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Tobit

Create Tobit model object for exposure at default

Description

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

  1. Use fitEADModel to create a Tobit 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 modelAccuracy to return the R-squared, RMSE, correlation, and sample mean error of predicted and observed EAD data. You can plot the results using modelAccuracyPlot.

Creation

Description

example

TobitEADModel = fitEADModel(data,ModelType) creates a Tobit EAD model object.

example

TobitEADModel = fitEADModel(___,Name=Value) specifies options using one or more name-value arguments in addition to the input arguments in the previous syntax. The optional name-value arguments set the 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 Tobit model type.

Input Arguments

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Data for exposure at default, specified as a table.

Data Types: table

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

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')

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

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

Data Types: string | char

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 ResponseVar.

Data Types: string | cell

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, ResponseVar is set to the last column.

Data Types: string | char

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 Conversion Measure Options.

Data Types: string | char

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 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 Conversion Measure Options.

Data Types: string | char

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)) .

    Note

    A Tobit model with "ccf" can be unstable.

  • "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 Conversion Measure Options.

Data Types: string | char

Censoring side, specified as CensoringSide and a character vector or string. CensoringSide indicates whether the desired Tobit model is left-censored, right-censored, or censored on both sides.

Data Types: string | char

Left-censoring limit, specified as LeftLimit and a scalar numeric between 0 and 1.

Data Types: double

Right-censoring limit, specified as RightLimit and a scalar numeric between 0 and 1.

Data Types: double

Options for fitting, specified as SolverOptions and an optimoptions object that is created using optimoptions from Optimization Toolbox™. The defaults for the optimoptions object are:

  • "Display""none"

  • "Algorithm""sqp"

  • "MaxFunctionEvaluations"500 ⨉ Number of model coefficients

  • "MaxIterations" — The number of Tobit model coefficients is determined at run time; it depends on the number of predictors and the number of categories in the categorical predictors.

Note

When using optimoptions with a Tobit model, specify the SolverName as fmincon.

Data Types: object

Properties

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User-defined model ID, returned as a string.

Data Types: string

User-defined description, returned as a string.

Data Types: string

This property is read-only.

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: string

Predictor variables, returned as a string array.

Data Types: string

Response variable, returned as a string.

Data Types: string

Limit variable, returned as a string.

Data Types: string

Drawn variable, returned as a string.

Data Types: string

Response transform, returned as a string.

Data Types: string

This property is read-only.

Censoring side, returned as a string.

Data Types: string

This property is read-only.

Left-censoring limit, returned as a scalar numeric between 0 and 1.

Data Types: double

This property is read-only.

Right-censoring limit, returned as a scalar numeric between 0 and 1.

Data Types: double

Object Functions

predictPredict exposure at default
modelDiscriminationCompute AUROC and ROC data
modelDiscriminationPlotPlot ROC curve
modelAccuracyCompute R-square, RMSE, correlation, and sample mean error of predicted and observed EADs
modelAccuracyPlotScatter plot of predicted and observed EADs

Examples

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This example shows how to use fitEADModel to create a Tobit 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 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 EADData.

eadModel = fitEADModel(EADData,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: [1x1 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)                0.22735      0.025005      9.0922           0
    UtilizationRate            0.47364      0.016531      28.652           0
    Age                     -0.0013929    0.00061479     -2.2657    0.023517
    Marriage_not married     -0.006888       0.01208    -0.57022     0.56856
    (Sigma)                    0.36419      0.003878      93.913           0

Number of observations: 4378
Number of left-censored observations: 0
Number of uncensored observations: 4377
Number of right-censored observations: 1
Log-likelihood: -1791.06

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, modelAccuracy, and modelAccuracyPlot.

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");

Figure contains an axes object. The axes object with title EAD_lcf ROC Segmented by Marriage contains 2 objects of type line. These objects represent Tobit, married, AUROC = 0.70789, Tobit, not married, AUROC = 0.70898.

Use modelAccuracy and then modelAccuracyPlot to show a scatter plot of the predictions.

YData = "Observed";

[AccMeasure1,AccData1] = modelAccuracy(eadModel,EADData(TestInd,:),ModelLevel=ModelLevel);
modelAccuracyPlot(eadModel,EADData(TestInd,:),ModelLevel=ModelLevel,YData=YData);

Figure contains an axes object. The axes object with title Scatter Tobit, R-Squared: 0.16231 contains 2 objects of type scatter, line. These objects represent Data, Fit.

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

figure;
histogram(AccData1.Observed);
hold on;
histogram(AccData1.(('Predicted_' + ModelType)));
legend('Observed','Predicted');

Figure contains an axes object. The axes object contains 2 objects of type histogram. These objects represent Observed, Predicted.

More About

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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