modelDiscriminationPlot
Syntax
Description
modelDiscriminationPlot(___,
specifies options using one or more name-value pair arguments in addition to the
input arguments in the previous syntax.Name,Value
)
specifies options using one or more name-value pair 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 Regression LGD Model
This example shows how to use fitLGDModel
to fit data with a Regression
model and then use modelDiscriminationPlot
to plot the ROC.
Load Data
Load the loss given default 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
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 a 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 R-squared: 0.206, Adjusted R-Squared: 0.205 F-statistic vs. constant model: 181, p-value = 2.42e-104
Plot ROC Data
Use modelDiscriminationPlot
to plot the ROC for the test data set.
modelDiscriminationPlot(lgdModel,data(TestInd,:))
Plot ROC Using Tobit LGD Model
This example shows how to use fitLGDModel
to fit data with a Tobit
model and then use modelDiscriminationPlot
to plot the ROC.
Load Data
Load the loss given default 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
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 a 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
Plot ROC Data
Use modelDiscriminationPlot
to plot the ROC for the test data set.
modelDiscriminationPlot(lgdModel,data(TestInd,:),"SegmentBy","Type","DiscretizeBy","median")
Plot ROC Using Beta LGD Model
This example shows how to use fitLGDModel
to fit data with a Beta
model and then use modelDiscriminationPlot
to plot the ROC.
Load Data
Load the loss given default 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
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 a 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
Plot ROC Data
Use modelDiscriminationPlot
to plot the ROC for the test data set.
modelDiscriminationPlot(lgdModel,data(TestInd,:),"SegmentBy","Type","DiscretizeBy","median")
Input Arguments
lgdModel
— Loss given default model
Regression
object | Tobit
object | Beta
object
Loss given default model, specified as a previously created Regression
,
Tobit
, or Beta
object using
fitLGDModel
.
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.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: modelDiscriminationPlot(lgdModel,data(TestInd,:),'DataID','Testing','DiscretizeBy','median')
DataID
— Data set identifier
""
(default) | character vector | string
Data set identifier, specified as the comma-separated pair consisting
of '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 LGD data
'mean'
(default) | character vector with value 'mean'
,
'median'
, 'positive'
, or
'total'
| string with value "mean"
,
"median"
, "positive"
, or
"total"
Discretization method for LGD data
, specified as
the comma-separated pair consisting of 'DiscretizeBy'
and a character vector or string.
'mean'
— Discretized response is1
if observed LGD is greater than or equal to the mean LGD,0
otherwise.'median'
— Discretized response is1
if observed LGD is greater than or equal to the median LGD,0
otherwise.'positive'
— Discretized response is1
if observed LGD is positive,0
otherwise (full recovery).'total'
— Discretized response is1
if observed LGD is greater than or equal to1
(total loss),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 the comma-separated pair consisting of
'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
ReferenceLGD
— LGD 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 the comma-separated
pair consisting of '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 LGD models, the predicted LGD is used directly as the prediction.
However, the observed LGD must be discretized into a binary variable. By default,
observed LGD values greater than or equal to the mean observed LGD are assigned a
value of 1, and values below the mean are assigned a value of 0. This discretized
response is interpreted as "high LGD" vs. "low LGD." The ROC curve and the AUROC
curve measure how well the predicted LGD separates the "high LGD" vs. the "low LGD"
observations. The discretization criterion can be changed with the
DiscretizeBy
name-value pair argument for
modelDiscriminationPlot
.
The ROC curve is a parametric curve that plots the proportion of
High LGD cases with predicted LGD greater than or equal to a parameter t, or true positive rate (TPR)
Low LGD cases with predicted LGD greater than or equal to the same parameter t, or false positive rate (FPR)
The parameter t sweeps through all the observed predicted LGD
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.
Version History
Introduced in R2021aR2022b: Support for Beta
model
The lgdModel
input supports an option for a
Beta
model object that you can create using fitLGDModel
.
R2022a: Support for reference LGD outside of [0,1]
range
The Regression
and Tobit
LGD models support a
reference LGD outside of the [0,1]
range.
See Also
Tobit
| Regression
| modelCalibration
| modelCalibrationPlot
| modelDiscrimination
| predict
| fitLGDModel
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