modelCalibrationPlot
Syntax
Description
modelCalibrationPlot(___,
specifies options using one or more name-value pair arguments in addition to the
input arguments in the previous syntax. You can use the
Name,Value
)ModelLevel
name-value pair argument to compute metrics
using the underlying model's transformed scale.
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
= modelCalibrationPlot(ax
,___,Name,Value
)h
.
Examples
Generate a Scatter Plot of Predicted and Observed LGDs Using Regression LGD Model
This example shows how to use fitLGDModel
to fit data with a Regression
model and then use modelCalibrationPlot
to generate a scatter plot for predicted and observed LGDs.
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 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.
lgdModel.UnderlyingModel
ans = 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
Generate Scatter Plot of Predicted and Observed LGDs
Use modelCalibrationPlot
to generate a scatter plot of predicted and observed LGDs for the test data set. The ModelLevel
name-value pair argument modifies the output only for Regression
models, not Tobit
models, because there are no response transformations for the Tobit
model.
modelCalibrationPlot(lgdModel,data(TestInd,:),ModelLevel="underlying")
Generate Scatter Plot of Predicted and Observed LGDs Using Tobit LGD Model
This example shows how to use fitLGDModel
to fit data with a Tobit
model and then use modelCalibrationPlot
to generate a scatter plot of predicted and observed LGDs.
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 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
Generate Scatter Plot of Predicted and Observed LGDs
Use modelCalibrationPlot
to generate a scatter plot of predicted and observed LGDs for the test data set.
modelCalibrationPlot(lgdModel,data(TestInd,:))
Generate Scatter Plot of Predicted and Observed LGDs Using Beta LGD Model
This example shows how to use fitLGDModel
to fit data with a Beta
model and then use modelCalibrationPlot
to generate a scatter plot of predicted and observed LGDs.
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 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
Generate Scatter Plot of Predicted and Observed LGDs
Use modelCalibrationPlot
to generate a scatter plot of predicted and observed LGDs for the test data set.
modelCalibrationPlot(lgdModel,data(TestInd,:))
Visualize Calibration for Residuals or Other Variables
modelCalibrationPlot
generates a scatter plot of observed vs. predicted LGD values. The 'XData'
and 'YData'
name-value arguments allow you to visualize the residuals or generate a scatter plot against a variable of interest.
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 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
Generate Scatter Plot of Predicted and Observed LGDs
Use modelCalibrationPlot
to generate a scatter plot of residuals against LTV values.
modelCalibrationPlot(lgdModel,data(TestInd,:),XData='LTV',YData='residuals')
For Regression
models, the 'ModelLevel'
name-value argument allows you to visualize the plot using the underlying model scale.
modelCalibrationPlot(lgdModel,data(TestInd,:),XData='LTV',YData='residuals',ModelLevel='underlying')
For categorical variables, modelCalibrationPlot
uses a swarm chart. For more information, see swarmchart
.
modelCalibrationPlot(lgdModel,data(TestInd,:),XData='Type',YData='residuals',ModelLevel='underlying')
Input Arguments
lgdModel
— Loss given default model
Regression
object | Tobit
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.
Example: modelCalibrationPlot(lgdModel,data(TestInd,:),DataID='Testing',YData=residuals,XData='LTV')
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
ModelLevel
— Model level
'top'
(default) | character vector with value 'top'
or
'underlying'
| string with value "top"
or
"underlying"
Model level, specified as ModelLevel
and a
character vector or string.
'top'
— The accuracy metrics are computed in the LGD scale at the top model level.'underlying'
— For aRegression
model only, the metrics are computed in the underlying model's transformed scale. The metrics are computed on the transformed LGD data.
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
ReferenceID
and a character vector or string.
'ReferenceID'
is used in the scatter plot output
for reporting purposes.
Data Types: char
| string
XData
— Data to plot on x-axis
'predicted'
(default) | character vector with value 'predicted'
,
'observed'
, 'residuals'
, or
VariableName | string with value | "predicted"
, "observed"
,
"residuals"
, or
VariableName
Data to plot on x-axis, specified as XData
and a
character vector or string for one of the following:
'predicted'
— Plot the predicted LGD values in the x-axis.'observed'
— Plot the observed LGD values in the x-axis.'residuals'
— Plot the residuals in the x-axis.VariableName — Use the name of the variable in the
data
input, not necessarily a model variable, to plot in the x-axis.
Data Types: char
| string
YData
— Data to plot on y-axis
'predicted'
(default) | character vector with value 'predicted'
,
'observed'
, or
'residuals'
| string with value | "predicted"
, "observed"
, or
"residuals"
Data to plot on y-axis, specified as YData
and a
character vector or string for one of the following:
'predicted'
— Plot the predicted LGD values in the y-axis.'observed'
— Plot the observed LGD values in the y-axis.'residuals'
— Plot the residuals in the y-axis.
Data Types: char
| string
Output Arguments
h
— Figure handle
handle object
Figure handle for the scatter and line objects, returned as handle object.
More About
Model Calibration Plot
The modelCalibrationPlot
function returns a
scatter plot of observed vs. predicted loss given default (LGD) data with a linear
fit and reports the R-square of the linear fit.
The XData
name-value pair argument allows you to change the
x values on the plot. By default, predicted LGD values are
plotted in the x-axis, but predicted LGD values, residuals, or
any variable in the data
input, not necessarily a model
variable, can be used as x values. If the selected
XData
is a categorical variable, a swarm chart is used. For
more information, see swarmchart
.
The YData
name-value pair argument allows users to change the
y values on the plot. By default, observed LGD values are
plotted in the y-axis, but predicted LGD values or residuals can
also be used as y values. YData
does not
support table variables.
For Regression
models, if
ModelLevel
is set to 'underlying'
, the
LGD data is transformed into the underlying model's scale. The transformed data is
shown on the plot. The ModelLevel
name-value pair argument has
no effect for Tobit
models.
The linear fit and reported R-squared value always correspond to the linear regression model with the plotted y values as response and the plotted x values as the only predictor.
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 R2023a
See Also
Tobit
| Regression
| Beta
| modelCalibration
| modelDiscriminationPlot
| modelDiscrimination
| predict
| fitLGDModel
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