predict

Predict exposure at default

Since R2021b

Syntax

predictedEAD = predict(eadModel,data)

predictedEAD = predict(___,Name=Value)

Description

predictedEAD = predict(eadModel,data) computes the exposure at default (EAD).

When using a Regression model, the predict function operates on the underlying compact statistical model and then transforms the predicted values back to the EAD scale.

predictedEAD = predict(___,Name=Value) specifies options using one or more name-value arguments in addition to the input arguments in the previous syntax.

Examples

Use Tobit EAD Model to Predict EAD

This example shows how to use fitEADModel to create a Tobit model and then predict exposure at default (EAD) values.

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 Tobit or Regression.

ModelType = "Tobit";

Select Conversion Measure

Select a conversion measure for the EAD response values.

ConversionMeasure = "LCF";

Create Tobit EAD Model

Use fitEADModel to create a Tobit model using the TrainingInd data.

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

  Tobit with properties:

        CensoringSide: "both"
            LeftLimit: 0
           RightLimit: 1
              ModelID: "Tobit"
          Description: ""
      UnderlyingModel: [1×1 risk.internal.credit.TobitModel]
        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 'LimitVar' and 'DrawnVar' name-value arguments to modify the transformation.

disp(eadModel.UnderlyingModel);

Tobit regression model:
     EAD_lcf = max(0,min(Y*,1))
     Y* ~ 1 + UtilizationRate + Age + Marriage

Estimated coefficients:
                             Estimate         SE         tStat       pValue  
                            __________    __________    _______    __________

    (Intercept)                0.22467      0.031504     7.1315    1.2783e-12
    UtilizationRate             0.4714       0.02066     22.817             0
    Age                     -0.0014209    0.00077019    -1.8449      0.065163
    Marriage_not married     -0.010543      0.015835    -0.6658        0.5056
    (Sigma)                     0.3618     0.0049955     72.426             0

Number of observations: 2627
Number of left-censored observations: 0
Number of uncensored observations: 2626
Number of right-censored observations: 1
Log-likelihood: -1057.9

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-value argument.

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

Use Beta EAD Model to Predict EAD

This example shows how to use fitEADModel to create a Beta model and then predict exposure at default (EAD) values.

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 Beta.

ModelType = "Beta";

Select Conversion Measure

Select a conversion measure for the EAD response values.

ConversionMeasure = "LCF";

Create Beta EAD Model

Use fitEADModel to create a Beta model using EADData.

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

  Beta with properties:

    BoundaryTolerance: 1.0000e-07
              ModelID: "Beta"
          Description: ""
      UnderlyingModel: [1×1 risk.internal.credit.BetaModel]
        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 'LimitVar' and 'DrawnVar' name-value arguments to modify the transformation.

disp(eadModel.UnderlyingModel);

Beta regression model:
     logit(EAD_lcf) ~ 1_mu + UtilizationRate_mu + Age_mu + Marriage_mu
     log(EAD_lcf) ~ 1_phi + UtilizationRate_phi + Age_phi + Marriage_phi

Estimated coefficients:
                                 Estimate        SE          tStat        pValue  
                                __________    _________    _________    __________

    (Intercept)_mu                -0.67409     0.087774      -7.6798     1.954e-14
    UtilizationRate_mu              1.6974     0.060621           28             0
    Age_mu                      -0.0046006    0.0021317      -2.1582      0.030964
    Marriage_not married_mu     -0.0020533     0.040397    -0.050828       0.95947
    (Intercept)_phi               -0.43363     0.071602      -6.0562    1.5108e-09
    UtilizationRate_phi            0.42461     0.051852       8.1889    4.4409e-16
    Age_phi                     -0.0036089    0.0017592      -2.0515      0.040279
    Marriage_not married_phi     -0.016664     0.032976     -0.50535       0.61334

Number of observations: 4378
Log-likelihood: -5255.12

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-value argument.

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

Input Arguments

eadModel — Exposure at default model

Regression object | Tobit object | Beta object

Exposure at default model, specified as a previously created Regression, Tobit, or Beta object using fitEADModel.

Data Types: object

data — Data

table

Data, specified as a NumRows-by-NumCols table with predictor and response values. The variable names and data types must be consistent with the underlying model.

Data Types: table

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: predictedEAD = predict(eadModel,EADData(TestInd,:),ModelLevel='ead')

ModelLevel — Model level

"ead" (default) | character vector with value 'ead', 'conversionMeasure', or 'conversionTransform' | string with value "ead", "conversionMeasure", or "conversionTransform"

Model level, specified as ModelLevel and a character vector or string.

Note

Regression models support all three model levels, but a Tobit or Beta model supports model levels only for 'ead' and 'conversionMeasure'.

Data Types: char | string

Output Arguments

predictedEAD — Exposure at default predicted values

vector

Exposure at default predicted values, returned as a NumRows-by-1 numeric vector.

More About

Prediction with EAD Models

Use a Regression, Tobit, or Beta model to predict EAD.

Regression, Tobit, or Beta EAD models first predict on the transformed space using the underlying linear regression model, and then apply the inverse transformation to return predictions on the EAD scale.

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 for Beta model

The eadModel input supports an option for a Beta model object that you can create using fitEADModel.