modelDiscriminationPlot
Syntax
Description
modelDiscriminationPlot(___,
specifies options using one or more name-value arguments in addition to the input
arguments in the previous syntax.Name=Value
)
specifies options using one or more name-value arguments in addition to the input
arguments in the previous syntax and returns the figure handle
h
= modelDiscriminationPlot(ax
,___,Name=Value
)h
.
Examples
Plot ROC Using a Tobit EAD Model
This example shows how to use fitEADModel
to create a Tobit
model and then use modelDiscriminationPlot
to plot the ROC.
Load EAD Data
Load the EAD data.
load EADData.mat
head(EADData)
UtilizationRate Age Marriage Limit Drawn EAD _______________ ___ ___________ __________ __________ __________ 0.24359 25 not married 44776 10907 44740 0.96946 44 not married 2.1405e+05 2.0751e+05 40678 0 40 married 1.6581e+05 0 1.6567e+05 0.53242 38 not married 1.7375e+05 92506 1593.5 0.2583 30 not married 26258 6782.5 54.175 0.17039 54 married 1.7357e+05 29575 576.69 0.18586 27 not married 19590 3641 998.49 0.85372 42 not married 2.0712e+05 1.7682e+05 1.6454e+05
rng('default'); NumObs = height(EADData); c = cvpartition(NumObs,'HoldOut',0.4); TrainingInd = training(c); TestInd = test(c);
Select Model Type
Select a model type for Tobit
or Regression
.
ModelType = "Tobit";
Select Conversion Measure
Select a conversion measure for the EAD response values.
ConversionMeasure = "LCF";
Create Tobit
EAD Model
Use fitEADModel
to create a Tobit
model using the TrainingInd
data.
eadModel = fitEADModel(EADData(TrainingInd,:),ModelType,PredictorVars={'UtilizationRate','Age','Marriage'}, ... ConversionMeasure=ConversionMeasure,DrawnVar="Drawn",LimitVar="Limit",ResponseVar="EAD"); disp(eadModel);
Tobit with properties: CensoringSide: "both" LeftLimit: 0 RightLimit: 1 ModelID: "Tobit" Description: "" UnderlyingModel: [1x1 risk.internal.credit.TobitModel] PredictorVars: ["UtilizationRate" "Age" "Marriage"] ResponseVar: "EAD" LimitVar: "Limit" DrawnVar: "Drawn" ConversionMeasure: "lcf"
Display the underlying model. The underlying model's response variable is the transformation of the EAD response data. Use the 'LimitVar'
and 'DrawnVar'
name-value arguments to modify the transformation.
disp(eadModel.UnderlyingModel);
Tobit regression model: EAD_lcf = max(0,min(Y*,1)) Y* ~ 1 + UtilizationRate + Age + Marriage Estimated coefficients: Estimate SE tStat pValue __________ __________ ________ __________ (Intercept) 0.22467 0.031085 7.2276 6.4149e-13 UtilizationRate 0.4714 0.020682 22.793 0 Age -0.0014209 0.00075844 -1.8735 0.061111 Marriage_not married -0.010543 0.015817 -0.66654 0.50512 (Sigma) 0.3618 0.0049991 72.374 0 Number of observations: 2627 Number of left-censored observations: 0 Number of uncensored observations: 2626 Number of right-censored observations: 1 Log-likelihood: -1057.9
Predict EAD
EAD prediction operates on the underlying compact statistical model and then transforms the predicted values back to the EAD scale. You can specify the predict
function with different options for the 'ModelLevel'
name-value argument.
predictedEAD = predict(eadModel,EADData(TestInd,:),ModelLevel="ead"); predictedConversion = predict(eadModel,EADData(TestInd,:),ModelLevel="ConversionMeasure");
Validate EAD Model
For model validation, use modelDiscrimination
, modelDiscriminationPlot
, modelCalibration
, and modelCalibrationPlot
.
Use modelDiscrimination
and then modelDiscriminationPlot
to plot the ROC curve.
ModelLevel = "ead"; [DiscMeasure1,DiscData1] = modelDiscrimination(eadModel,EADData(TestInd,:),ModelLevel=ModelLevel); modelDiscriminationPlot(eadModel,EADData(TestInd,:),ModelLevel=ModelLevel,SegmentBy="Marriage");
Plot ROC Using a Beta EAD Model
This example shows how to use fitEADModel
to create a Beta
model and then use modelDiscriminationPlot
to plot the ROC.
Load EAD Data
Load the EAD data.
load EADData.mat
head(EADData)
UtilizationRate Age Marriage Limit Drawn EAD _______________ ___ ___________ __________ __________ __________ 0.24359 25 not married 44776 10907 44740 0.96946 44 not married 2.1405e+05 2.0751e+05 40678 0 40 married 1.6581e+05 0 1.6567e+05 0.53242 38 not married 1.7375e+05 92506 1593.5 0.2583 30 not married 26258 6782.5 54.175 0.17039 54 married 1.7357e+05 29575 576.69 0.18586 27 not married 19590 3641 998.49 0.85372 42 not married 2.0712e+05 1.7682e+05 1.6454e+05
rng('default'); NumObs = height(EADData); c = cvpartition(NumObs,'HoldOut',0.4); TrainingInd = training(c); TestInd = test(c);
Select Model Type
Select a model type for Beta
.
ModelType = "Beta";
Select Conversion Measure
Select a conversion measure for the EAD response values.
ConversionMeasure = "LCF";
Create Beta
EAD Model
Use fitEADModel
to create a Beta
model using the TrainingInd
data.
eadModel = fitEADModel(EADData(TrainingInd,:),ModelType,PredictorVars={'UtilizationRate','Age','Marriage'}, ... ConversionMeasure=ConversionMeasure,DrawnVar="Drawn",LimitVar="Limit",ResponseVar="EAD"); disp(eadModel);
Beta with properties: BoundaryTolerance: 1.0000e-07 ModelID: "Beta" Description: "" UnderlyingModel: [1x1 risk.internal.credit.BetaModel] PredictorVars: ["UtilizationRate" "Age" "Marriage"] ResponseVar: "EAD" LimitVar: "Limit" DrawnVar: "Drawn" ConversionMeasure: "lcf"
Display the underlying model. The underlying model's response variable is the transformation of the EAD response data. Use the 'LimitVar'
and 'DrawnVar'
name-value arguments to modify the transformation.
disp(eadModel.UnderlyingModel);
Beta regression model: logit(EAD_lcf) ~ 1_mu + UtilizationRate_mu + Age_mu + Marriage_mu log(EAD_lcf) ~ 1_phi + UtilizationRate_phi + Age_phi + Marriage_phi Estimated coefficients: Estimate SE tStat pValue _________ _________ ________ __________ (Intercept)_mu -0.65566 0.11484 -5.7093 1.2614e-08 UtilizationRate_mu 1.7014 0.078094 21.787 0 Age_mu -0.00559 0.0027603 -2.0252 0.042952 Marriage_not married_mu -0.012576 0.052098 -0.2414 0.80926 (Intercept)_phi -0.50132 0.094625 -5.2979 1.2685e-07 UtilizationRate_phi 0.39731 0.066707 5.956 2.9304e-09 Age_phi -0.001167 0.0023161 -0.50386 0.61441 Marriage_not married_phi -0.013275 0.042627 -0.31143 0.7555 Number of observations: 2627 Log-likelihood: -3140.21
Predict EAD
EAD prediction operates on the underlying compact statistical model and then transforms the predicted values back to the EAD scale. You can specify the predict
function with different options for the 'ModelLevel'
name-value argument.
predictedEAD = predict(eadModel,EADData(TestInd,:),ModelLevel="ead"); predictedConversion = predict(eadModel,EADData(TestInd,:),ModelLevel="ConversionMeasure");
Validate EAD Model
For model validation, use modelDiscrimination
, modelDiscriminationPlot
, modelCalibration
, and modelCalibrationPlot
.
Use modelDiscrimination
and then modelDiscriminationPlot
to plot the ROC curve.
ModelLevel = "ead"; [DiscMeasure1,DiscData1] = modelDiscrimination(eadModel,EADData(TestInd,:),ModelLevel=ModelLevel); modelDiscriminationPlot(eadModel,EADData(TestInd,:),ModelLevel=ModelLevel,SegmentBy="Marriage");
Input Arguments
eadModel
— Exposure at model
Regression
object | Tobit
object | Beta
object
Exposure at default model, specified as a previously created Regression
,
Tobit
, or Beta
object using
fitEADModel
.
Data Types: object
data
— Data
table
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
ax
— Valid axis object
object
(Optional) Valid axis object, specified as an ax
object
that is created using axes
. The plot will be
created in the axes specified by the optional ax
argument
instead of in the current axes (gca). The optional argument
ax
must precede any of the input argument
combinations.
Data Types: object
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.
Example: modelDiscriminationPlot(eadModel,data(TestInd,:),DataID='Testing',DiscretizeBy='median')
DataID
— Data set identifier
""
(default) | character vector | string
Data set identifier, specified as DataID
and a
character vector or string. The DataID
is included in
the output for reporting purposes.
Data Types: char
| string
DiscretizeBy
— Discretization method for EAD data
at defined ModelLevel
'mean'
(default) | character vector with value 'mean'
or
'median'
| string with value "mean"
or
"median"
Discretization method for EAD data
at the defined
ModelLevel
, specified as
DiscretizeBy
and a character vector or string.
'mean'
— Discretized response is1
if observed EAD is greater than or equal to the mean EAD,0
otherwise.'median'
— Discretized response is1
if observed EAD is greater than or equal to the median EAD,0
otherwise.
Data Types: char
| string
SegmentBy
— Name of column in data
input used to segment data set
""
(default) | character vector | string
Name of a column in the data
input, not
necessarily a model variable, to be used to segment the data set,
specified as SegmentBy
and a character vector or
string. One AUROC is reported for each segment, and the corresponding
ROC data for each segment is returned in the optional output.
Data Types: char
| string
ModelLevel
— Model level
"ead"
(default) | character vector with value 'ead'
,
'conversionMeasure'
, or
'conversionTransform'
| string with value "ead"
,
"conversionMeasure"
, or
"conversionTransform"
Model level, specified as ModelLevel
and a
character vector or string.
Note
Regression
models support all three model levels,
but a Tobit
or Beta
model supports model levels only for "ead"
and "conversionMeasure"
.
Data Types: char
| string
ReferenceEAD
— EAD values predicted for data
by reference model
[]
(default) | numeric vector
ReferenceID
— Identifier for the reference model
'Reference'
(default) | character vector | string
Identifier for the reference model, specified as
ReferenceID
and a character vector or string.
'ReferenceID'
is used in the plot for reporting
purposes.
Data Types: char
| string
Output Arguments
h
— Figure handle
handle object
Figure handle for the line objects, returned as handle object.
More About
Model Discrimination Plot
The modelDiscriminationPlot
function plots the
receiver operator characteristic (ROC) curve.
The modelDiscriminationPlot
function also shows the area under
the receiver operator characteristic (AUROC) curve, sometimes called simply the area
under the curve (AUC). This metric is between 0 and 1 and higher values indicate
better discrimination.
A numeric prediction and a binary response are needed to plot the ROC and compute
the AUROC. For EAD models, the predicted EAD is used directly as the prediction.
However, the observed EAD must be discretized into a binary variable. By default,
observed EAD values greater than or equal to the mean observed EAD are assigned a
value of 1, and values below the mean are assigned a value of 0. This discretized
response is interpreted as "high EAD" vs. "low EAD." The ROC curve and the AUROC
curve measure how well the predicted EAD separates the "high EAD" vs. the "low EAD"
observations. You can change the level to compute the model discrimination with the
ModelLevel
name-value pair argument and the discretization
criterion with the DiscretizeBy
name-value pair
argument.
The ROC curve is a parametric curve that plots the proportion of
High EAD cases with predicted EAD greater than or equal to a parameter t, or true positive rate (TPR)
Low EAD cases with predicted EAD greater than or equal to the same parameter t, or false positive rate (FPR)
The parameter t sweeps through all the observed predicted EAD
values for the given data. If the AUROC value or the ROC curve data are needed
programmatically, use the modelDiscrimination
function. For more information about ROC curves,
see ROC Curve and Performance Metrics.
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] Brown, Iain. Developing Credit Risk Models Using SAS Enterprise Miner and SAS/STAT: Theory and Applications. SAS Institute, 2014.
[4] Roesch, Daniel and Harald Scheule. Deep Credit Risk. Independently published, 2020.
Version History
Introduced in R2021bR2022b: Support for Beta
model
The eadModel
input supports an option for a
Beta
model object that you can create using fitEADModel
.
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