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Basic Loss Given Default Model Validation

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

Load Data

Load the portfolio data.

loadLGDData.mathead(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 reproducibilityNumObs = height(data); c = cvpartition(NumObs,'HoldOut',0.4); TrainingInd = training(c); TestInd = test(c);

Fit the model usingfitLifetimePDModel.

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: [1x1 classreg.regr.CompactLinearModel] PredictorVars: ["LTV" "Age" "Type"] ResponseVar: "LGD"

Display the underlying statistical model. The displayed information contains the coefficient estimates, as well as their standard errors,t-statistics andp-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 aRegressionmodel, the underlying model is returned as a compact linear model object. The compact version of the underlyingRegressionmodel is an instance of theclassreg.regr.CompactLinearModelclass. For more information, seefitlmandCompactLinearModel.

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