fitmodel
Fit logistic regression model to Weight of Evidence (WOE) data
Description
fits a logistic regression model to the Weight of Evidence (WOE) data and stores
the model predictor names and corresponding coefficients in the
sc
= fitmodel(sc
)creditscorecard
object.
fitmodel
internally transforms all the predictor variables
into WOE values, using the bins found with the automatic or manual binning
process. The response variable is mapped so that "Good" is 1
,
and "Bad" is 0
. This implies that higher (unscaled) scores
correspond to better (less risky) individuals (smaller probability of
default).
Alternatively, you can use setmodel
to provide names of
the predictors that you want in the logistic regression model, along with their
corresponding coefficients.
[
fits a logistic regression model to the Weight of Evidence (WOE) data and stores
the model predictor names and corresponding coefficients in the
sc
,mdl
]
= fitmodel(sc
)creditscorecard
object. fitmodel
returns an updated creditscorecard
object and a
GeneralizedLinearModel
object containing the fitted
model.
fitmodel
internally transforms all the predictor variables
into WOE values, using the bins found with the automatic or manual binning
process. The response variable is mapped so that "Good" is 1
,
and "Bad" is 0
. This implies that higher (unscaled) scores
correspond to better (less risky) individuals (smaller probability of
default).
Alternatively, you can use setmodel
to provide names of
the predictors that you want in the logistic regression model, along with their
corresponding coefficients.
[
fits a logistic regression model to the Weight of Evidence (WOE) data using
optional name-value pair arguments and stores the model predictor names and
corresponding coefficients in the sc
,mdl
]
= fitmodel(___,Name,Value
)creditscorecard
object.
Using name-value pair arguments, you can select which Generalized Linear Model
to fit the data. fitmodel
returns an updated
creditscorecard
object and a
GeneralizedLinearModel
object containing the fitted
model.
Examples
Fit a Stepwise Logistic Model
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011).
load CreditCardData sc = creditscorecard(data,'IDVar','CustID')
sc = creditscorecard with properties: GoodLabel: 0 ResponseVar: 'status' WeightsVar: '' VarNames: {'CustID' 'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate' 'status'} NumericPredictors: {'CustAge' 'TmAtAddress' 'CustIncome' 'TmWBank' 'AMBalance' 'UtilRate'} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 0 IDVar: 'CustID' PredictorVars: {'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate'} Data: [1200x11 table]
Perform automatic binning.
sc = autobinning(sc)
sc = creditscorecard with properties: GoodLabel: 0 ResponseVar: 'status' WeightsVar: '' VarNames: {'CustID' 'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate' 'status'} NumericPredictors: {'CustAge' 'TmAtAddress' 'CustIncome' 'TmWBank' 'AMBalance' 'UtilRate'} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 0 IDVar: 'CustID' PredictorVars: {'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate'} Data: [1200x11 table]
Use fitmodel
to fit a logistic regression model using Weight of Evidence (WOE) data. fitmodel
internally transforms all the predictor variables into WOE values, using the bins found with the automatic binning process. fitmodel
then fits a logistic regression model using a stepwise method (by default).
sc = fitmodel(sc);
1. Adding CustIncome, Deviance = 1490.8527, Chi2Stat = 32.588614, PValue = 1.1387992e-08 2. Adding TmWBank, Deviance = 1467.1415, Chi2Stat = 23.711203, PValue = 1.1192909e-06 3. Adding AMBalance, Deviance = 1455.5715, Chi2Stat = 11.569967, PValue = 0.00067025601 4. Adding EmpStatus, Deviance = 1447.3451, Chi2Stat = 8.2264038, PValue = 0.0041285257 5. Adding CustAge, Deviance = 1441.994, Chi2Stat = 5.3511754, PValue = 0.020708306 6. Adding ResStatus, Deviance = 1437.8756, Chi2Stat = 4.118404, PValue = 0.042419078 7. Adding OtherCC, Deviance = 1433.707, Chi2Stat = 4.1686018, PValue = 0.041179769 Generalized linear regression model: logit(status) ~ 1 + CustAge + ResStatus + EmpStatus + CustIncome + TmWBank + OtherCC + AMBalance Distribution = Binomial Estimated Coefficients: Estimate SE tStat pValue ________ ________ ______ __________ (Intercept) 0.70239 0.064001 10.975 5.0538e-28 CustAge 0.60833 0.24932 2.44 0.014687 ResStatus 1.377 0.65272 2.1097 0.034888 EmpStatus 0.88565 0.293 3.0227 0.0025055 CustIncome 0.70164 0.21844 3.2121 0.0013179 TmWBank 1.1074 0.23271 4.7589 1.9464e-06 OtherCC 1.0883 0.52912 2.0569 0.039696 AMBalance 1.045 0.32214 3.2439 0.0011792 1200 observations, 1192 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 89.7, p-value = 1.4e-16
Fit a Stepwise Logistic Model For a creditscorecard Object Containing Weights
Use the CreditCardData.mat
file to load the data (dataWeights
) that contains a column (RowWeights
) for the weights (using a dataset from Refaat 2011).
load CreditCardData
Create a creditscorecard
object using the optional name-value pair argument for 'WeightsVar'
.
sc = creditscorecard(dataWeights,'IDVar','CustID','WeightsVar','RowWeights')
sc = creditscorecard with properties: GoodLabel: 0 ResponseVar: 'status' WeightsVar: 'RowWeights' VarNames: {'CustID' 'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate' 'RowWeights' 'status'} NumericPredictors: {'CustAge' 'TmAtAddress' 'CustIncome' 'TmWBank' 'AMBalance' 'UtilRate'} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 0 IDVar: 'CustID' PredictorVars: {'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate'} Data: [1200x12 table]
Perform automatic binning.
sc = autobinning(sc)
sc = creditscorecard with properties: GoodLabel: 0 ResponseVar: 'status' WeightsVar: 'RowWeights' VarNames: {'CustID' 'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate' 'RowWeights' 'status'} NumericPredictors: {'CustAge' 'TmAtAddress' 'CustIncome' 'TmWBank' 'AMBalance' 'UtilRate'} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 0 IDVar: 'CustID' PredictorVars: {'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate'} Data: [1200x12 table]
Use fitmodel
to fit a logistic regression model using Weight of Evidence (WOE) data. fitmodel
internally transforms all the predictor variables into WOE values, using the bins found with the automatic binning process. fitmodel
then fits a logistic regression model using a stepwise method (by default). When the optional name-value pair argument 'WeightsVar'
is used to specify observation (sample) weights, the mdl
output uses the weighted counts with stepwiseglm
and fitglm
.
[sc,mdl] = fitmodel(sc);
1. Adding CustIncome, Deviance = 764.3187, Chi2Stat = 15.81927, PValue = 6.968927e-05 2. Adding TmWBank, Deviance = 751.0215, Chi2Stat = 13.29726, PValue = 0.0002657942 3. Adding AMBalance, Deviance = 743.7581, Chi2Stat = 7.263384, PValue = 0.007037455 Generalized linear regression model: logit(status) ~ 1 + CustIncome + TmWBank + AMBalance Distribution = Binomial Estimated Coefficients: Estimate SE tStat pValue ________ ________ ______ __________ (Intercept) 0.70642 0.088702 7.964 1.6653e-15 CustIncome 1.0268 0.25758 3.9862 6.7132e-05 TmWBank 1.0973 0.31294 3.5063 0.0004543 AMBalance 1.0039 0.37576 2.6717 0.0075464 1200 observations, 1196 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 36.4, p-value = 6.22e-08
Fit a Logistic Model with All Predictors
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011).
load CreditCardData sc = creditscorecard(data,'IDVar','CustID')
sc = creditscorecard with properties: GoodLabel: 0 ResponseVar: 'status' WeightsVar: '' VarNames: {'CustID' 'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate' 'status'} NumericPredictors: {'CustAge' 'TmAtAddress' 'CustIncome' 'TmWBank' 'AMBalance' 'UtilRate'} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 0 IDVar: 'CustID' PredictorVars: {'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate'} Data: [1200x11 table]
Perform automatic binning.
sc = autobinning(sc,'Algorithm','EqualFrequency')
sc = creditscorecard with properties: GoodLabel: 0 ResponseVar: 'status' WeightsVar: '' VarNames: {'CustID' 'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate' 'status'} NumericPredictors: {'CustAge' 'TmAtAddress' 'CustIncome' 'TmWBank' 'AMBalance' 'UtilRate'} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 0 IDVar: 'CustID' PredictorVars: {'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate'} Data: [1200x11 table]
Use fitmodel
to fit a logistic regression model using Weight of Evidence (WOE) data. fitmodel
internally transforms all the predictor variables into WOE values, using the bins found with the automatic binning process. Set the VariableSelection
name-value pair argument to FullModel
to specify that all predictors must be included in the fitted logistic regression model.
sc = fitmodel(sc,'VariableSelection','FullModel');
Generalized linear regression model: logit(status) ~ 1 + CustAge + TmAtAddress + ResStatus + EmpStatus + CustIncome + TmWBank + OtherCC + AMBalance + UtilRate Distribution = Binomial Estimated Coefficients: Estimate SE tStat pValue ________ ________ _______ _________ (Intercept) 0.70262 0.063862 11.002 3.734e-28 CustAge 0.57683 0.27064 2.1313 0.033062 TmAtAddress 1.0653 0.55233 1.9287 0.053762 ResStatus 1.4189 0.65162 2.1775 0.029441 EmpStatus 0.89916 0.29217 3.0776 0.002087 CustIncome 0.77506 0.21942 3.5323 0.0004119 TmWBank 1.0826 0.26583 4.0727 4.648e-05 OtherCC 1.1354 0.52827 2.1493 0.031612 AMBalance 0.99315 0.32642 3.0425 0.0023459 UtilRate 0.16723 0.55745 0.29999 0.76419 1200 observations, 1190 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 85.6, p-value = 1.25e-14
Fit a Stepwise Logistic Model When Using Missing Data
Create a creditscorecard
object using the CreditCardData.mat
file to load the dataMissing
with missing values.
load CreditCardData.mat
head(dataMissing,5)
CustID CustAge TmAtAddress ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance UtilRate status ______ _______ ___________ ___________ _________ __________ _______ _______ _________ ________ ______ 1 53 62 <undefined> Unknown 50000 55 Yes 1055.9 0.22 0 2 61 22 Home Owner Employed 52000 25 Yes 1161.6 0.24 0 3 47 30 Tenant Employed 37000 61 No 877.23 0.29 0 4 NaN 75 Home Owner Employed 53000 20 Yes 157.37 0.08 0 5 68 56 Home Owner Employed 53000 14 Yes 561.84 0.11 0
fprintf('Number of rows: %d\n',height(dataMissing))
Number of rows: 1200
fprintf('Number of missing values CustAge: %d\n',sum(ismissing(dataMissing.CustAge)))
Number of missing values CustAge: 30
fprintf('Number of missing values ResStatus: %d\n',sum(ismissing(dataMissing.ResStatus)))
Number of missing values ResStatus: 40
Use creditscorecard
with the name-value argument 'BinMissingData'
set to true
to bin the missing numeric or categorical data in a separate bin.
sc = creditscorecard(dataMissing,'IDVar','CustID','BinMissingData',true); sc = autobinning(sc); disp(sc)
creditscorecard with properties: GoodLabel: 0 ResponseVar: 'status' WeightsVar: '' VarNames: {'CustID' 'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate' 'status'} NumericPredictors: {'CustAge' 'TmAtAddress' 'CustIncome' 'TmWBank' 'AMBalance' 'UtilRate'} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 1 IDVar: 'CustID' PredictorVars: {'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate'} Data: [1200×11 table]
Display and plot bin information for numeric data for 'CustAge'
that includes missing data in a separate bin labelled <missing>
.
[bi,cp] = bininfo(sc,'CustAge');
disp(bi)
Bin Good Bad Odds WOE InfoValue _____________ ____ ___ ______ ________ __________ {'[-Inf,33)'} 69 52 1.3269 -0.42156 0.018993 {'[33,37)' } 63 45 1.4 -0.36795 0.012839 {'[37,40)' } 72 47 1.5319 -0.2779 0.0079824 {'[40,46)' } 172 89 1.9326 -0.04556 0.0004549 {'[46,48)' } 59 25 2.36 0.15424 0.0016199 {'[48,51)' } 99 41 2.4146 0.17713 0.0035449 {'[51,58)' } 157 62 2.5323 0.22469 0.0088407 {'[58,Inf]' } 93 25 3.72 0.60931 0.032198 {'<missing>'} 19 11 1.7273 -0.15787 0.00063885 {'Totals' } 803 397 2.0227 NaN 0.087112
plotbins(sc,'CustAge')
Display and plot bin information for categorical data for 'ResStatus'
that includes missing data in a separate bin labelled <missing>
.
[bi,cg] = bininfo(sc,'ResStatus');
disp(bi)
Bin Good Bad Odds WOE InfoValue ______________ ____ ___ ______ _________ __________ {'Tenant' } 296 161 1.8385 -0.095463 0.0035249 {'Home Owner'} 352 171 2.0585 0.017549 0.00013382 {'Other' } 128 52 2.4615 0.19637 0.0055808 {'<missing>' } 27 13 2.0769 0.026469 2.3248e-05 {'Totals' } 803 397 2.0227 NaN 0.0092627
plotbins(sc,'ResStatus')
Use fitmodel
to fit a logistic regression model using Weight of Evidence (WOE) data. fitmodel
internally transforms all the predictor variables into WOE values, using the bins found with the automatic binning process. fitmodel
then fits a logistic regression model using a stepwise method (by default). For predictors that have missing data, there is an explicit <missing>
bin, with a corresponding WOE value computed from the data. When using fitmodel
, the corresponding WOE value for the <missing> bin is applied when performing the WOE transformation. For example, a missing value for customer age (CustAge
) is replaced with -0.15787
which is the WOE value for the <missing>
bin for the CustAge
predictor. However, when 'BinMissingData'
is false, a missing value for CustAge
remains as missing (NaN
) when applying the WOE transformation.
[sc,mdl] = fitmodel(sc);
1. Adding CustIncome, Deviance = 1490.8527, Chi2Stat = 32.588614, PValue = 1.1387992e-08 2. Adding TmWBank, Deviance = 1467.1415, Chi2Stat = 23.711203, PValue = 1.1192909e-06 3. Adding AMBalance, Deviance = 1455.5715, Chi2Stat = 11.569967, PValue = 0.00067025601 4. Adding EmpStatus, Deviance = 1447.3451, Chi2Stat = 8.2264038, PValue = 0.0041285257 5. Adding CustAge, Deviance = 1442.8477, Chi2Stat = 4.4974731, PValue = 0.033944979 6. Adding ResStatus, Deviance = 1438.9783, Chi2Stat = 3.86941, PValue = 0.049173805 7. Adding OtherCC, Deviance = 1434.9751, Chi2Stat = 4.0031966, PValue = 0.045414057 Generalized linear regression model: logit(status) ~ 1 + CustAge + ResStatus + EmpStatus + CustIncome + TmWBank + OtherCC + AMBalance Distribution = Binomial Estimated Coefficients: Estimate SE tStat pValue ________ ________ ______ __________ (Intercept) 0.70229 0.063959 10.98 4.7498e-28 CustAge 0.57421 0.25708 2.2335 0.025513 ResStatus 1.3629 0.66952 2.0356 0.04179 EmpStatus 0.88373 0.2929 3.0172 0.002551 CustIncome 0.73535 0.2159 3.406 0.00065929 TmWBank 1.1065 0.23267 4.7556 1.9783e-06 OtherCC 1.0648 0.52826 2.0156 0.043841 AMBalance 1.0446 0.32197 3.2443 0.0011775 1200 observations, 1192 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 88.5, p-value = 2.55e-16
Input Arguments
sc
— Credit scorecard model
creditscorecard
object
Credit scorecard model, specified as a
creditscorecard
object. Use creditscorecard
to create
a creditscorecard
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: [sc,mdl] =
fitmodel(sc,'VariableSelection','FullModel')
PredictorVars
— Predictor variables for fitting creditscorecard
object
all predictors in the
creditscorecard
object (default) | cell array of character vectors
Predictor variables for fitting the
creditscorecard
object, specified as the
comma-separated pair consisting of 'PredictorVars'
and a cell array of character vectors. When provided, the
creditscorecard
object property
PredictorsVars
is updated. Note that the order of
predictors in the original dataset is enforced, regardless of the order
in which 'PredictorVars'
is provided. When not
provided, the predictors used to create the
creditscorecard
object (by using creditscorecard
) are
used.
Data Types: cell
VariableSelection
— Variable selection method to fit logistic regression model
'Stepwise'
(default) | character vector with values 'Stepwise'
,
'FullModel'
The variable selection method to fit the logistic regression
model, specified as the comma-separated pair consisting of
'VariableSelection'
and a character vector with
values 'Stepwise'
or 'FullModel'
:
Stepwise
— Uses a stepwise selection method which calls the Statistics and Machine Learning Toolbox™ functionstepwiseglm
. Only variables inPredictorVars
can potentially become part of the model and uses theStartingModel
name-value pair argument to select the starting model.
FullModel
— Fits a model with all predictor variables in thePredictorVars
name-value pair argument and callsfitglm
.
Note
Only variables in the PredictorVars
property of the creditscorecard
object can
potentially become part of the logistic regression model and
only linear terms are included in this model with no
interactions or any other higher-order terms.
The response variable is mapped so that “Good”
is 1
and “Bad” is
0
.
Data Types: char
StartingModel
— Initial model for Stepwise
variable selection
'Constant'
(default) | character vector with values 'Constant'
,
'Linear'
Initial model for the Stepwise
variable
selection method, specified as the comma-separated pair consisting of
'StartingModel'
and a character vector with
values 'Constant'
or 'Linear'
.
This option determines the initial model (constant or linear) that the
Statistics and Machine Learning Toolbox function stepwiseglm
starts with.
Constant
— Starts the stepwise method with an empty (constant only) model.Linear
— Starts the stepwise method from a full (all predictors in) model.
Note
StartingModel
is used only for the
Stepwise
option of
VariableSelection
and has no effect for
the FullModel
option of
VariableSelection
.
Data Types: char
Display
— Indicator to display model information at command line
'On'
(default) | character vector with values 'On'
,
'Off'
Indicator to display model information at command line, specified
as the comma-separated pair consisting of 'Display'
and a character vector with value 'On'
or
'Off'
.
Data Types: char
Output Arguments
sc
— Credit scorecard model
creditscorecard
object
Credit scorecard model, returned as an updated
creditscorecard
object. The
creditscorecard
object contains information about
the model predictors and coefficients used to fit the WOE data. For more
information on using the creditscorecard
object, see
creditscorecard
.
mdl
— Fitted logistic model
GeneralizedLinearModel
object
Fitted logistic model, returned as an object of type
GeneralizedLinearModel
containing the fitted model.
For more information on a GeneralizedLinearModel
object,
see GeneralizedLinearModel
.
Note
When creating the creditscorecard
object with
creditscorecard
, if
the optional name-value pair argument WeightsVar
was used to specify observation (sample) weights, then
mdl
uses the weighted counts with stepwiseglm
and
fitglm
.
More About
Using fitmodel
with Weights
When observation weights are provided in the credit scorecard
data
, the weights are used to calibrate the model
coefficients.
The underlying Statistics and Machine Learning Toolbox functionality for stepwiseglm
and fitglm
supports observation weights. The weights also affect the
logistic model through the WOE values. The WOE transformation is applied to all
predictors before fitting the logistic model. The observation weights directly
impact the WOE values. For more information, see Using bininfo with Weights and Credit Scorecard Modeling Using Observation Weights.
Therefore, the credit scorecard points and final score depend on the observation weights through both the logistic model coefficients and the WOE values.
Models
A logistic regression model is used in the
creditscorecard
object.
For the model, the probability of being “Bad” is defined as:
ProbBad = exp(-s) / (1 + exp(-s))
.
References
[1] Anderson, R. The Credit Scoring Toolkit. Oxford University Press, 2007.
[2] Refaat, M. Credit Risk Scorecards: Development and Implementation Using SAS. lulu.com, 2011.
Version History
Introduced in R2014b
See Also
fitConstrainedModel
| creditscorecard
| autobinning
| bininfo
| predictorinfo
| modifypredictor
| plotbins
| modifybins
| bindata
| displaypoints
| formatpoints
| score
| stepwiseglm
| fitglm
| setmodel
| probdefault
| validatemodel
| GeneralizedLinearModel
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