Regression

Create Regression model object for exposure at default

Since R2021b

Description

Create and analyze a Regression model object to calculate the exposure at default (EAD) using this workflow:

1. Use fitEADModel to create a Regression model object.

2. Use predict to predict the EAD.

3. Use modelDiscrimination to return AUROC and ROC data. You can plot the results using modelDiscriminationPlot.

4. Use modelCalibration to return the R-square, RMSE, correlation, and sample mean error of the predicted and observed EAD data. You can plot the results using modelCalibrationPlot.

Creation

Syntax

RegressionEADModel = fitEADModel(data,ModelType)

RegressionEADModel = fitEADModel(___,Name=Value)

Description

RegressionEADModel = fitEADModel(data,ModelType) creates a Regression EAD model object.

RegressionEADModel = fitEADModel(___,Name=Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax. The optional name-value pair arguments set model object properties. For example, eadModel = fitEADModel(EADData,ModelType,PredictorVars={'UtilizationRate','Age','Marriage'},ConversionMeasure="ccf",DrawnVar='Drawn',LimitVar='Limit',ResponseVar='EAD') creates an eadModel object using a Regression model type.

Input Arguments

data — Data for loss given default

table

Data for loss given default, specified as a table.

Data Types: table

ModelType — Model type

string with value "Regression" | character vector with value 'Regression'

Model type, specified as a string with the value of "Regression" or a character vector with the value of 'Regression'.

Data Types: char | string

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')

ModelID — User-defined model ID

"Regression" (default) | string | character vector

User-defined model ID, specified as ModelID and a string or character vector. The software uses the ModelID text to format outputs and is expected to be short.

Data Types: string | char

Description — User-defined description for model

"" (default) | string | character vector

User-defined description for model, specified as Description and a string or character vector.

Data Types: string | char

PredictorVars — Predictor variables

all columns of data except for the ResponseVar (default) | string array | cell array of character vectors

Predictor variables, specified as PredictorVars and a string array or cell array of character vectors. PredictorVars indicates which columns in the data input contain the predictor information. By default, PredictorVars is set to all the columns in the data input except for the ResponseVar.

Data Types: string | cell

ResponseVar — Response variable

last column of data (default) | string | character vector

Response variable, specified as ResponseVar and a string or character vector. The response variable contains the EAD data and must be a numeric variable. By default, the ResponseVar is set to the last column of data.

Data Types: string | char

BoundaryTolerance — Boundary tolerance

1e-7 (default) | positive numeric

Boundary tolerance, specified as BoundaryTolerance and a positive scalar numeric. The BoundaryTolerance value perturbs the EAD response values away from 0 and 1, before applying a response transformation.

Data Types: double

LimitVar — Limit variable

string | character vector

Limit variable, specified as LimitVar and a string or character vector. LimitVar indicates which column in data contains the limit amount. The limit amount value in the data must be a positive numeric value. The limit depends on the loan. If its a credit card, the limit is the credit limit, and if this is a mortgage limit it is the initial loan amount. In general, LimitVar is the maximum amount that can be borrowed.

Note

LimitVar is required when ConversionMeasure is 'ccf' or 'lcf'. For more information on CCF and LCF, see Exposure at Default Regression Models.

Data Types: string | char

DrawnVar — Drawn variable

string | character vector

Drawn variable, specified as DrawnVar and a string or character vector. DrawnVar is the balance on the account at the time of observation, prior to default and EAD is the balance at the time of default. DrawnVar indicates which column in the data contains the drawn amount. The drawn variable value in the data can be a positive or negative numeric value.

Note

DrawnVar is required when ConversionMeasure is 'ccf'.

If the ConversionMeasure is 'lcf', DrawnVar is not required. In this case, DrawnVar is set to "".

For more information on CCF, see Exposure at Default Regression Models.

Data Types: string | char

ConversionMeasure — Conversion measure for EAD response values

"ccf" (default) | character vector with value of 'ccf' or 'lcf' | string with value of "ccf" or "lcf"

Response transform, specified as ConversionMeasure and a character vector or string.

• "ccf" — Credit conversion factor (CCF) is the portion of the undrawn amount that will be converted into credit. The undrawn amount is the limit minus the drawn amount. The EAD thus becomes the drawn amount plus the CCF times the limit minus the drawn amount (EAD = Drawn + CCF*(Limit - Drawn)).

• "lcf" — Limit conversion factor (LCF) is a fraction of the limit representing the total exposure. The EAD is then defined as the LCF times the limit (EAD = LCF*Limit).

For more information on CCF and LCF, see Exposure at Default Regression Models.

Data Types: string | char

Properties

ModelID — User-defined model ID

"Regression" (default) | string

User-defined model ID, returned as a string.

Data Types: string

Description — User-defined description

"" (default) | string

User-defined description, returned as a string.

Data Types: string

UnderlyingModel — Underlying statistical model

compact linear model

Underlying statistical model, returned as a compact linear model object. The compact version of the underlying regression model is an instance of the classreg.regr.CompactLinearModel class. For more information, see fitlm and CompactLinearModel.

Data Types: CompactLinearModel

PredictorVars — Predictor variables

all columns of data except for ResponseVar (default) | string array

Predictor variables, returned as a string array.

Data Types: string

ResponseVar — Response variable

last column of data (default) | string

Response variable, returned as a scalar string.

Data Types: string

LimitVar — Limit variable

string

Limit variable, returned as a string.

Data Types: string

DrawnVar — Drawn variable

string

Drawn variable, returned as a string.

Data Types: string

BoundaryTolerance — Boundary tolerance

1e-7 (default) | positive numeric

This property is read-only.

Boundary tolerance, returned as a scalar positive numeric.

Data Types: double

ConversionMeasure — Conversion measure for EAD response values

"ccf" (default) | string with value of "ccf" or "lcf"

Conversion measure, returned as a string.

Data Types: string

ConversionTransform — Conversion transform

"complog" (default) | string with value "complog" or "logit"

This property is read-only.

Conversion transform, returned as a string that is "complog" if ConversionMeasure is "ccf" and "logit" when ConversionMeasure is "lcf".

Data Types: string

Object Functions

predict	Predict exposure at default
modelDiscrimination	Compute AUROC and ROC data
modelDiscriminationPlot	Plot ROC curve
modelCalibration	Compute R-square, RMSE, correlation, and sample mean error of predicted and observed EADs
modelCalibrationPlot	Scatter plot of predicted and observed EADs

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');

More About

Exposure at Default Regression Models

You can transform EAD data using linear regression models.

You can relate the EAD to a scaling variable and derive conversion measures like credit conversion factor (CCF) and limit conversion factor (LCF) using the 'ccf' or 'lcf' options for the ConversionMeasure name-value argument. In general, Regression models that use a ConversionMeasure for conversion factors are more robust, as all observations scale to a common denomination.

The following table summarizes the supported transformations using the 'ccf' or 'lcf' options for the ConversionMeasure name-value argument:

Measure	EAD Formula	Lower Bound	Upper Bound	Inverse Transformation
CCF	EAD = Drawn + CCF*(Limit - Drawn)	-Inf	1	CCF = 1 - e(- CCFt)
LCF	EAD = LCF*Limit	0	1	LCF = eLCFt/(1 + eLCFt)

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

R2023a: modelAccuracy object function is renamed to modelCalibration function

The modelAccuracy object function is renamed to modelCalibration function. The use of modelAccuracy is discouraged, use modelCalibration instead.

R2023a: modelAccuracyPlot object function is renamed to modelCalibrationPlot function

The modelAccuracyPlot object function is renamed to modelCalibrationPlot function. The use of modelAccuracyPlot is discouraged, use modelCalibrationPlot instead.