Credit Scorecard Modeling with Missing Values

Develop a Credit Scorecard with Explicit Bins for Missing Values

When you create a creditscorecard object, the data can contain missing values. When using creditscorecard to create a creditscorecard object, you can set the name-value pair argument for 'BinMissingData' set to true. In this case, the missing data for numeric predictors (NaN values) and for categorical predictors (<undefined> values) is binned in a separate bin labeled <missing> that appears at the end of the bins. Predictors with no missing values in the training data have no <missing> bin. If you do not specify the 'BinMissingData' argument or if you set 'BinMissingData' to false, the creditscorecard function discards missing observations when computing frequencies of Good and Bad, and neither the bininfo nor plotbins functions reports such observations.

The <missing> bin remains in place throughout the scorecard modeling process. The final scorecard explicitly indicates the points to be assigned to missing values for predictors that have a <missing> bin. These points are determined from the weight-of-evidence (WOE) value of the <missing> bin and the predictor's coefficient in the logistic model. For predictors without an explicit <missing> bin, you can assign points to missing values using the name-value pair argument 'Missing' in formatpoints, as described in this example, or by using one of the four different ways to "treat" the missing data.

The dataMissing table in the CreditCardData.mat file has two predictors with missing values — CustAge and ResStatus.

load CreditCardData.mat
head(dataMissing,5)

    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   

Create a creditscorecard object using the CreditCardData.mat file to load the dataMissing table with missing values. Set the 'BinMissingData' argument to true. Apply automatic binning.

sc = creditscorecard(dataMissing,'IDVar','CustID','BinMissingData',true);
sc = autobinning(sc);

The bin information and bin plots for the predictors that have missing data both show a <missing> bin at the end.

bi = bininfo(sc,'CustAge');
disp(bi)

         Bin         Good    Bad     Odds       WOE       InfoValue 
    _____________    ____    ___    ______    ________    __________

    {'[-Inf,33)'}     69      52    1.3269    -0.42156      0.018993
    {'[33,37)'  }     63      45       1.4    -0.36795      0.012839
    {'[37,40)'  }     72      47    1.5319     -0.2779     0.0079824
    {'[40,46)'  }    172      89    1.9326    -0.04556     0.0004549
    {'[46,48)'  }     59      25      2.36     0.15424     0.0016199
    {'[48,51)'  }     99      41    2.4146     0.17713     0.0035449
    {'[51,58)'  }    157      62    2.5323     0.22469     0.0088407
    {'[58,Inf]' }     93      25      3.72     0.60931      0.032198
    {'<missing>'}     19      11    1.7273    -0.15787    0.00063885
    {'Totals'   }    803     397    2.0227         NaN      0.087112

plotbins(sc,'CustAge')

bi = bininfo(sc,'ResStatus');
disp(bi)

         Bin          Good    Bad     Odds        WOE       InfoValue 
    ______________    ____    ___    ______    _________    __________

    {'Tenant'    }    296     161    1.8385    -0.095463     0.0035249
    {'Home Owner'}    352     171    2.0585     0.017549    0.00013382
    {'Other'     }    128      52    2.4615      0.19637     0.0055808
    {'<missing>' }     27      13    2.0769     0.026469    2.3248e-05
    {'Totals'    }    803     397    2.0227          NaN     0.0092627

plotbins(sc,'ResStatus')

The training data for the 'CustAge' and 'ResStatus' predictors has missing data (NaNs and <undefined>). The binning process estimates WOE values of -0.15787 and 0.026469, respectively, for the missing data in these predictors.

The training data for EmpStatus and CustIncome has no explicit bin for <missing> values because there are no missing values for these predictors.

bi = bininfo(sc,'EmpStatus');
disp(bi)

        Bin         Good    Bad     Odds       WOE       InfoValue
    ____________    ____    ___    ______    ________    _________

    {'Unknown' }    396     239    1.6569    -0.19947    0.021715 
    {'Employed'}    407     158    2.5759      0.2418    0.026323 
    {'Totals'  }    803     397    2.0227         NaN    0.048038 

bi = bininfo(sc,'CustIncome');
disp(bi)

           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

Use fitmodel to fit a logistic regression model using WOE values. fitmodel internally transforms all the predictor variables into WOE values, using the bins found during the automatic binning process. By default, fitmodel then fits a logistic regression model using a stepwise method. For predictors that have missing data, there is an explicit <missing> bin with a corresponding WOE value computed from the data. When you use fitmodel, the corresponding WOE value for the <missing> bin is applied when the function performs the WOE transformation.

[sc,mdl] = fitmodel(sc,'display','off');

Scale the scorecard points by the points-to-double-the-odds (PDO) method using the 'PointsOddsAndPDO' argument of formatpoints. Suppose that you want a score of 500 points to have odds of 2 (twice as likely to be good than to be bad) and that the odds double every 50 points (so that 550 points would have odds of 4).

Display the scorecard showing the scaled points for predictors retained in the fitting model.

sc = formatpoints(sc,'PointsOddsAndPDO',[500 2 50]);
PointsInfo = displaypoints(sc)

PointsInfo=38×3 table
     Predictors           Bin          Points
    _____________    ______________    ______

    {'CustAge'  }    {'[-Inf,33)' }    54.062
    {'CustAge'  }    {'[33,37)'   }    56.282
    {'CustAge'  }    {'[37,40)'   }    60.012
    {'CustAge'  }    {'[40,46)'   }    69.636
    {'CustAge'  }    {'[46,48)'   }    77.912
    {'CustAge'  }    {'[48,51)'   }     78.86
    {'CustAge'  }    {'[51,58)'   }     80.83
    {'CustAge'  }    {'[58,Inf]'  }     96.76
    {'CustAge'  }    {'<missing>' }    64.984
    {'ResStatus'}    {'Tenant'    }    62.138
    {'ResStatus'}    {'Home Owner'}    73.248
    {'ResStatus'}    {'Other'     }    90.828
    {'ResStatus'}    {'<missing>' }    74.125
    {'EmpStatus'}    {'Unknown'   }    58.807
    {'EmpStatus'}    {'Employed'  }    86.937
    {'EmpStatus'}    {'<missing>' }       NaN
      ⋮

Notice that points for the <missing> bins for CustAge and ResStatus are explicitly shown (as 64.9836 and 74.1250, respectively). These points are computed from the WOE value for the <missing> bin and the logistic model coefficients.

Points for predictors that have no missing data in the training set, by default, are set to NaN and they lead to a score of NaN when you run score. This can be changed by updating the name-value pair argument 'Missing' in formatpoints to indicate how to treat missing data for scoring purposes.

The scorecard is ready for scoring new data sets. You can also use the scorecard to compute probabilities of default or perform model validation. For details, see score, probdefault, and validatemodel. To further explore the handling of missing data, take a few rows from the original data as test data and introduce some missing data.

tdata = dataMissing(11:14,mdl.PredictorNames); % Keep only the predictors retained in the model
% Set some missing values
tdata.CustAge(1) = NaN;
tdata.ResStatus(2) = missing;
tdata.EmpStatus(3) = missing;
tdata.CustIncome(4) = NaN;
disp(tdata)

    CustAge     ResStatus      EmpStatus     CustIncome    TmWBank    OtherCC    AMBalance
    _______    ___________    ___________    __________    _______    _______    _________

      NaN      Tenant         Unknown          34000         44         Yes        119.8  
       48      <undefined>    Unknown          44000         14         Yes       403.62  
       65      Home Owner     <undefined>      48000          6         No        111.88  
       44      Other          Unknown            NaN         35         No        436.41  

Score the new data and see how points for missing data are differently assigned for CustAge and ResStatus and for EmpStatus and CustIncome. CustAge and ResStatus have an explicit <missing> bin for missing data. However, for EmpStatus and CustIncome, the score function sets the points to NaN.

[Scores,Points] = score(sc,tdata);
disp(Scores)

  481.2231
  520.8353
       NaN
       NaN

disp(Points)

    CustAge    ResStatus    EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance
    _______    _________    _________    __________    _______    _______    _________

    64.984      62.138       58.807        67.893      61.858     75.622      89.922  
     78.86      74.125       58.807        82.439      61.061     75.622      89.922  
     96.76      73.248          NaN        96.969      51.132     50.914      89.922  
    69.636      90.828       58.807           NaN      61.858     50.914      89.922  

Use the name-value pair argument 'Missing' in formatpoints to choose how to assign points to missing values for predictors that do not have an explicit <missing> bin. For this example, use the 'MinPoints' option for the 'Missing' argument. For EmpStatus and CustIncome, the minimum numbers of points in the scorecard are 58.8072 and 29.3753, respectively. You can also treat missing values using one of the four different ways to "treat" the missing data.

sc = formatpoints(sc,'Missing','MinPoints');
[Scores,Points] = score(sc,tdata);
disp(Scores)

  481.2231
  520.8353
  517.7532
  451.3405

disp(Points)

    CustAge    ResStatus    EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance
    _______    _________    _________    __________    _______    _______    _________

    64.984      62.138       58.807        67.893      61.858     75.622      89.922  
     78.86      74.125       58.807        82.439      61.061     75.622      89.922  
     96.76      73.248       58.807        96.969      51.132     50.914      89.922  
    69.636      90.828       58.807        29.375      61.858     50.914      89.922  

Four Approaches for Treating Missing Data and Developing a New Credit Scorecard

There are four different approaches for treating missing data.

Approach 1: Fill missing data using the fillmissing function of the creditscorecard object

The creditscorecard object supports a fillmissing function. When you call the function on a predictor or group of predictors, the fillmissing function fills the missing data with the user-specified statistic. fillmissing supports the fill values 'mean', 'median', 'mode', and 'constant', as well as the option to switch back to the original data.

The advantage of using fillmissing is that the creditscorecard object keeps track of the fill value and also applies it to the validation data. The limitation of this approach is that only basic statistics are used to fill missing data.

For more information on Approach 1, see fillmissing.

Approach 2: Fill missing data using the MATLAB® fillmissing function

MATLAB® supports a fillmissing function that you can use before creating a creditscorecard object to treat missing values in numeric and categorical data. The advantage of this method is that you can use all the options available in fillmissing to fill missing data, as well as other MATLAB functionality, such as standardizeMissing and features for the treatment of outliers. However, the downside is that you are responsible for the same transformations to the validation data before scoring as the fillmissing function is outside of the creditscorecard object.

For more information on Approach 2, see Treat Missing Data in a Credit Scorecard Workflow Using MATLAB fillmissing.

Approach 3: Impute missing data using the k-nearest neighbors (KNN) algorithm

This KNN approach considers multiple predictors as compared to Approach 1 and Approach 2. Like Approach 2, the KNN approach is done outside the creditscoreacrd workflow, and consequently, you need to perform imputation for both the training and validation data.

For more information on Approach 3, see Impute Missing Data in the Credit Scorecard Workflow Using the k-Nearest Neighbors Algorithm.

Approach 4: Impute missing data using the random forest algorithm

This random forest approach is similar to Approach 3 and uses multiple predictors to impute missing values. Because the approach is outside the creditscorecard workflow, you need to perform imputation for both the training and validation data.

For more information on Approach 4, see Impute Missing Data in the Credit Scorecard Workflow Using the Random Forest Algorithm.