Basic Loss Given Default Model Validation

This example shows how to perform basic model validation on a loss given default (LGD) model by viewing the fitted model, estimated coefficients, and p-values. For more information on model validation, see modelDiscrimination and modelCalibration.

Load Data

Load the portfolio data.

load LGDData.mat
head(data)

      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

Fit Model and Review Model Goodness of Fit

Create training and test datasets to perform a basic model validation.

rng('default'); % for reproducibility
NumObs = height(data);

c = cvpartition(NumObs,'HoldOut',0.4);
TrainingInd = training(c);
TestInd = test(c);

Fit the model using fitLifetimePDModel.

ModelType = "regression";
lgdModel = fitLGDModel(data(TrainingInd,:),ModelType,...
    'ModelID','Example',...
     'Description','Example LGD regression model.',...
     'PredictorVars',{'LTV' 'Age' 'Type'},...
     'ResponseVar','LGD');
disp(lgdModel)

  Regression with properties:

    ResponseTransform: "logit"
    BoundaryTolerance: 1.0000e-05
              ModelID: "Example"
          Description: "Example LGD regression model."
      UnderlyingModel: [1×1 classreg.regr.CompactLinearModel]
        PredictorVars: ["LTV"    "Age"    "Type"]
          ResponseVar: "LGD"
           WeightsVar: ""

Display the underlying statistical model. The displayed information contains the coefficient estimates, as well as their standard errors, t-statistics and p-values. The underlying statistical model also shows the number of observations and other fit metrics.

lgdModel.UnderlyingModel

ans = 
Compact linear regression model:
    LGD_logit ~ 1 + LTV + Age + Type

Estimated Coefficients:
                       Estimate       SE        tStat       pValue  
                       ________    ________    _______    __________

    (Intercept)        -4.7549      0.36041    -13.193    3.0997e-38
    LTV                 2.8565      0.41777     6.8377    1.0531e-11
    Age                -1.5397     0.085716    -17.963    3.3172e-67
    Type_investment     1.4358       0.2475     5.8012     7.587e-09


Number of observations: 2093, Error degrees of freedom: 2089
Root Mean Squared Error: 4.24
R-squared: 0.206,  Adjusted R-Squared: 0.205
F-statistic vs. constant model: 181, p-value = 2.42e-104

In the case of the underlying statistical model for a Regression model, the underlying model is 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.