# predict

Predict loss given default

Since R2021a

## Description

example

LGD = predict(lgdModel,data) computes the loss given default (LGD).

When using a Regression model, the predict function operates on the underlying compact statistical model and then transforms the predicted values back to the LGD scale.

When using a Tobit model, the predict function operates on the underlying Tobit regression model and returns the unconditional expected value of the response, given the predictor values.

## Examples

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This example shows how to use fitLGDModel to fit data with a Regression model and then predict the loss given default (LGD) values.

Load the loss given default 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

Partition Data

Separate the data into training and test partitions.

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

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

Create Regression LGD Model

Use fitLGDModel to create a Regression model using training data.

lgdModel = fitLGDModel(data(TrainingInd,:),'regression');
disp(lgdModel)
Regression with properties:

ResponseTransform: "logit"
BoundaryTolerance: 1.0000e-05
ModelID: "Regression"
Description: ""
UnderlyingModel: [1x1 classreg.regr.CompactLinearModel]
PredictorVars: ["LTV"    "Age"    "Type"]
ResponseVar: "LGD"
WeightsVar: ""

Display the underlying model.

disp(lgdModel.UnderlyingModel)
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
F-statistic vs. constant model: 181, p-value = 2.42e-104

Predict LGD on Test Data

Use predict to predict the LGD for the test data set.

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

0.0009
0.0037
0.1877
0.0011
0.0112
0.0420
0.0529
0.0000
0.0090
0.0239
⋮

You can analyze and validate these predictions using modelDiscrimination and modelCalibration.

This example shows how to use fitLGDModel to fit data with a Tobit model and then predict the loss given default (LGD) values.

Load the loss given default 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

Partition Data

Separate the data into training and test partitions.

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

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

Create Tobit LGD Model

Use fitLGDModel to create a Tobit model using training data.

lgdModel = fitLGDModel(data(TrainingInd,:),'tobit');
disp(lgdModel)
Tobit with properties:

CensoringSide: "both"
LeftLimit: 0
RightLimit: 1
Weights: [0x1 double]
ModelID: "Tobit"
Description: ""
UnderlyingModel: [1x1 risk.internal.credit.TobitModel]
PredictorVars: ["LTV"    "Age"    "Type"]
ResponseVar: "LGD"
WeightsVar: ""

Display the underlying model.

disp(lgdModel.UnderlyingModel)
Tobit regression model:
LGD = max(0,min(Y*,1))
Y* ~ 1 + LTV + Age + Type

Estimated coefficients:
Estimate        SE         tStat       pValue
_________    _________    _______    __________

(Intercept)         0.058257     0.027277     2.1357      0.032819
LTV                  0.20126     0.031352     6.4193    1.6887e-10
Age                -0.095407    0.0072648    -13.133             0
Type_investment      0.10208     0.018077     5.6471    1.8544e-08
(Sigma)              0.29288    0.0057081     51.309             0

Number of observations: 2093
Number of left-censored observations: 547
Number of uncensored observations: 1521
Number of right-censored observations: 25
Log-likelihood: -698.383

Predict LGD on Test Data

Use predict to predict the LGD for the test data set.

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

0.0879
0.1243
0.3204
0.0934
0.1672
0.2238
0.2370
0.0102
0.1592
0.1989
⋮

You can analyze and validate these predictions using modelDiscrimination and modelCalibration.

This example shows how to use fitLGDModel to fit data with a Beta model and then predict the loss given default (LGD) values.

Load the loss given default 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

Partition Data

Separate the data into training and test partitions.

rng('default'); % for reproducibility
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 using training data.

lgdModel = fitLGDModel(data(TrainingInd,:),'Beta');
disp(lgdModel)
Beta with properties:

BoundaryTolerance: 1.0000e-05
ModelID: "Beta"
Description: ""
UnderlyingModel: [1x1 risk.internal.credit.BetaModel]
PredictorVars: ["LTV"    "Age"    "Type"]
ResponseVar: "LGD"
WeightsVar: ""

Display the underlying model.

disp(lgdModel.UnderlyingModel)
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          -1.3772     0.13201    -10.433             0
LTV_mu                   0.6027     0.15087     3.9948    6.6993e-05
Age_mu                 -0.47464    0.040264    -11.788             0
Type_investment_mu      0.45372    0.085143     5.3289    1.0941e-07
(Intercept)_phi        -0.16336     0.12591    -1.2974       0.19462
LTV_phi                0.055886     0.14719    0.37969       0.70421
Age_phi                 0.22887    0.040335     5.6743     1.586e-08
Type_investment_phi    -0.14102    0.078155    -1.8044      0.071313

Number of observations: 2093
Log-likelihood: -5291.04

Predict LGD on Test Data

Use predict to predict the LGD for the test data set.

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

0.0937
0.1492
0.3526
0.0964
0.1886
0.2595
0.2677
0.0213
0.1774
0.2256
⋮

You can analyze and validate these predictions using modelDiscrimination and modelCalibration.

## Input Arguments

collapse all

Loss given default model, specified as a previously created Regression, Tobit, or Beta object using fitLGDModel.

Data Types: object

Data, specified as a NumRows-by-NumCols table with predictor and response values. The variable names and data types must be consistent with the underlying model.

Data Types: table

## Output Arguments

collapse all

Loss given default values, returned as a NumRows-by-1 numeric vector.

collapse all

### Prediction with LGD Models

Use a Regression, Tobit, or Beta model to predict LGD.

Regression LGD models first predict on the transformed space using the underlying linear regression model, and then apply the inverse transformation to return predictions on the LGD scale. For more information on the supported transformations and their inverses, see Loss Given Default Regression Models.

Tobit LGD models return the unconditional expected value of the response, given the predictor values. For more information, see Loss Given Default Tobit Models.

Beta LGD models return the mean of the beta distribution, given the predictor values. For more information, see Beta Regression Models.

## 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.

## Version History

Introduced in R2021a

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