictor is initially binned into before merging. Valid for numeric predictors only. Default is`50`

.`{'Measure',`

— Specifies the measure where*MeasureName*}*'MeasureName'*is one of the following:`'Chi2'`

(default),`'Gini'`

,`'InfoValue'`

, or`'Entropy'`

.`{'MinNumBins',`

— Specifies the minimum number*n*}*n*(*n*>=`2`

) of bins that result from merging. The default value is`2`

.`{'MaxNumBins',`

— Specifies the maximum number*n*}*n*(*n*>=`2`

) of bins that result from merging. The default value is`5`

.`{'Tolerance',`

— Specifies the minimum threshold below which merging happens for the information value and entropy statistics. Valid values are in the interval*n*}`(0.1)`

. Default is`1e-3`

.`{'Significance',`

— Significance level threshold for the chi-square statistic, below which merging happens. Values are in the interval*n*}`[0,1]`

. Default is`0.9`

(90% significance level).`{'SortCategories','SortOption'}`

— Used for categorical predictors only. Used to determine how the predictor categories are sorted as a preprocessing step before applying the algorithm. The values of`'SortOption'`

are:`'Goods'`

— The categories are sorted by order of increasing values of “Good.”`'Bads'`

— The categories are sorted by order of increasing values of “Bad.”`'Odds'`

— (default) The categories are sorted by order of increasing values of odds, defined as the ratio of “Good” to “Bad” observations, for the given category.`'Totals'`

— The categories are sorted by order of increasing values of total number of observations (“Good” plus “Bad”).`'None'`

— No sorting is applied. The existing order of the categories is unchanged before applying the algorithm. (The existing order of the categories can be seen in the category grouping optional output from`bininfo`

.)

For more information, see Sort Categories

For

`EqualFrequency`

algorithm:`{'NumBins',`

— Specifies the desired number (*n*}*n*) of bins. The default is`{'NumBins',5}`

and the number of bins must be a positive number.`{'SortCategories','SortOption'}`

— Used for categorical predictors only. Used to determine how the predictor categories are sorted as a preprocessing step before applying the algorithm. The values of`'SortOption'`

are:`'Odds'`

— (default) The categories are sorted by order of increasing values of odds, defined as the ratio of “Good” to “Bad” observations, for the given category.`'Goods'`

— The categories are sorted by order of increasing values of “Good.”`'Bads'`

— The categories are sorted by order of increasing values of “Bad.”`'Totals'`

— The categories are sorted by order of increasing values of total number of observations (“Good” plus “Bad”).`'None'`

— No sorting is applied. The existing order of the categories is unchanged before applying the algorithm. (The existing order of the categories can be seen in the category grouping optional output from`bininfo`

.)

For more information, see Sort Categories

For

`EqualWidth`

algorithm:`{'NumBins',`

— Specifies the desired number (*n*}*n*) of bins. The default is`{'NumBins',5}`

and the number of bins must be a positive number.`{'SortCategories','SortOption'}`

— Used for categorical predictors only. Used to determine how the predictor categories are sorted as a preprocessing step before applying the algorithm. The values of`'SortOption'`

are:`'Odds'`

— (default) The categories are sorted by order of increasing values of odds, defined as the ratio of “Good” to “Bad” observations, for the given category.`'Goods'`

— The categories are sorted by order of increasing values of “Good.”`'Bads'`

— The categories are sorted by order of increasing values of “Bad.”`'Totals'`

— The categories are sorted by order of increasing values of total number of observations (“Good” plus “Bad”).`'None'`

— No sorting is applied. The existing order of the categories is unchanged before applying the algorithm. (The existing order of the categories can be seen in the category grouping optional output from`bininfo`

.)

For more information, see Sort Categories

**Example: **```
sc =
autobinning(sc,'CustAge','Algorithm','Monotone','AlgorithmOptions',{'Trend','Increasing'})
```

**Data Types: **`cell`

`Display`

— Indicator to display information on status of the binning process at command line

`'Off'`

(default) | character vector with values `'On'`

,
`'Off'`

Indicator to display the information on status of the binning
process at command line, specified as the comma-separated pair
consisting of `'Display'`

and a character vector with a
value of `'On'`

or `'Off'`

.

**Data Types: **`char`

## Output Arguments

`sc`

— Credit scorecard model

`creditscorecard`

object

Credit scorecard model, returned as an updated
`creditscorecard`

object containing the
automatically determined binning maps or rules (cut points or category
groupings) for one or more predictors. For more information on using the
`creditscorecard`

object, see `creditscorecard`

.

**Note**

If you have previously used the `modifybins`

function to manually modify bins, these changes are lost when
running `autobinning`

because all the data is
automatically binned based on internal autobinning rules.

## More About

### Monotone

The `'Monotone'`

algorithm is an
implementation of the Monotone Adjacent Pooling Algorithm (MAPA), also known as
Maximum Likelihood Monotone Coarse Classifier (MLMCC); see Anderson or Thomas in
the References.

**Preprocessing**

During the preprocessing phase, preprocessing of numeric predictors consists
in applying equal frequency binning, with the number of bins determined by the
`'InitialNumBins'`

parameter (the default is 10 bins). The
preprocessing of categorical predictors consists in sorting the categories
according to the `'SortCategories'`

criterion (the default is
to sort by odds in increasing order). Sorting is not applied to ordinal
predictors. See the Sort Categories definition or the
description of `AlgorithmOptions`

option for
`'SortCategories'`

for more information.

**Main Algorithm**

The following example illustrates how the `'Monotone'`

algorithm arrives at cut points for numeric data.

Bin | Good | Bad | Iteration1 | Iteration2 | Iteration3 | Iteration4 |
---|---|---|---|---|---|---|

| 127 | 107 | 0.543 | |||

| 194 | 90 | 0.620 | 0.683 | ||

| 135 | 78 | 0.624 | 0.662 | ||

| 164 | 66 | 0.645 | 0.678 | 0.713 | |

| 183 | 56 | 0.669 | 0.700 | 0.740 | 0.766 |

Initially, the numeric data is preprocessed with an equal frequency binning. In this example, for simplicity, only the five initial bins are used. The first column indicates the equal frequency bin ranges, and the second and third columns have the “Good” and “Bad” counts per bin. (The number of observations is 1,200, so a perfect equal frequency binning would result in five bins with 240 observations each. In this case, the observations per bin do not match 240 exactly. This is a common situation when the data has repeated values.)

Monotone finds break points based on the cumulative proportion of
“Good” observations. In the`'Iteration1'`

column,
the first value (0.543) is the number of “Good” observations in
the first bin (127), divided by the total number of observations in the bin
(127+107). The second value (0.620) is the number of “Good”
observations in bins 1 and 2, divided by the total number of observations in
bins 1 and 2. And so forth. The first cut point is set where the minimum of this
cumulative ratio is found, which is in the first bin in this example. This is
the end of iteration 1.

Starting from the second bin (the first bin after the location of the minimum value in the previous iteration), cumulative proportions of “Good” observations are computed again. The second cut point is set where the minimum of this cumulative ratio is found. In this case, it happens to be in bin number 3, therefore bins 2 and 3 are merged.

The algorithm proceeds the same way for two more iterations. In this particular example, in the end it only merges bins 2 and 3. The final binning has four bins with cut points at 33,000, 42,000, and 47,000.

For categorical data, the only difference is that the preprocessing step consists in reordering the categories. Consider the following categorical data:

Bin | Good | Bad | Odds |
---|---|---|---|

| 365 | 177 | 2.062 |

| 307 | 167 | 1.838 |

| 131 | 53 | 2.474 |

The preprocessing step, by default, sorts the categories by
`'Odds'`

. (See the Sort Categories definition or the
description of `AlgorithmOptions`

option for
`'SortCategories'`

for more information.) Then, it applies
the same steps described above, shown in the following table:

Bin | Good | Bad | Odds | Iteration1 | Iteration2 | Iteration3 |
---|---|---|---|---|---|---|

'Tenant' | 307 | 167 | 1.838 | 0.648 | ||

'Home Owner' | 365 | 177 | 2.062 | 0.661 | 0.673 | |

'Other' | 131 | 53 | 2.472 | 0.669 | 0.683 | 0.712 |

In this case, the Monotone algorithm would not merge any categories. The only
difference, compared with the data before the application of the algorithm, is
that the categories are now sorted by `'Odds'`

.

In both the numeric and categorical examples above, the implicit
`'Trend'`

choice is `'Increasing'`

. (See
the description of `AlgorithmOptions`

option for the
`'Monotone'`

`'Trend'`

option.) If you set the trend to
`'Decreasing'`

, the algorithm looks for the maximum
(instead of the minimum) cumulative ratios to determine the cut points. In that
case, at iteration 1, the maximum would be in the last bin, which would imply
that all bins should be merged into a single bin. Binning into a single bin is a
total loss of information and has no practical use. Therefore, when the chosen
trend leads to a single bin, the Monotone implementation rejects it, and the
algorithm returns the bins found after the preprocessing step. This state is the
initial equal frequency binning for numeric data and the sorted categories for
categorical data. The implementation of the Monotone algorithm by default uses a
heuristic to identify the trend (`'Auto'`

option for
`'Trend'`

).

### Split

*Split* is a supervised automatic binning
algorithm, where a measure is used to split the data into buckets. The supported
measures are `gini`

, `chi2`

,
`infovalue`

, and `entropy`

.

Internally, the split algorithm proceeds as follows:

All categories are merged into a single bin.

At the first iteration, all potential cutpoint indices are tested to see which one results in the maximum increase in the information function (

`Gini`

,`InfoValue`

,`Entropy`

, or`Chi2`

). That cutpoint is then selected, and the bin is split.The same procedure is reiterated for the next sub-bins.

The algorithm stops when the maximum number of bins is reached or when the splitting does not result in any additional change in the information change function.

The following table for a categorical predictor summarizes the values of the
change function at each iteration. In this example, `'Gini'`

is the
measure of choice, such that the goal is to see a decrease of the Gini measure at
each iteration.

Iteration 0 Bin Number | Member | Gini | Iteration 1 Bin Number | Member | Gini | Iteration 2 Bin Number | Member | Gini |
---|---|---|---|---|---|---|---|---|

1 | 'Tenant' | 1 | 'Tenant' | 1 | 'Tenant' | 0.45638 | ||

1 | 'Subletter' | 1 | 'Subletter' | 0.44789 | 1 | 'Subletter' | ||

1 | 'Home Owner' | 1 | 'Home Owner' | 2 | 'Home Owner' | 0.43984 | ||

1 | 'Other' | 2 | 'Other' | 0.41015 | 3 | 'Other' | 0.41015 | |

| 0.442765 | 0.442102 | 0.441822 | |||||

Relative Change | 0 | 0.001498 | 0.002128 |

The relative change at iteration *i* is with respect to the Gini
measure of the entire bins at iteration *i*-1. The final result
corresponds to that from the last iteration which, in this example, is iteration
2.

The following table for a numeric predictor summarizes the values of the change
function at each iteration. In this example, `'Gini'`

is the
measure of choice, such that the goal is to see a decrease of the Gini measure at
each iteration. Since most numeric predictors in datasets contain many bins, there
is a preprocessing step where the data is pre-binned into 50 equal-frequency bins.
This makes the pool of valid cutpoints to choose from for splitting smaller and more
manageable.

Iteration 0 Bin Number | Member | Gini | Iteration 1 Bin Number | Gini | Iteration 2 Bin Number | Gini | Iteration 3 Bin Number | Gini |
---|---|---|---|---|---|---|---|---|

1 | `'21'` | `'[-Inf,47]'` | 0.473897 | `'[-Inf,47]'` | 0.473897 | `'[-Inf,35]'` | 0.494941 | |

1 | `'22'` | `'[47,Inf]'` | 0.385238 | `'[47,61]'` | 0.407072 | `'[35, 47]'` | 0.463201 | |

1 | `'23'` | `'[61,Inf]'` | 0.208795 | `'[47, 61]'` | 0.407072 | |||

1 | `'74'` | 0 | `'[61,Inf]'` | 0.208795 | ||||

| 0.442765 | 0.435035 | 0.432048 | 0.430511 | ||||

Relative Change | 0 | 0.01746 | 0.006867 | 0.0356 |

The resulting split must be such that the information function (content) increases. As such, the best split is the one that results in the maximum information gain. The information functions supported are:

Gini: Each split results in an increase in the Gini Ratio, defined as:

G_r = 1- G_hat/G_p

`G_p`

is the Gini measure of the parent node, that is, of the given bins/categories prior to splitting.`G_hat`

is the weighted Gini measure for the current split:G_hat = Sum((nj/N) * Gini(j), j=1..m)

where

`nj`

is the total number of observations in the*j*th bin.`N`

is the total number of observations in the dataset.`m`

is the number of splits for the given variable.`Gini(j)`

is the Gini measure for the*j*th bin.The Gini measure for the split/node

*j*is:whereGini(j) = 1 - (Gj^2+Bj^2) / (nj)^2

`Gj`

,`Bj`

= Number of Goods and Bads for bin*j*.`InfoValue`

: The information value for each split results in an increase in the total information. The split that is retained is the one which results in the maximum gain, within the acceptable gain tolerance. The Information Value (IV) for a given observation*j*is defined as:whereIV = sum( (pG_i-pB_i) * log(pG_i/pB_i), i=1..n)

`pG_i`

is the distribution of Goods at observation`i`

, that is`Goods(i)/Total_Goods`

.`pB_i`

is the distribution of Bads at observation`i`

, that is`Bads(i)/Total_Bads`

.`n`

is the total number of bins.`Entropy`

: Each split results in a decrease in entropy variance defined as:E = -sum(ni * Ei, i=1..n)

where

`ni`

is the total count for bin`i`

, that is`(ni = Gi + Bi)`

.`Ei`

is the entropy for row (or bin)`i`

, defined as:Ei = -sum(Gi*log2(Gi/ni) + Bi*log2(Bi/ni))/N, i=1..n

`Chi2`

: Chi2 is computed pairwise for each pair of bins and measures the statistical difference between two groups. Splitting is selected at a point (cutpoint or category indexing) where the maximum Chi2 value is:Chi2 = sum(sum((Aij - Eij)^2/Eij , j=1..k), i=m,m+1)

where

`m`

takes values from`1 ... n-1`

, where`n`

is the number of bins.`k`

is the number of classes. Here`k = 2`

for the (Goods, Bads).`Aij`

is the number of observations in bin`i`

,`j`

th class.`Eij`

is the expected frequency of`Aij`

, which is equal to`(Ri*Cj)/N`

.`Ri`

is the number of observations in bin`i`

, which is equal to`sum(Aij, j=1..k)`

.`Cj`

is the number of observations in the`j`

th class, which is equal to`sum(Aij, I = m,m+1)`

.`N`

is the total number of observations, which is equal to`sum(Cj, j=1..k)`

.

The `Chi2`

measure for the entire sample (as opposed to the
pairwise `Chi2`

measure for adjacent bins)
is:

Chi2 = sum(sum((Aij - Eij)^2/Eij , j=1..k), i=1..n)

### Merge

*Merge* is a supervised automatic binning
algorithm, where a measure is used to merge bins into buckets. The supported
measures are `chi2`

, `gini`

,
`infovalue`

, and `entropy`

.

Internally, the merge algorithm proceeds as follows:

All categories are initially in separate bins.

The user selected information function (

`Chi2`

,`Gini`

,`InfoValue`

or`Entropy`

) is computed for any pair of adjacent bins.At each iteration, the pair with the smallest information change measured by the selected information function is merged.

The merging continues until either:

All pairwise information values are greater than the threshold set by the significance level or the relative change is smaller than the tolerance.

If at the end, the number of bins is still greater than the

`MaxNumBins`

allowed, merging is forced until there are at most`MaxNumBins`

bins. Similarly, merging stops when there are only`MinNumBins`

bins.

For categorical, original bins/categories are pre-sorted according to the sorting of choice set by the user. For numeric data, the data is preprocessed to get

`IntialNumBins`

bins of equal frequency before the merging algorithm starts.

The following table for a categorical predictor summarizes the values of the
change function at each iteration. In this example, `'Chi2'`

is the
measure of choice. The default sorting by `Odds`

is applied as a
preprocessing step. The `Chi2`

value reported below at row
*i* is for bins *i* and
*i*+1. The significance level is `0.9`

(90%), so
that the inverse `Chi2`

value is `2.705543`

. This
is the threshold below which adjacent pairs of bins are merged. The minimum number
of bins is 2.

Iteration 0 Bin Number | Member | Chi2 | Iteration 1 Bin Number | Member | Chi2 | Iteration 2 Bin Number | Member | Chi2 |
---|---|---|---|---|---|---|---|---|

1 | 'Tenant' | 1.007613 | 1 | 'Tenant' | 0.795920 | 1 | 'Tenant' | |

2 | 'Subletter' | 0.257347 | 2 | 'Subletter' | 1 | 'Subletter' | ||

3 | 'Home Owner' | 1.566330 | 2 | 'Home Owner' | 1.522914 | 1 | 'Home Owner' | 1.797395 |

4 | 'Other' | 3 | 'Other' | 2 | 'Other' | |||

| 2.573943 | 2.317717 | 1.797395 |

The following table for a numeric predictor summarizes the values of the change
function at each iteration. In this example, `'Chi2'`

is the
measure of choice.

Iteration 0 Bin Number | Chi2 | Iteration 1 Bins | Chi2 | Final Iteration Bins | Chi2 | |
---|---|---|---|---|---|---|

`'[-Inf,22]'` | 0.11814 | `'[-Inf,22]'` | 0.11814 | `'[-Inf,33]'` | 8.4876 | |

`'[22,23]'` | 1.6464 | `'[22,23]'` | 1.6464 | `'[33, 48]'` | 7.9369 | |

... | ... | `'[48,64]'` | 9.956 | |||

`'[58,59]'` | 0.311578 | `'[58,59]'` | 0.27489 | `'[64,65]'` | 9.6988 | |

`'[59,60]'` | 0.068978 | `'[59,61]'` | 1.8403 | `'[65,Inf]'` | NaN | |

`'[60,61]'` | 1.8709 | `'[61,62]'` | 5.7946 | ... | ||

`'[61,62]'` | 5.7946 | ... | ||||

... | `'[69,70]'` | 6.4271 | ||||

`'[69,70]'` | 6.4271 | `'[70,Inf]'` | NaN | |||

`'[70,Inf]'` | NaN | |||||

| 67.467 | 67.399 | 23.198 |

The resulting merging must be such that any pair of adjacent bins is statistically
different from each other, according to the chosen measure. The measures supported
for `Merge`

are:

`Chi2`

: Chi2 is computed pairwise for each pair of bins and measures the statistical difference between two groups. Merging is selected at a point (cutpoint or category indexing) where the maximum Chi2 value is:Chi2 = sum(sum((Aij - Eij)^2/Eij , j=1..k), i=m,m+1)

where

`m`

takes values from`1 ... n-1`

, and`n`

is the number of bins.`k`

is the number of classes. Here`k = 2`

for the (Goods, Bads).`Aij`

is the number of observations in bin`i`

,`j`

th class.`Eij`

is the expected frequency of`Aij`

, which is equal to`(Ri*Cj)/N`

.`Ri`

is the number of observations in bin`i`

, which is equal to`sum(Aij, j=1..k)`

.`Cj`

is the number of observations in the`j`

th class, which is equal to`sum(Aij, I = m,m+1)`

.`N`

is the total number of observations, which is equal to`sum(Cj, j=1..k)`

.The

`Chi2`

measure for the entire sample (as opposed to the pairwise`Chi2`

measure for adjacent bins) is:Chi2 = sum(sum((Aij - Eij)^2/Eij , j=1..k), i=1..n)

Gini: Each merge results in a decrease in the Gini Ratio, defined as:

G_r = 1- G_hat/G_p

`G_p`

is the Gini measure of the parent node, that is, of the given bins/categories prior to merging.`G_hat`

is the weighted Gini measure for the current merge:G_hat = Sum((nj/N) * Gini(j), j=1..m)

where

`nj`

is the total number of observations in the*j*th bin.`N`

is the total number of observations in the dataset.`m`

is the number of merges for the given variable.`Gini(j)`

is the Gini measure for the*j*th bin.The Gini measure for the merge/node

*j*is:whereGini(j) = 1 - (Gj^2+Bj^2) / (nj)^2

`Gj`

,`Bj`

= Number of Goods and Bads for bin*j*.`InfoValue`

: The information value for each merge will result in a decrease in the total information. The merge that is retained is the one which results in the minimum gain, within the acceptable gain tolerance. The Information Value (IV) for a given observation*j*is defined as:whereIV = sum( (pG_i-pB_i) * log(pG_i/pB_i), i=1..n)

`pG_i`

is the distribution of Goods at observation`i`

, that is`Goods(i)/Total_Goods`

.`pB_i`

is the distribution of Bads at observation`i`

, that is`Bads(i)/Total_Bads`

.`n`

is the total number of bins.`Entropy`

: Each merge results in an increase in entropy variance defined as:E = -sum(ni * Ei, i=1..n)

where

`ni`

is the total count for bin`i`

, that is`(ni = Gi + Bi)`

.`Ei`

is the entropy for row (or bin)`i`

, defined as:Ei = -sum(Gi*log2(Gi/ni) + Bi*log2(Bi/ni))/N, i=1..n

**Note**

When using the Merge algorithm, if there are pure bins (bins that have
either zero count of `Goods`

or zero count of
`Bads`

), the statistics such as Information Value and
Entropy have non-finite values. To account for this, a frequency shift of
`.5`

is applied for computing various statistics
whenever the algorithm finds pure bins.

### Equal Frequency

Unsupervised algorithm that divides the data into a predetermined number of bins that contain approximately the same number of observations.

`EqualFrequency`

is defined as:

Let v[1], v[2],..., v[N] be the sorted list of different values or categories
observed in the data. Let f[*i*] be the frequency of
v[*i*]. Let F[*k*] =
f[1]+...+f[*k*] be the cumulative sum of frequencies up to
the *k*th sorted value. Then F[*N*] is the
same as the total number of observations.

Define `AvgFreq`

= F[*N*] /
*NumBins*, which is the ideal average frequency per bin after
binning. The *n*th cut point index is the index
*k* such that the distance abs(F[*k*] -
*n**`AvgFreq`

) is minimized.

This rule attempts to match the cumulative frequency up to the
*n*th bin. If a single value contains too many
observations, equal frequency bins are not possible, and the above rule yields
less than *NumBins* total bins. In that case, the algorithm
determines *NumBins* bins by breaking up bins, in the order in
which the bins were constructed.

The preprocessing of categorical predictors consists in sorting the categories
according to the `'SortCategories'`

criterion (the default is
to sort by odds in increasing order). Sorting is not applied to ordinal
predictors. See the Sort Categories definition or the
description of `AlgorithmOptions`

option for
`'SortCategories'`

for more information.

### Equal Width

Unsupervised algorithm that divides the range of values in the domain of the predictor variable into a predetermined number of bins of “equal width.” For numeric data, the width is measured as the distance between bin edges. For categorical data, width is measured as the number of categories within a bin.

The `EqualWidth`

option is defined as:

For numeric data, if `MinValue`

and
`MaxValue`

are the minimum and maximum data values,
then

Width = (MaxValue - MinValue)/NumBins

`CutPoints`

are set to `MinValue`

+ Width,
`MinValue`

+ 2*Width, ... `MaxValue`

– Width.
If a `MinValue`

or `MaxValue`

have not been
specified using the `modifybins`

function, the
`EqualWidth`

option sets `MinValue`

and
`MaxValue`

to the minimum and maximum values observed in the
data.For categorical data, if there are *NumCats* numbers of
original categories,
then

Width = NumCats / NumBins,

*NumCats*– Width, plus 1.

The preprocessing of categorical predictors consists in sorting the categories
according to the `'SortCategories'`

criterion (the default is
to sort by odds in increasing order). Sorting is not applied to ordinal
predictors. See the Sort Categories definition or the
description of `AlgorithmOptions`

option for
`'SortCategories'`

for more information.

### Sort Categories

As a preprocessing step for categorical data,
`'Monotone'`

, `'EqualFrequency'`

, and
`'EqualWidth'`

support the
`'SortCategories'`

input. This serves the purpose of
reordering the categories before applying the main algorithm. The default
sorting criterion is to sort by `'Odds'`

. For example, suppose
that the data originally looks like this:

Bin | Good | Bad | Odds |
---|---|---|---|

`'Home Owner'` | 365 | 177 | 2.062 |

`'Tenant'` | 307 | 167 | 1.838 |

`'Other'` | 131 | 53 | 2.472 |

After the preprocessing step, the rows would be sorted by
`'Odds'`

and the table looks like this:

Bin | Good | Bad | Odds |
---|---|---|---|

`'Tenant'` | 307 | 167 | 1.838 |

`'Home Owner'` | 365 | 177 | 2.062 |

`'Other'` | 131 | 53 | 2.472 |

The three algorithms only merge adjacent bins, so the initial order of the
categories makes a difference for the final binning. The
`'None'`

option for `'SortCategories'`

would leave the original table unchanged. For a description of the sorting
criteria supported, see the description of the
`AlgorithmOptions`

option for
`'SortCategories'`

.

Upon the construction of a scorecard, the initial order of the categories,
before any algorithm or any binning modifications are applied, is the order
shown in the first output of `bininfo`

. If the bins have been
modified (either manually with `modifybins`

or automatically
with `autobinning`

), use the optional output
(`cg`

,`'category grouping'`

) from
`bininfo`

to get the current
order of the categories.

The `'SortCategories'`

option has no effect on categorical
predictors for which the `'Ordinal'`

parameter is set to true
(see the `'Ordinal'`

input parameter in MATLAB^{®} categorical arrays for `categorical`

. Ordinal data has a
natural order, which is honored in the preprocessing step of the algorithms by
leaving the order of the categories unchanged. Only categorical predictors whose
`'Ordinal'`

parameter is false (default option) are subject
to reordering of categories according to the `'SortCategories'`

criterion.

### Using `autobinning`

with Weights

When observation weights are defined using the optional
`WeightsVar`

argument when creating a
`creditscorecard`

object, instead of counting the rows that
are good or bad in each bin, the `autobinning`

function
accumulates the weight of the rows that are good or bad in each bin.

The “frequencies” reported are no longer the basic “count” of rows, but the
“cumulative weight” of the rows that are good or bad and fall in a particular
bin. Once these “weighted frequencies” are known, all other relevant statistics
(`Good`

, `Bad`

, `Odds`

,
`WOE`

, and `InfoValue`

) are computed with
the usual formulas. For more information, see Credit Scorecard Modeling Using Observation Weights.

## References

[1] Anderson, R. *The Credit Scoring Toolkit.* Oxford
University Press, 2007.

[2] Kerber, R. "ChiMerge: Discretization of Numeric Attributes." *AAAI-92
Proceedings.* 1992.

[3] Liu, H., et. al. *Data Mining, Knowledge, and Discovery.*
Vol 6. Issue 4. October 2002, pp. 393-423.

[4] Refaat, M. *Data Preparation for Data Mining Using
SAS.* Morgan Kaufmann, 2006.

[5] Refaat, M. *Credit Risk Scorecards: Development and
Implementation Using SAS.* lulu.com, 2011.

[6] Thomas, L., et al. *Credit Scoring and Its
Applications.* Society for Industrial and Applied Mathematics,
2002.

## See Also

`creditscorecard`

| `bininfo`

| `predictorinfo`

| `modifypredictor`

| `modifybins`

| `bindata`

| `plotbins`

| `fitmodel`

| `displaypoints`

| `formatpoints`

| `score`

| `setmodel`

| `probdefault`

| `validatemodel`

**Introduced in R2014b**

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