fitEADModel

Create specified EAD model object type

Since R2021b

Syntax

eadModel = fitEADModel(data,ModelType)

eadModel = fitEADModel(___,Name=Value)

Description

eadModel = fitEADModel(data,ModelType) creates an exposure at default (EAD) model object specified by data and ModelType. fitEADModel takes in credit data in table form and fits an EAD model. ModelType is supported for a Regression, Tobit, or Beta model.

eadModel = fitEADModel(___,Name=Value) specifies options using one or more name-value arguments in addition to the input arguments in the previous syntax. The available optional name-value arguments depend on the specified ModelType.

Examples

Create Regression EAD Model

This example shows how to use fitEADModel to create a Regression model for exposure at default (EAD).

Load EAD Data

Load the EAD data.

load EADData.mat
head(EADData)

    UtilizationRate    Age     Marriage        Limit         Drawn          EAD    
    _______________    ___    ___________    __________    __________    __________

        0.24359        25     not married         44776         10907         44740
        0.96946        44     not married    2.1405e+05    2.0751e+05         40678
              0        40     married        1.6581e+05             0    1.6567e+05
        0.53242        38     not married    1.7375e+05         92506        1593.5
         0.2583        30     not married         26258        6782.5        54.175
        0.17039        54     married        1.7357e+05         29575        576.69
        0.18586        27     not married         19590          3641        998.49
        0.85372        42     not married    2.0712e+05    1.7682e+05    1.6454e+05

rng('default');
NumObs = height(EADData);
c = cvpartition(NumObs,'HoldOut',0.4);
TrainingInd = training(c);
TestInd = test(c);

Select Model Type

Select a model type for Regression or Tobit.

ModelType = "Regression";

Select Conversion Measure

Select a conversion measure for the EAD response values.

ConversionMeasure = "LCF";

Create Regression EAD Model

Use fitEADModel to create a Regression model using EADData.

eadModel = fitEADModel(EADData,ModelType,PredictorVars={'UtilizationRate','Age','Marriage'}, ...
    ConversionMeasure=ConversionMeasure,DrawnVar="Drawn",LimitVar="Limit",ResponseVar="EAD");
disp(eadModel);

  Regression with properties:

    ConversionTransform: "logit"
      BoundaryTolerance: 1.0000e-07
                ModelID: "Regression"
            Description: ""
        UnderlyingModel: [1x1 classreg.regr.CompactLinearModel]
          PredictorVars: ["UtilizationRate"    "Age"    "Marriage"]
            ResponseVar: "EAD"
               LimitVar: "Limit"
               DrawnVar: "Drawn"
      ConversionMeasure: "lcf"

Display the underlying model. The underlying model's response variable is the transformation of the EAD response data. Use the 'BoundaryTolerance', 'LimitVar', and 'DrawnVar' name-value arguments to modify the transformation.

eadModel.UnderlyingModel

ans = 
Compact linear regression model:
    EAD_lcf_logit ~ 1 + UtilizationRate + Age + Marriage

Estimated Coefficients:
                            Estimate        SE         tStat       pValue  
                            _________    _________    _______    __________

    (Intercept)               -2.4745      0.29892    -8.2781    1.6448e-16
    UtilizationRate            6.0045      0.19901     30.172    7.703e-182
    Age                     -0.020095    0.0073019     -2.752     0.0059471
    Marriage_not married     -0.03509      0.13935    -0.2518        0.8012


Number of observations: 4378, Error degrees of freedom: 4374
Root Mean Squared Error: 4.48
R-squared: 0.173,  Adjusted R-Squared: 0.173
F-statistic vs. constant model: 305, p-value = 5.7e-180

Predict EAD

EAD prediction operates on the underlying compact statistical model and then transforms the predicted values back to the EAD scale. You can specify the predict function with different options for the 'ModelLevel' name-vale argument.

predictedEAD = predict(eadModel, EADData(TestInd,:),ModelLevel="ead");
predictedConversion = predict(eadModel, EADData(TestInd,:),ModelLevel="ConversionMeasure");

Validate EAD Model

For model validation, use modelDiscrimination, modelDiscriminationPlot, modelCalibration, and modelCalibrationPlot.

Use modelDiscrimination and then modelDiscriminationPlot to plot the ROC curve.

ModelLevel = "ConversionMeasure";
[DiscMeasure1, DiscData1] = modelDiscrimination(eadModel, EADData(TestInd,:),ModelLevel=ModelLevel);
modelDiscriminationPlot(eadModel, EADData(TestInd, :), ModelLevel=ModelLevel,SegmentBy="Marriage");

Use modelCalibration and then modelCalibrationPlot to show a scatter plot of the predictions.

YData = "Observed";

[CalMeasure1, CalData1] = modelCalibration(eadModel, EADData(TestInd,:), ModelLevel=ModelLevel);
modelCalibrationPlot(eadModel, EADData(TestInd,:),ModelLevel=ModelLevel,YData=YData);

Plot a histogram of observed with respect to the predicted EAD.

figure;
histogram(CalData1.Observed);
hold on;
histogram(CalData1.(('Predicted_' + ModelType)));
xlabel(ConversionMeasure); 
legend('Observed', 'Predicted');

Input Arguments

data — Data for loss given default

table

Data for loss given default, specified as a table.

Data Types: table

ModelType — Type of EAD model

character vector with values 'Regression', 'Tobit', or 'Beta' | string with values "Regression", "Tobit", or "Beta"

Type of EAD model, specified as a scalar string or character vector. Use one of following values:

• Regression —Transform the EAD response variable and fit a linear regression model. For more information, see Exposure at Default Regression Models.

• Tobit — Fit a Tobit "censored" regression model. For more information, see Exposure at Default Tobit Models.

• Beta — Fit a Beta regression model. For more information, see Beta Regression Models.

Data Types: string | char

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: eadModel = fitEADModel(EADData,ModelType,PredictorVars={'UtilizationRate','Age','Marriage'},ConversionMeasure="ccf",DrawnVar='Drawn',LimitVar='Limit',ResponseVar='EAD')

The available name-value arguments depend on the value you specify for ModelType.

• Regression — See Name-Value Arguments.

• Tobit — See Name-Value Arguments.

• Beta — See Name-Value Arguments.

Output Arguments

eadModel — Exposure at default model

eadModel object

Loss given default model, returned as an eadModel object for a Regression, Tobit, or Beta model.

References

[1] Baesens, Bart, Daniel Roesch, and Harald Scheule. Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS. Wiley, 2016.

[2] Bellini, Tiziano. IFRS 9 and CECL Credit Risk Modelling and Validation: A Practical Guide with Examples Worked in R and SAS. San Diego, CA: Elsevier, 2019.

[3] Brown, Iain. Developing Credit Risk Models Using SAS Enterprise Miner and SAS/STAT: Theory and Applications. SAS Institute, 2014.

[4] Roesch, Daniel and Harald Scheule. Deep Credit Risk. Independently published, 2020.

Version History

Introduced in R2021b

R2022b: Support Beta regression for EAD model

To create a Beta model use a ModelType of "Beta".