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Create Beta model object for loss given default


Create and analyze a Beta model object to calculate loss given default (LGD) using this workflow:

  1. Use fitLGDModel to create a Beta model object.

  2. Use predict to predict the LGD.

  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 LGD data. You can plot the results using modelAccuracyPlot.




BetaLGDModel = fitLGDModel(data,ModelType) creates a Beta LGD model object.


BetaLGDModel = fitLGDModel(___,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 the model object properties. For example, BetaLGDModel = fitLGDModel(data,'Beta',PredictorVars={'LTV' 'Age' 'Type'},ResponseVar='LGD',BoundaryTolerance=1e-4) creates a BetaLGDModel object using a Beta model type.

Input Arguments

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Data for loss given default, specified as a table.

Data Types: table

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

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: BetaLGDModel = fitLGDModel(data,'Beta',PredictorVars={'LTV' 'Age' 'Type'},ResponseVar='LGD',BoundaryTolerance=1e-4)

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 LGD data and must be a numeric variable. An LGD value of 0 indicates no loss (full recovery), 1 indicates total loss (no recovery), and values between 0 and 1 indicate a partial loss. By default, ResponseVar is set to the last column.

Data Types: string | char

Value to perturb LGD response values away from 0 to 1, specified as BoundaryTolerance and a positive scalar numeric.

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""quasi-newton"

  • "MaxFunctionEvaluations"500 ✕ Number of model coefficients

  • "MaxIterations" — 1000


When using optimoptions with a Beta model, specify the SolverName as fminunc.

The number of Beta model coefficients is determined at run time, depending on the number of predictors and the number of categories in the categorical predictors.

Data Types: object


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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 class.

Data Types: object

Predictor variables, returned as a string array.

Data Types: string

Response variable, returned as a string.

Data Types: string

Value to perturb LGD response values away from 0 to 1, returned as a positive scalar numeric.

Data Types: double

Object Functions

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


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This example shows how to use fitLGDModel to create a Beta model object for loss given default (LGD).

Load LGD Data

Load the LGD data.

load LGDData.mat
      LTV        Age         Type           LGD   
    _______    _______    ___________    _________

    0.89101    0.39716    residential     0.032659
    0.70176     2.0939    residential      0.43564
    0.72078     2.7948    residential    0.0064766
    0.37013      1.237    residential     0.007947
    0.36492     2.5818    residential            0
      0.796     1.5957    residential      0.14572
    0.60203     1.1599    residential     0.025688
    0.92005    0.50253    investment      0.063182
NumObs = height(data);
c = cvpartition(NumObs,'HoldOut',0.4);
TrainingInd = training(c);
TestInd = test(c);

Create Beta LGD Model

Use fitLGDModel to create a Beta model object using the TrainingInd data.

BetaLGDModel = fitLGDModel(data(TrainingInd,:),'Beta',...
   ModelID='Example LGD Beta',...
   PredictorVars={'LTV' 'Age' 'Type'},...
  Beta with properties:

    BoundaryTolerance: 2.0000e-05
              ModelID: "Example LGD Beta"
          Description: ""
      UnderlyingModel: [1x1]
        PredictorVars: ["LTV"    "Age"    "Type"]
          ResponseVar: "LGD"

Display the underlying model.

Beta regression model:
     logit(LGD) ~ 1_mu + LTV_mu + Age_mu + Type_mu
     log(LGD) ~ 1_phi + LTV_phi + Age_phi + Type_phi

Estimated coefficients:
                           Estimate       SE        tStat        pValue  
                           ________    ________    ________    __________

    (Intercept)_mu          -1.3884     0.13116     -10.585             0
    LTV_mu                  0.61404     0.14989      4.0967    4.3502e-05
    Age_mu                 -0.47446    0.039808     -11.919             0
    Type_investment_mu       0.4516    0.084719      5.3305    1.0846e-07
    (Intercept)_phi        -0.11299     0.12578    -0.89834       0.36911
    LTV_phi                0.030895     0.14692     0.21028       0.83347
    Age_phi                 0.23972    0.040152      5.9702    2.7758e-09
    Type_investment_phi    -0.14724    0.078187     -1.8831      0.059821

Number of observations: 2093
Log-likelihood: -4976.51

Predict LGD

For Beta models, use predict to calculate the predicted LGD value, which is the unconditional expected value of the response, given the predictor values.

predictedLGD = predict(BetaLGDModel,data(TestInd,:))
predictedLGD = 1394×1


Validate LGD Model

Use modelDiscriminationPlot to plot the ROC curve.


Figure contains an axes object. The axes object with title ROC Example LGD Beta, AUROC = 0.67671 contains an object of type line. This object represents Example LGD Beta.

Use modelAccuracyPlot to show a scatter plot of the predictions.


Figure contains an axes object. The axes object with title Scatter Example LGD Beta, R-Squared: 0.081078 contains 2 objects of type scatter, line. These objects represent Data, Fit.

More About

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[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.

Version History

Introduced in R2022b