Compare Logistic Model for Lifetime PD to Champion Model
This example shows how to compare a new Logistic model for lifetime PD against a "champion" model.
Load Data
Load the portfolio data, which includes loan and macro information.
load RetailCreditPanelData.mat
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
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));
Fit Logistic Model
For this example, fit a new Logistic model using only score group information but no age information. First, you can validate this model in a standalone fashion. For more information, see Basic Lifetime PD Model Validation.
Age information is important in this data set. The new model does not perform as well as the champion model (which includes age, score group, and macro vars).
Fit a new Logistic model using fitLifetimePDModel.
ModelType = "logistic"; pdModel = fitLifetimePDModel(data(TrainDataInd,:),ModelType,... 'ModelID','LogisticNoAge',... 'IDVar','ID',... 'LoanVars','ScoreGroup',... 'MacroVars',{'GDP','Market'},... 'ResponseVar','Default'); disp(pdModel)
Logistic with properties:
ModelID: "LogisticNoAge"
Description: ""
UnderlyingModel: [1x1 classreg.regr.CompactGeneralizedLinearModel]
IDVar: "ID"
AgeVar: ""
LoanVars: "ScoreGroup"
MacroVars: ["GDP" "Market"]
ResponseVar: "Default"
Compare Performance of the Logistic Model to Champion Model
To compare the new Logistic model to a champion model, you need access to the predictions of the champion model. The champion model might even have different predictors, so the mapping between the data being used and the exact inputs of the champion model might require an intermediate preprocessing step. This example assumes that you have a black-box tool to get the predictions from the champion model.
Compare the model performance for both models using modelDiscrimination.
DataSetChoice ="Testing"; if DataSetChoice=="Training" Ind = TrainDataInd; else Ind = TestDataInd; end ChampionPD = getChampionModelPDs(data(Ind,:)); [DiscMeasure,DiscData] = modelDiscrimination(pdModel,data(Ind,:),'ShowDetails',true,'DataID',DataSetChoice,... 'ReferencePD',ChampionPD,'ReferenceID',"Champion"); disp(DiscMeasure)
AUROC Segment SegmentCount
_______ __________ ____________
LogisticNoAge, Testing 0.66503 "all_data" 2.5863e+05
Champion, Testing 0.70018 "all_data" 2.5863e+05
disp(head(DiscData))
ModelID X Y T
_______________ ________ ________ ________
"LogisticNoAge" 0 0 0.02287
"LogisticNoAge" 0.04673 0.090978 0.02287
"LogisticNoAge" 0.064656 0.14922 0.022711
"LogisticNoAge" 0.10982 0.22764 0.020553
"LogisticNoAge" 0.14421 0.311 0.018483
"LogisticNoAge" 0.19237 0.41454 0.01722
"LogisticNoAge" 0.23558 0.43738 0.014125
"LogisticNoAge" 0.27979 0.52037 0.012812
disp(tail(DiscData))
ModelID X Y T
__________ _______ _______ __________
"Champion" 0.88743 0.98021 0.0032242
"Champion" 0.90293 0.98477 0.0025583
"Champion" 0.91884 0.98896 0.0023801
"Champion" 0.93303 0.99239 0.0018756
"Champion" 0.94995 0.99391 0.0017711
"Champion" 0.96705 0.99695 0.0016436
"Champion" 0.98295 0.99886 0.0012847
"Champion" 1 1 0.00086887
Use modelDiscriminationPlot to plot the ROC.
modelDiscriminationPlot(pdModel,data(Ind,:),'DataID',DataSetChoice,... 'ReferencePD',ChampionPD,'ReferenceID',"Champion");
[DiscMeasure,DiscData] = modelDiscrimination(pdModel,data(Ind,:),'ShowDetails',true,'SegmentBy','YOB','DataID',DataSetChoice,... 'ReferencePD',ChampionPD,'ReferenceID',"Champion"); disp(DiscMeasure)
AUROC Segment SegmentCount
_______ _______ ____________
LogisticNoAge, YOB=1, Testing 0.64879 1 38728
Champion, YOB=1, Testing 0.64972 1 38728
LogisticNoAge, YOB=2, Testing 0.65699 2 37812
Champion, YOB=2, Testing 0.66496 2 37812
LogisticNoAge, YOB=3, Testing 0.63508 3 36973
Champion, YOB=3, Testing 0.64774 3 36973
LogisticNoAge, YOB=4, Testing 0.62656 4 36418
Champion, YOB=4, Testing 0.66204 4 36418
LogisticNoAge, YOB=5, Testing 0.6205 5 35818
Champion, YOB=5, Testing 0.65439 5 35818
LogisticNoAge, YOB=6, Testing 0.61739 6 35384
Champion, YOB=6, Testing 0.63156 6 35384
LogisticNoAge, YOB=7, Testing 0.64016 7 24730
Champion, YOB=7, Testing 0.63117 7 24730
LogisticNoAge, YOB=8, Testing 0.63339 8 12764
Champion, YOB=8, Testing 0.63339 8 12764
disp(head(DiscData))
ModelID YOB X Y T
_______________ ___ _______ _______ _________
"LogisticNoAge" 1 0 0 0.022711
"LogisticNoAge" 1 0.12062 0.22401 0.022711
"LogisticNoAge" 1 0.23459 0.41435 0.018483
"LogisticNoAge" 1 0.33329 0.59151 0.01722
"LogisticNoAge" 1 0.45578 0.69107 0.01151
"LogisticNoAge" 1 0.5683 0.77452 0.009347
"LogisticNoAge" 1 0.67031 0.84919 0.0087028
"LogisticNoAge" 1 0.78943 0.9063 0.0064814
disp(tail(DiscData))
ModelID YOB X Y T
_______________ ___ _______ ______ __________
"LogisticNoAge" 8 0 0 0.014125
"LogisticNoAge" 8 0.31762 0.5625 0.014125
"LogisticNoAge" 8 0.65751 0.8125 0.0071273
"LogisticNoAge" 8 1 1 0.0040058
"Champion" 8 0 0 0.0040291
"Champion" 8 0.31762 0.5625 0.0040291
"Champion" 8 0.65751 0.8125 0.0017711
"Champion" 8 1 1 0.00086887
Compare Calibration Against Champion Model
Compare the calibration of the two models with modelCalibration.
GroupingVar ="YOB"; [CalMeasure,CalData] = modelCalibration(pdModel,data(Ind,:),GroupingVar,'DataID',DataSetChoice,... 'ReferencePD',ChampionPD,'ReferenceID',"Champion"); disp(CalMeasure)
RMSE
__________
LogisticNoAge, grouped by YOB, Testing 0.0031021
Champion, grouped by YOB, Testing 0.00046476
disp(head(CalData))
ModelID YOB PD GroupCount
__________ ___ _________ __________
"Observed" 1 0.017636 38728
"Observed" 2 0.013303 37812
"Observed" 3 0.010846 36973
"Observed" 4 0.010709 36418
"Observed" 5 0.0093528 35818
"Observed" 6 0.0060197 35384
"Observed" 7 0.0034776 24730
"Observed" 8 0.0012535 12764
disp(tail(CalData))
ModelID YOB PD GroupCount
__________ ___ _________ __________
"Champion" 1 0.017244 38728
"Champion" 2 0.012999 37812
"Champion" 3 0.011428 36973
"Champion" 4 0.010693 36418
"Champion" 5 0.0085574 35818
"Champion" 6 0.005937 35384
"Champion" 7 0.0035193 24730
"Champion" 8 0.0021802 12764
Use modelCalibrationPlot to visualize the model calibration.
modelCalibrationPlot(pdModel,data(Ind,:),GroupingVar,'DataID',DataSetChoice,... 'ReferencePD',ChampionPD,'ReferenceID',"Champion");
[CalMeasure,CalData] = modelCalibration(pdModel,data(Ind,:),["YOB","ScoreGroup"],'DataID',DataSetChoice,... 'ReferencePD',ChampionPD,'ReferenceID',"Champion"); disp(CalMeasure)
RMSE
_________
LogisticNoAge, grouped by YOB, ScoreGroup, Testing 0.0036974
Champion, grouped by YOB, ScoreGroup, Testing 0.0010716
disp(head(CalData))
ModelID YOB ScoreGroup PD GroupCount
__________ ___ ___________ _________ __________
"Observed" 1 High Risk 0.030877 13084
"Observed" 1 Medium Risk 0.013541 12998
"Observed" 1 Low Risk 0.0081449 12646
"Observed" 2 High Risk 0.022838 12567
"Observed" 2 Medium Risk 0.012376 12767
"Observed" 2 Low Risk 0.0046482 12478
"Observed" 3 High Risk 0.017651 12067
"Observed" 3 Medium Risk 0.0092652 12520
unstack(CalData,'PD','ModelID')
ans=24×6 table
YOB ScoreGroup GroupCount Champion LogisticNoAge Observed
___ ___________ __________ _________ _____________ _________
1 High Risk 13084 0.028165 0.019641 0.030877
1 Medium Risk 12998 0.014833 0.0099388 0.013541
1 Low Risk 12646 0.008422 0.0055911 0.0081449
2 High Risk 12567 0.02167 0.019337 0.022838
2 Medium Risk 12767 0.011123 0.0098141 0.012376
2 Low Risk 12478 0.0061856 0.0055194 0.0046482
3 High Risk 12067 0.019285 0.020139 0.017651
3 Medium Risk 12520 0.0098085 0.010179 0.0092652
3 Low Risk 12386 0.0054096 0.0057356 0.005813
4 High Risk 11798 0.018136 0.019175 0.018562
4 Medium Risk 12325 0.0091921 0.0096563 0.0094929
4 Low Risk 12295 0.0050562 0.0054292 0.004392
5 High Risk 11481 0.014818 0.014806 0.016288
5 Medium Risk 12120 0.0072853 0.007454 0.0080033
5 Low Risk 12217 0.0039358 0.0041822 0.0041745
6 High Risk 11250 0.01049 0.012153 0.0096889
⋮
Compare Two Models Under Development
You can also compare two new models under development.
pdModelTTC = fitLifetimePDModel(data(TrainDataInd,:),"probit",... 'ModelID','ProbitTTC',... 'AgeVar','YOB',... 'IDVar','ID',... 'LoanVars','ScoreGroup',... 'ResponseVar','Default',... 'Description',"TTC model, no macro variables, probit."); disp(pdModelTTC)
Probit with properties:
ModelID: "ProbitTTC"
Description: "TTC model, no macro variables, probit."
UnderlyingModel: [1x1 classreg.regr.CompactGeneralizedLinearModel]
IDVar: "ID"
AgeVar: "YOB"
LoanVars: "ScoreGroup"
MacroVars: ""
ResponseVar: "Default"
pdModelTTC.UnderlyingModel
ans =
Compact generalized linear regression model:
probit(Default) ~ 1 + ScoreGroup + YOB
Distribution = Binomial
Estimated Coefficients:
Estimate SE tStat pValue
_________ _________ _______ ___________
(Intercept) -1.8275 0.013636 -134.02 0
ScoreGroup_Medium Risk -0.26441 0.014158 -18.676 7.7165e-78
ScoreGroup_Low Risk -0.46734 0.016327 -28.624 3.371e-180
YOB -0.081761 0.0031333 -26.094 4.2244e-150
388097 observations, 388093 error degrees of freedom
Dispersion: 1
Chi^2-statistic vs. constant model: 1.7e+03, p-value = 0
Compare the calibrations.
[CalMeasureTTC,CalDataTTC] = modelCalibration(pdModelTTC,data(Ind,:),["YOB","ScoreGroup"],'DataID',DataSetChoice,... 'ReferencePD',predict(pdModel,data(Ind,:)),'ReferenceID',pdModel.ModelID); disp(CalMeasureTTC)
RMSE
_________
ProbitTTC, grouped by YOB, ScoreGroup, Testing 0.0016726
LogisticNoAge, grouped by YOB, ScoreGroup, Testing 0.0036974
unstack(CalDataTTC,'PD','ModelID')
ans=24×6 table
YOB ScoreGroup GroupCount LogisticNoAge Observed ProbitTTC
___ ___________ __________ _____________ _________ _________
1 High Risk 13084 0.019641 0.030877 0.028114
1 Medium Risk 12998 0.0099388 0.013541 0.014865
1 Low Risk 12646 0.0055911 0.0081449 0.0087364
2 High Risk 12567 0.019337 0.022838 0.023239
2 Medium Risk 12767 0.0098141 0.012376 0.012053
2 Low Risk 12478 0.0055194 0.0046482 0.0069786
3 High Risk 12067 0.020139 0.017651 0.019096
3 Medium Risk 12520 0.010179 0.0092652 0.0097145
3 Low Risk 12386 0.0057356 0.005813 0.0055406
4 High Risk 11798 0.019175 0.018562 0.015599
4 Medium Risk 12325 0.0096563 0.0094929 0.0077825
4 Low Risk 12295 0.0054292 0.004392 0.0043722
5 High Risk 11481 0.014806 0.016288 0.012666
5 Medium Risk 12120 0.007454 0.0080033 0.0061971
5 Low Risk 12217 0.0041822 0.0041745 0.0034292
6 High Risk 11250 0.012153 0.0096889 0.010223
⋮
Black-Box Champion Prediction Function
function PD = getChampionModelPDs(data) m = load('LifetimeChampionModel.mat'); PD = predict(m.pdModel,data); end
See Also
fitLifetimePDModel | predict | predictLifetime | modelDiscrimination | modelCalibration | modelCalibrationPlot | Logistic | Probit | Cox
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