Regression

Create Regression model object for loss given default

Since R2021a

Description

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

1. Use fitLGDModel to create a Regression 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 modelCalibration to return the R-square, RMSE, correlation, and sample mean error of the predicted and observed LGD data. You can plot the results using modelCalibrationPlot.

Creation

Syntax

RegressionLGDModel = fitLGDModel(data,ModelType)

RegressionLGDModel = fitLGDModel(___,Name,Value)

Description

RegressionLGDModel = fitLGDModel(data,ModelType) creates a Regression LGD model object.

RegressionLGDModel = fitLGDModel(___,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 model object properties. For example, lgdModel = fitLGDModel(data,'regression',PredictorVars={'LTV' 'Age' 'Type'},ResponseVar="LGD",ResponseTransform="probit",BoundaryTolerance=1e-6,WeightsVar="Weights") creates a lgdModel object using a Regression model type.

Input Arguments

data — Data for loss given default

table

Data for loss given default, specified as a table where the first column and all other columns except the last column are PredictorVars, the last column is ResponseVar.

Data Types: table

ModelType — Model type

string with value "Regression" | character vector with value 'Regression'

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

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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: lgdModel = fitLGDModel(data,'regression',PredictorVars={'LTV' 'Age' 'Type'},ResponseVar="LGD",ResponseTransform="probit",BoundaryTolerance=1e-6)

ModelID — User-defined model ID

"Regression" (default) | string | character vector

User-defined model ID, specified as the comma-separated pair consisting of '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

Description — User-defined description for model

"" (default) | string | character vector

User-defined description for model, specified as the comma-separated pair consisting of 'Description' and a string or character vector.

Data Types: string | char

PredictorVars — Predictor variables

all columns of data except for the ResponseVar (default) | string array | cell array of character vectors

Predictor variables, specified as the comma-separated pair consisting of '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 the ResponseVar.

Data Types: string | cell

ResponseVar — Response variable

last column of data (default) | string | character vector

Response variable, specified as the comma-separated pair consisting of '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, the ResponseVar is set to the last column of data.

Data Types: string | char

BoundaryTolerance — Boundary tolerance

1e-5 (default) | positive numeric

Boundary tolerance, specified as the comma-separated pair consisting of 'BoundaryTolerance' and a positive scalar numeric. The BoundaryTolerance value perturbs the LGD response values away from 0 and 1, before applying a ResponseTransform.

Data Types: double

ResponseTransform — Response transform

"logit" (default) | character vector with value of'logit', 'probit', or 'log' | string with value of "logit", "probit", or "log"

Response transform, specified as the comma-separated pair consisting of 'ResponseTransform' and a character vector or string.

Data Types: string | char

WeightsVar — Column name containing weights

"" (default) | string scalar

Column name of the input table containing weights, specified as a string scalar.

Note

The default value ("") results in a weight of 1 for each row in data. All weight values in data must be nonnegative.

For an example using WeightsVar, see Create Weighted LGD Model.

Properties

ModelID — User-defined model ID

"Regression" (default) | string

User-defined model ID, returned as a string.

Data Types: string

Description — User-defined description

"" (default) | string

User-defined description, returned as a string.

Data Types: string

UnderlyingModel — Underlying statistical model

compact linear model

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: CompactLinearModel

PredictorVars — Predictor variables

all columns of data except for ResponseVar (default) | string array

Predictor variables, returned as a string array.

Data Types: string

ResponseVar — Response variable

last column of data (default) | string

Response variable, returned as a scalar string.

Data Types: string

BoundaryTolerance — Boundary tolerance

Read-only: 1e-5 (default) | numeric

This property is read-only.

Boundary tolerance, returned as a scalar numeric.

Data Types: double

ResponseTransform — Response transform

Read-only: "logit" (default) | string

This property is read-only.

Response transform, returned as a string.

Data Types: string

WeightsVar — Column name containing weights

"" (default) | string scalar

Column name of the input table containing weights, returned as a string scalar. This property is also used to determine the weights variable for validation data when you use the modelDiscrimination or modelCalibration functions.

Object Functions

predict	Predict loss given default
modelDiscrimination	Compute AUROC and ROC data
modelDiscriminationPlot	Plot ROC curve
modelCalibration	Compute R-square, RMSE, correlation, and sample mean error of predicted and observed LGDs
modelCalibrationPlot	Scatter plot of predicted and observed LGDs

Examples

Create Regression LGD Model

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

Load LGD Data

Load the LGD 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

rng('default');
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 the TrainingInd data.

lgdModel = fitLGDModel(data(TrainingInd,:),'regression',...
        'ModelID','Example Probit',...
        'Description','Example LGD probit regression model.',...
        'PredictorVars',{'LTV' 'Age' 'Type'},...
        'ResponseVar','LGD','ResponseTransform','probit','BoundaryTolerance',1e-6);
disp(lgdModel)

  Regression with properties:

    ResponseTransform: "probit"
    BoundaryTolerance: 1.0000e-06
              ModelID: "Example Probit"
          Description: "Example LGD probit regression model."
      UnderlyingModel: [1×1 classreg.regr.CompactLinearModel]
        PredictorVars: ["LTV"    "Age"    "Type"]
          ResponseVar: "LGD"
           WeightsVar: ""

Display the underlying model. The underlying model's response variable is the probit transformation of the LGD response data. Use the 'ResponseTransform' and 'BoundaryTolerance' arguments to modify the transformation.

lgdModel.UnderlyingModel

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

Estimated Coefficients:
                       Estimate       SE        tStat       pValue  
                       ________    ________    _______    __________

    (Intercept)         -2.2212     0.14824    -14.984    2.7409e-48
    LTV                   1.192     0.17183     6.9372    5.3152e-12
    Age                -0.60356    0.035256    -17.119    1.3828e-61
    Type_investment     0.61814      0.1018     6.0723    1.4933e-09


Number of observations: 2093, Error degrees of freedom: 2089
Root Mean Squared Error: 1.74
R-squared: 0.197,  Adjusted R-Squared: 0.196
F-statistic vs. constant model: 171, p-value = 4.39e-99

Predict LGD

For LGD prediction, use predict. The LGD model applies the inverse transformation so the predictions are in the LGD scale, not in the transformed scale used to fit the underlying model.

predictedLGD = predict(lgdModel,data(TestInd,:))

predictedLGD = 1394×1

    0.0011
    0.0058
    0.2091
    0.0015
    0.0192
    0.0620
    0.0757
    0.0000
    0.0156
    0.0388
    0.0059
    0.0110
    0.1052
    0.0105
    0.0016
      ⋮

Validate LGD Model

Use modelDiscriminationPlot to plot the ROC curve.

modelDiscriminationPlot(lgdModel,data(TestInd,:))

Use modelCalibrationPlot to show a scatter plot of the predictions.

modelCalibrationPlot(lgdModel,data(TestInd,:))

More About

Loss Given Default Regression Models

You can transform LGD data using linear regression models.

The loss given default (LGD) regression models transform the LGD response variable

$$TransformedLGD=f(LGD)$$

and fit a linear regression model

$$\begin{array}{l}TransformedLGD={\beta }_0+{\beta }_1{X}_1+\mathrm{...}{\beta }_p{X}_p+\epsilon \\ \text{ = X}\beta +\epsilon \end{array}$$

For prediction, the models first predict on the transformed space using the underlying linear regression model and the estimated coefficients $$\stackrel{\wedge }{\beta }$$

$$TransformedLG{D}_{pred}=X\stackrel{\wedge }{\beta }$$

You can then apply the inverse transformation to return predictions on the LGD scale

$$LG{D}_{pred}=f^{-1}(TransformedLG{D}_{pred})$$

The following table summarizes the supported transformations using the ResponseTransform name-value argument and their corresponding inverses, where Φ(x) is the cumulative normal distribution:

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

R2024a: Added WeightsVar name-value argument for Regression model

The Regression model supports a WeightsVar name-value argument for observation weights.

R2023a: modelAccuracy object function is renamed to modelCalibration function

The modelAccuracy object function is renamed to modelCalibration function. The use of modelAccuracy is discouraged, use modelCalibration instead.

R2023a: modelAccuracyPlot object function is renamed to modelCalibrationPlot function

The modelAccuracyPlot object function is renamed to modelCalibrationPlot function. The use of modelAccuracyPlot is discouraged, use modelCalibrationPlot instead.