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Impute Missing Data in the Credit Scorecard Workflow Using the Random Forest Algorithm

This example shows how to perform imputation of missing data in the credit scorecard workflow using the random forest algorithm.

Random forests are an ensemble learning method for classification or regression that operates by constructing a multitude of decision trees at training time and obtaining the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees. Random forests correct for the tendency of decision trees to overfit to the training set. For more information on the random forest algorithm, see fitrensemble and fitcensemble.

For additional information on alternative approaches for "treating" missing data, see Credit Scorecard Modeling with Missing Values.

Impute Missing Data Using Random Forest Algorithm

Use the dataMissing data set to impute missing values for the CustAge (numeric) and ResStatus (categorical) predictors.

load CreditCardData.mat
disp(head(dataMissing));
    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   
      6          65          13         Home Owner     Employed       48000         59         Yes       968.18        0.15        0   
      7          34          32         Home Owner     Unknown        32000         26         Yes       717.82        0.02        1   
      8          50          57         Other          Employed       51000         33         No        3041.2        0.13        0   

Remove the 'CustID' and 'status' columns in the imputation process as these are the id and response values respectively. Alternatively, you can choose to leave the 'status' column in.

dataToImpute = dataMissing(:,setdiff(dataMissing.Properties.VariableNames,...
    {'CustID','status'},'stable'));

rfImputedData = dataMissing;

Because multiple predictors contain missing data, turn on the 'Surrogate' flag when you create the decision tree template.

rng('default');
tmp = templateTree('Surrogate','on','Reproducible',true);

Next, use the fitrensemble and fitcensemble functions, which return the trained regression and classification ensemble model objects contain the results of boosting 100 regression and classification trees using LSBoost, respectively.

missingCustAge = ismissing(dataToImpute.CustAge);
% Fit ensemble of regression learners
rfCustAge = fitrensemble(dataToImpute,'CustAge','Method','Bag',...
    'NumLearningCycles',200,'Learners',tmp,'CategoricalPredictors',...
    {'ResStatus','EmpStatus','OtherCC'});
rfImputedData.CustAge(missingCustAge) = predict(rfCustAge,...
    dataToImpute(missingCustAge,:));

missingResStatus = ismissing(dataToImpute.ResStatus);
% Fit ensemble of classification learners
rfResStatus = fitcensemble(dataToImpute,'ResStatus','Method','Bag',...
    'NumLearningCycles',200,'Learners',tmp,'CategoricalPredictors',...
    {'EmpStatus','OtherCC'});
rfImputedData.ResStatus(missingResStatus) = predict(rfResStatus,...
    dataToImpute(missingResStatus,:));

% Optionally, round the age to the nearest integer
rfImputedData.CustAge = round(rfImputedData.CustAge);

Compare Imputed Data to Original Data

disp(rfImputedData(5:10,:));
    CustID    CustAge    TmAtAddress    ResStatus     EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance    UtilRate    status
    ______    _______    ___________    __________    _________    __________    _______    _______    _________    ________    ______

       5        68           56         Home Owner    Employed       53000         14         Yes       561.84        0.11        0   
       6        65           13         Home Owner    Employed       48000         59         Yes       968.18        0.15        0   
       7        34           32         Home Owner    Unknown        32000         26         Yes       717.82        0.02        1   
       8        50           57         Other         Employed       51000         33         No        3041.2        0.13        0   
       9        50           10         Tenant        Unknown        52000         25         Yes       115.56        0.02        1   
      10        49           30         Home Owner    Unknown        53000         23         Yes        718.5        0.17        1   
disp(rfImputedData(find(missingCustAge,5),:));
    CustID    CustAge    TmAtAddress    ResStatus     EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance    UtilRate    status
    ______    _______    ___________    __________    _________    __________    _______    _______    _________    ________    ______

       4        55           75         Home Owner    Employed       53000         20         Yes       157.37        0.08        0   
      19        54           14         Home Owner    Employed       51000         11         Yes       519.46        0.42        1   
     138        52           31         Other         Employed       41000          2         Yes       1101.8        0.32        0   
     165        46           21         Home Owner    Unknown        38000         70         No          1217         0.2        0   
     207        52           38         Home Owner    Employed       48000         12         No         573.9         0.1        0   
disp(rfImputedData(find(missingResStatus,5),:));
    CustID    CustAge    TmAtAddress    ResStatus     EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance    UtilRate    status
    ______    _______    ___________    __________    _________    __________    _______    _______    _________    ________    ______

       1        53           62         Tenant        Unknown        50000         55         Yes       1055.9        0.22        0   
      22        51           13         Home Owner    Employed       35000         33         Yes       468.85        0.01        0   
      33        46            8         Home Owner    Unknown        32000         26         Yes       940.78         0.3        0   
      47        52           56         Tenant        Employed       56000         79         Yes       294.46        0.12        0   
     103        64           49         Home Owner    Employed       50000         35         Yes       118.43           0        0   

Plot a histogram of the predictor values before and after imputation.

Predictor = "CustAge";
f1 = figure;
ax1 = axes(f1);
histogram(ax1,rfImputedData.(Predictor),'FaceColor','red','FaceAlpha',1);
hold on
histogram(ax1,dataMissing.(Predictor),'FaceColor','blue','FaceAlpha',1);
legend(strcat("Imputed ", Predictor), strcat("Observed ", Predictor));
title(strcat("Histogram of ", Predictor));

Figure contains an axes. The axes with title Histogram of CustAge contains 2 objects of type histogram. These objects represent Imputed CustAge, Observed CustAge.

Create Credit Scorecard Model Using New Imputed Data

Use the imputed data to create the creditscorecard object, and then use autobinning, fitmodel, and formatpoints to create a credit scorecard model.

sc = creditscorecard(rfImputedData,'IDVar','CustID');
sc = autobinning(sc);
[sc,mdl] = fitmodel(sc,'display','off');
sc = formatpoints(sc,'PointsOddsAndPDO',[500 2 50]);
PointsInfo = displaypoints(sc);
disp(PointsInfo);
      Predictors               Bin             Points
    ______________    _____________________    ______

    {'CustAge'   }    {'[-Inf,33)'        }    54.313
    {'CustAge'   }    {'[33,37)'          }    57.145
    {'CustAge'   }    {'[37,40)'          }     59.04
    {'CustAge'   }    {'[40,46)'          }    68.806
    {'CustAge'   }    {'[46,51)'          }    78.204
    {'CustAge'   }    {'[51,58)'          }    81.041
    {'CustAge'   }    {'[58,Inf]'         }    96.395
    {'CustAge'   }    {'<missing>'        }       NaN
    {'ResStatus' }    {'Tenant'           }    62.768
    {'ResStatus' }    {'Home Owner'       }    72.621
    {'ResStatus' }    {'Other'            }    92.228
    {'ResStatus' }    {'<missing>'        }       NaN
    {'EmpStatus' }    {'Unknown'          }    58.839
    {'EmpStatus' }    {'Employed'         }    86.897
    {'EmpStatus' }    {'<missing>'        }       NaN
    {'CustIncome'}    {'[-Inf,29000)'     }    29.765
    {'CustIncome'}    {'[29000,33000)'    }    56.167
    {'CustIncome'}    {'[33000,35000)'    }    67.926
    {'CustIncome'}    {'[35000,40000)'    }    70.119
    {'CustIncome'}    {'[40000,42000)'    }     70.93
    {'CustIncome'}    {'[42000,47000)'    }    82.337
    {'CustIncome'}    {'[47000,Inf]'      }    96.733
    {'CustIncome'}    {'<missing>'        }       NaN
    {'TmWBank'   }    {'[-Inf,12)'        }    51.023
    {'TmWBank'   }    {'[12,23)'          }    61.005
    {'TmWBank'   }    {'[23,45)'          }    61.806
    {'TmWBank'   }    {'[45,71)'          }     92.95
    {'TmWBank'   }    {'[71,Inf]'         }    133.22
    {'TmWBank'   }    {'<missing>'        }       NaN
    {'OtherCC'   }    {'No'               }    50.796
    {'OtherCC'   }    {'Yes'              }    75.644
    {'OtherCC'   }    {'<missing>'        }       NaN
    {'AMBalance' }    {'[-Inf,558.88)'    }    89.941
    {'AMBalance' }    {'[558.88,1254.28)' }    63.018
    {'AMBalance' }    {'[1254.28,1597.44)'}    59.613
    {'AMBalance' }    {'[1597.44,Inf]'    }    48.972
    {'AMBalance' }    {'<missing>'        }       NaN

Calculate Scores and Probability of Default for New Customers

Create a data set of 'new customers' and then calculate the scores and probabilities of default.

dataNewCustomers = dataMissing(1:20,1:end-1);
disp(head(dataNewCustomers));
    CustID    CustAge    TmAtAddress     ResStatus     EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance    UtilRate
    ______    _______    ___________    ___________    _________    __________    _______    _______    _________    ________

      1          53          62         <undefined>    Unknown        50000         55         Yes       1055.9        0.22  
      2          61          22         Home Owner     Employed       52000         25         Yes       1161.6        0.24  
      3          47          30         Tenant         Employed       37000         61         No        877.23        0.29  
      4         NaN          75         Home Owner     Employed       53000         20         Yes       157.37        0.08  
      5          68          56         Home Owner     Employed       53000         14         Yes       561.84        0.11  
      6          65          13         Home Owner     Employed       48000         59         Yes       968.18        0.15  
      7          34          32         Home Owner     Unknown        32000         26         Yes       717.82        0.02  
      8          50          57         Other          Employed       51000         33         No        3041.2        0.13  

Predict missing data in the scoring data set with the same imputation model as before.

missingCustAgeNewCustomers = isnan(dataNewCustomers.CustAge);
missingResStatusNewCustomers = ismissing(dataNewCustomers.ResStatus);
imputedCustAgeNewCustomers = round(predict(rfCustAge, dataNewCustomers(missingCustAgeNewCustomers,:)));
imputedResStatusNewCustomers = predict(rfResStatus, dataNewCustomers(missingResStatusNewCustomers,:));
dataNewCustomers.CustAge(missingCustAgeNewCustomers) = imputedCustAgeNewCustomers;
dataNewCustomers.ResStatus(missingResStatusNewCustomers) = imputedResStatusNewCustomers;

Use score to calculate the scores of the new customers.

[scores, points] = score(sc, dataNewCustomers);
disp(scores);
  530.9936
  553.1144
  504.7522
  563.8821
  552.3131
  584.2581
  445.2402
  515.6361
  523.9354
  506.8645
  497.9661
  538.1986
  516.3480
  493.3467
  566.2568
  487.2501
  477.0996
  470.1861
  553.9004
  510.7086
disp(points);
    CustAge    ResStatus    EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance
    _______    _________    _________    __________    _______    _______    _________

    81.041      62.768       58.839        96.733       92.95     75.644      63.018  
    96.395      72.621       86.897        96.733      61.806     75.644      63.018  
    78.204      62.768       86.897        70.119       92.95     50.796      63.018  
    81.041      72.621       86.897        96.733      61.005     75.644      89.941  
    96.395      72.621       86.897        96.733      61.005     75.644      63.018  
    96.395      72.621       86.897        96.733       92.95     75.644      63.018  
    57.145      72.621       58.839        56.167      61.806     75.644      63.018  
    78.204      92.228       86.897        96.733      61.806     50.796      48.972  
    78.204      62.768       58.839        96.733      61.806     75.644      89.941  
    78.204      72.621       58.839        96.733      61.806     75.644      63.018  
    81.041      62.768       58.839        67.926      61.806     75.644      89.941  
    78.204      92.228       58.839        82.337      61.005     75.644      89.941  
    96.395      72.621       58.839        96.733      51.023     50.796      89.941  
    68.806      92.228       58.839         70.93      61.806     50.796      89.941  
    78.204      92.228       86.897        82.337      61.005     75.644      89.941  
    57.145      72.621       86.897        70.119      61.806     75.644      63.018  
     59.04      62.768       86.897        67.926      61.806     75.644      63.018  
    54.313      72.621       86.897        29.765      61.005     75.644      89.941  
    81.041      72.621       86.897        96.733      51.023     75.644      89.941  
    81.041      92.228       58.839        82.337      61.005     75.644      59.613