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Probit

Create Probit model object for lifetime probability of default

Since R2020b

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Description

Create and analyze a Probit model object to calculate lifetime probability of default (PD) using this workflow:

  1. Use fitLifetimePDModel to create a Probit model object.

  2. Use predict to predict the conditional PD and predictLifetime to predict the lifetime PD.

  3. Use modelDiscrimination to return AUROC and ROC data. You can plot the results using modelDiscriminationPlot.

  4. Use modelCalibration to return the RMSE of observed and predicted PD data. You can plot the results using modelCalibrationPlot.

Creation

Syntax

ProbitPDModel = fitLifetimePDModel(data,ModelType)
ProbitPDModel = fitLifetimePDModel(___,Name,Value)

Description

ProbitPDModel = fitLifetimePDModel(data,ModelType) creates a Probit PD model object.

If you do not specify variable information for IDVar, AgeVar, LoanVars, MacroVars, and ResponseVar, then:

  • IDVar is set to the first column in the data input.

  • LoanVars is set to include all columns from the second to the second-to-last columns of the data input.

  • ResponseVar is set to the last column in the data input.

example

ProbitPDModel = fitLifetimePDModel(___,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 the model object properties. For example, ProbitPDModel = fitLifetimePDModel(data(TrainDataInd,:),"Probit",ModelID="Probit_A",Description="Probit_model",AgeVar="YOB",IDVar="ID",LoanVars="ScoreGroup",MacroVars={'GDP','Market'},ResponseVar="Default",WeightsVar="Weights") creates a ProbitPDModel object using a Probit model type.

example

Input Arguments

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Data, specified as a table, in panel data form. The data must contain an ID column. The response variable must be a binary variable with the value 0 or 1, with 1 indicating default.

Data, specified as a table where the first column is IDVar, the last column is the ResponseVar, and all other columns are LoanVars.

Data Types: table

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

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: ProbitPDModel = fitLifetimePDModel(data(TrainDataInd,:),"Probit",ModelID="Probit_A",Description="Probit_model",AgeVar="YOB",IDVar="ID",LoanVars="ScoreGroup",MacroVars={'GDP','Market'},ResponseVar="Default",WeightsVar="Weights")

User-defined model ID, specified as the comma-separated pair consisting of 'ModelID' and a string or character vector. The software uses the ModelID to format outputs and is expected to be short.

Data Types: string | char

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

Data Types: string | char

ID variable indicating which column in data contains the loan or borrower ID, specified as the comma-separated pair consisting of 'IDVar' and a string or character vector.

Data Types: string | char

Age variable indicating which column in data contains the loan age information, specified as the comma-separated pair consisting of 'AgeVar' and a string or character vector.

Data Types: string | char

Loan variables indicating which column in data contains the loan-specific information, such as origination score or loan-to-value ratio, specified as the comma-separated pair consisting of 'LoanVars' and a string array or cell array of character vectors.

Data Types: string | cell

Macro variables indicating which column in data contains the macroeconomic information, such as gross domestic product (GDP) growth or unemployment rate, specified as the comma-separated pair consisting of 'MacroVars' and a string array or cell array of character vectors.

Data Types: string | cell

Variable indicating which column in data contains the response variable, specified as the comma-separated pair consisting of 'ResponseVar' and a string or character vector.

Note

The response variable values in the data must be a binary variable with 0 or 1 values, with 1 indicating default.

Data Types: string | char

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 Lifetime PD Model.

Data Types: string

Time interval value, specified as a positive numeric scalar indicating the time interval used to define the 0-1 default indicator values in the response variable. The time interval typically coincides with the distance between age values in training data in the panel data input. For example, if the age data (AgeVar) is 1, 2, 3, ..., then the TimeInterval is 1; if the age data is 0.25, 0.5, 0.75, ..., then the TimeInterval is 0.25. For more information, see Time Interval for Probit Models and Lifetime Prediction and Time Interval.

By default, if you do not specify a TimeInterval when creating a Probit model, the TimeInterval is inferred from the increments in the AgeVar values in the training data. If AgeVar does not contain numeric values, TimeInterval is set to [].

Data Types: double

Properties

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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

Underlying statistical model, returned as a compact generalized linear model object. For more information, see fitglm and CompactGeneralizedLinearModel.

Data Types: CompactGneralizedLinearModel

ID variable indicating which column in data contains the loan or borrower ID, returned as a string.

Data Types: string

Age variable indicating which column in data contains the loan age information, returned as a string.

Data Types: string

Loan variables indicating which column in data contains the loan-specific information, returned as a string array.

Data Types: string

Macro variables indicating which column in data contains the macroeconomic information, returned as a string array.

Data Types: string

Variable indicating which column in data contains the response variable, returned as a string.

Data Types: logical

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

Data Types: string

Time interval value, returned as a positive numeric scalar.

Data Types: double

Object Functions

predictCompute conditional PD
predictLifetimeCompute cumulative lifetime PD, marginal PD, and survival probability
modelDiscriminationCompute AUROC and ROC data
modelCalibrationCompute RMSE of predicted and observed PDs on grouped data
modelDiscriminationPlotPlot ROC curve
modelCalibrationPlotPlot observed default rates compared to predicted PDs on grouped data

Examples

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Open Live Script

This example shows how to use fitLifetimePDModel to create a Probit model using credit and macroeconomic data.

Load Data

Load the credit portfolio data.

load RetailCreditPanelData.mat
disp(head(data))
    ID    ScoreGroup    YOB    Default    Year
    __    __________    ___    _______    ____

    1      Low Risk      1        0       1997
    1      Low Risk      2        0       1998
    1      Low Risk      3        0       1999
    1      Low Risk      4        0       2000
    1      Low Risk      5        0       2001
    1      Low Risk      6        0       2002
    1      Low Risk      7        0       2003
    1      Low Risk      8        0       2004

disp(head(dataMacro))
    Year     GDP     Market
    ____    _____    ______

    1997     2.72      7.61
    1998     3.57     26.24
    1999     2.86      18.1
    2000     2.43      3.19
    2001     1.26    -10.51
    2002    -0.59    -22.95
    2003     0.63      2.78
    2004     1.85      9.48

Join the two data components into a single data set.

data = join(data,dataMacro);
disp(head(data))
    ID    ScoreGroup    YOB    Default    Year     GDP     Market
    __    __________    ___    _______    ____    _____    ______

    1      Low Risk      1        0       1997     2.72      7.61
    1      Low Risk      2        0       1998     3.57     26.24
    1      Low Risk      3        0       1999     2.86      18.1
    1      Low Risk      4        0       2000     2.43      3.19
    1      Low Risk      5        0       2001     1.26    -10.51
    1      Low Risk      6        0       2002    -0.59    -22.95
    1      Low Risk      7        0       2003     0.63      2.78
    1      Low Risk      8        0       2004     1.85      9.48

Partition Data

Separate the data into training and test partitions. 

nIDs = max(data.ID);
uniqueIDs = unique(data.ID);

rng('default'); % for reproducibility
c = cvpartition(nIDs,'HoldOut',0.4);

TrainIDInd = training(c);
TestIDInd = test(c);

TrainDataInd = ismember(data.ID,uniqueIDs(TrainIDInd));
TestDataInd = ismember(data.ID,uniqueIDs(TestIDInd));

Create a Probit Lifetime PD Model

Use fitLifetimePDModel to create a Probit model using the training data.

pdModel = fitLifetimePDModel(data(TrainDataInd,:),"Probit",...
    'AgeVar','YOB',...
    'IDVar','ID',...
    'LoanVars','ScoreGroup',...
    'MacroVars',{'GDP','Market'},...
    'ResponseVar','Default');
disp(pdModel)
  Probit with properties:

            ModelID: "Probit"
        Description: ""
    UnderlyingModel: [1x1 classreg.regr.CompactGeneralizedLinearModel]
              IDVar: "ID"
             AgeVar: "YOB"
           LoanVars: "ScoreGroup"
          MacroVars: ["GDP"    "Market"]
        ResponseVar: "Default"
         WeightsVar: ""
       TimeInterval: 1

Display the underlying model.

disp(pdModel.UnderlyingModel)
Compact generalized linear regression model:
    probit(Default) ~ 1 + ScoreGroup + YOB + GDP + Market
    Distribution = Binomial

Estimated Coefficients:
                               Estimate        SE         tStat       pValue   
                              __________    _________    _______    ___________

    (Intercept)                  -1.6267      0.03811    -42.685              0
    ScoreGroup_Medium Risk      -0.26542      0.01419    -18.704     4.5503e-78
    ScoreGroup_Low Risk         -0.46794     0.016364    -28.595     7.775e-180
    YOB                         -0.11421    0.0049724    -22.969    9.6208e-117
    GDP                        -0.041537     0.014807    -2.8052      0.0050291
    Market                    -0.0029609    0.0010618    -2.7885      0.0052954


388097 observations, 388091 error degrees of freedom
Dispersion: 1
Chi^2-statistic vs. constant model: 1.85e+03, p-value = 0

Predict Conditional and Lifetime PD

Use the predict function to predict conditional PD values. The prediction is a row-by-row prediction.

dataCustomer1 = data(1:8,:);
CondPD = predict(pdModel,dataCustomer1)
CondPD = 8×1

    0.0095
    0.0054
    0.0045
    0.0039
    0.0036
    0.0036
    0.0017
    0.0009

Use predictLifetime to predict the lifetime cumulative PD values (computing marginal and survival PD values is also supported). The predictLifetime function uses the ID variable (see the 'IDVar' property for the Logistic object) to transform conditional PDs to cumulative PDs for each ID.

LifetimePD = predictLifetime(pdModel,dataCustomer1)
LifetimePD = 8×1

    0.0095
    0.0149
    0.0193
    0.0232
    0.0267
    0.0302
    0.0318
    0.0327

Validate Model

Use modelDiscrimination to measure the ranking of customers by PD.

DiscMeasure = modelDiscrimination(pdModel,data(TestDataInd,:),DataID='test data');
disp(DiscMeasure)
                          AUROC 
                         _______

    Probit, test data    0.69984

Use modelDiscriminationPlot to visualize the ROC curve.

modelDiscriminationPlot(pdModel,data(TestDataInd,:),DataID='test data');

Figure contains an axes object. The axes object with title ROC test data Probit, AUROC = 0.69984, xlabel Fraction of Non-Defaulters, ylabel Fraction of Defaulters contains an object of type line. This object represents Probit.

Use modelCalibration to measure the calibration of the predicted PD values. The modelCalibration function requires a grouping variable and compares the accuracy of the observed default rate in the group with the average predicted PD for the group. For example, you can group by calendar year using the 'Year' variable.

CalMeasure = modelCalibration(pdModel,data(TestDataInd,:),'Year',DataID='test data');
disp(CalMeasure)
                                             RMSE   
                                          __________

    Probit, grouped by Year, test data    0.00039494

Use modelCalibrationPlot to visualize the observed default rates compared to the predicted probabilities of default (PD).

modelCalibrationPlot(pdModel,data(TestDataInd,:),'Year',DataID='test data');

Figure contains an axes object. The axes object with title Scatter Grouped by Year test data Probit, RMSE = 0.00039494, xlabel Year, ylabel PD contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Observed, Probit.

More About

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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.

[3] Breeden, Joseph. Living with CECL: The Modeling Dictionary. Santa Fe, NM: Prescient Models LLC, 2018.

[4] Roesch, Daniel and Harald Scheule. Deep Credit Risk: Machine Learning with Python. Independently published, 2020.

Version History

Introduced in R2020b

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See Also

Functions

Topics