formatpoints
Format scorecard points and scaling
Description
modifies the scorecard points and scaling using optional name-value pair
arguments. For example, use optional name-value pair arguments to change the
scaling of the scores or the rounding of the points. sc
= formatpoints(sc,Name,Value
)
Examples
Scale Points Using Points, Odds Levels, and PDO
This example shows how to use formatpoints
to scale by providing the points, odds levels, and PDO (points to double the odds). By using formatpoints
to scale, you can put points and scores in a desired range that is more meaningful for practical purposes. Technically, this involves a linear transformation from the unscaled to the scaled points by the formatpoints
function.
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011). Use the 'IDVar'
argument in creditscorecard
to indicate that 'CustID'
contains ID information and should not be included as a predictor variable.
load CreditCardData sc = creditscorecard(data,'IDVar','CustID');
Perform automatic binning to bin for all predictors.
sc = autobinning(sc);
Fit a linear regression model using default parameters.
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
Display unscaled points for predictors retained in the fitting model and display the minimum and maximum possible unscaled scores.
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ _________
{'CustAge' } {'[-Inf,33)' } -0.15894
{'CustAge' } {'[33,37)' } -0.14036
{'CustAge' } {'[37,40)' } -0.060323
{'CustAge' } {'[40,46)' } 0.046408
{'CustAge' } {'[46,48)' } 0.21445
{'CustAge' } {'[48,58)' } 0.23039
{'CustAge' } {'[58,Inf]' } 0.479
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } -0.031252
{'ResStatus' } {'Home Owner' } 0.12696
{'ResStatus' } {'Other' } 0.37641
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } -0.076317
{'EmpStatus' } {'Employed' } 0.31449
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} -0.45716
⋮
MinScore = -1.3100
MaxScore = 3.0726
Scale by providing the points, odds levels, and PDO (points to double the odds). Suppose that you want a score of 500 points to have odds of 2 (twice as likely to be good than to be bad) and that the odds double every 50 points (so that 550 points would have odds of 4).
sc = formatpoints(sc,'PointsOddsAndPDO',[500 2 50]);
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ ______
{'CustAge' } {'[-Inf,33)' } 52.821
{'CustAge' } {'[33,37)' } 54.161
{'CustAge' } {'[37,40)' } 59.934
{'CustAge' } {'[40,46)' } 67.633
{'CustAge' } {'[46,48)' } 79.755
{'CustAge' } {'[48,58)' } 80.905
{'CustAge' } {'[58,Inf]' } 98.838
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } 62.031
{'ResStatus' } {'Home Owner' } 73.444
{'ResStatus' } {'Other' } 91.438
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } 58.781
{'EmpStatus' } {'Employed' } 86.971
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} 31.309
⋮
MinScore = 355.5051
MaxScore = 671.6403
Scale Points Using Worst and Best Scores
This example shows how to use formatpoints
to scale by providing the Worst
and Best
score values. By using formatpoints
to scale, you can put points and scores in a desired range that is more meaningful for practical purposes. Technically, this involves a linear transformation from the unscaled to the scaled points.
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011). Use the 'IDVar'
argument in creditscorecard
to indicate that 'CustID'
contains ID information and should not be included as a predictor variable.
load CreditCardData sc = creditscorecard(data,'IDVar','CustID');
Perform automatic binning to bin for all predictors.
sc = autobinning(sc);
Fit a linear regression model using default parameters.
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
Display unscaled points for predictors retained in the fitting model and display the minimum and maximum possible unscaled scores.
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ _________
{'CustAge' } {'[-Inf,33)' } -0.15894
{'CustAge' } {'[33,37)' } -0.14036
{'CustAge' } {'[37,40)' } -0.060323
{'CustAge' } {'[40,46)' } 0.046408
{'CustAge' } {'[46,48)' } 0.21445
{'CustAge' } {'[48,58)' } 0.23039
{'CustAge' } {'[58,Inf]' } 0.479
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } -0.031252
{'ResStatus' } {'Home Owner' } 0.12696
{'ResStatus' } {'Other' } 0.37641
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } -0.076317
{'EmpStatus' } {'Employed' } 0.31449
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} -0.45716
⋮
MinScore = -1.3100
MaxScore = 3.0726
Scale by providing the 'Worst'
and 'Best'
score values. The range provided below is a common score range. Display the points information again to verify that they are now scaled and also display the scaled minimum and maximum scores.
sc = formatpoints(sc,'WorstAndBestScores',[300 850]);
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ ______
{'CustAge' } {'[-Inf,33)' } 46.396
{'CustAge' } {'[33,37)' } 48.727
{'CustAge' } {'[37,40)' } 58.772
{'CustAge' } {'[40,46)' } 72.167
{'CustAge' } {'[46,48)' } 93.256
{'CustAge' } {'[48,58)' } 95.256
{'CustAge' } {'[58,Inf]' } 126.46
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } 62.421
{'ResStatus' } {'Home Owner' } 82.276
{'ResStatus' } {'Other' } 113.58
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } 56.765
{'EmpStatus' } {'Employed' } 105.81
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} 8.9706
⋮
MinScore = 300
MaxScore = 850
As expected, the values of MinScore
and MaxScore
correspond to the desired worst and best scores.
Scale Points Using Shift and Slope
This example shows how to use formatpoints
to scale by providing the Shift
and Slope
values. By using formatpoints
to scale, you can put points and scores in a desired range that is more meaningful for practical purposes. Technically, this involves a linear transformation from the unscaled to the scaled points by the formatpoints
function.
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011). Use the 'IDVar'
argument in creditscorecard
to indicate that 'CustID'
contains ID information and should not be included as a predictor variable.
load CreditCardData sc = creditscorecard(data,'IDVar','CustID');
Perform automatic binning to bin for all predictors.
sc = autobinning(sc);
Fit a linear regression model using default parameters.
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
Display unscaled points for predictors retained in the fitting model and display the minimum and maximum possible unscaled scores.
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ _________
{'CustAge' } {'[-Inf,33)' } -0.15894
{'CustAge' } {'[33,37)' } -0.14036
{'CustAge' } {'[37,40)' } -0.060323
{'CustAge' } {'[40,46)' } 0.046408
{'CustAge' } {'[46,48)' } 0.21445
{'CustAge' } {'[48,58)' } 0.23039
{'CustAge' } {'[58,Inf]' } 0.479
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } -0.031252
{'ResStatus' } {'Home Owner' } 0.12696
{'ResStatus' } {'Other' } 0.37641
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } -0.076317
{'EmpStatus' } {'Employed' } 0.31449
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} -0.45716
⋮
MinScore = -1.3100
MaxScore = 3.0726
Scale by providing the 'Shift'
and 'Slope'
values. In this example, there is an arbitrary choice of shift and slope. Display the points information again to verify that they are now scaled and also display the scaled minimum and maximum scores.
sc = formatpoints(sc,'ShiftAndSlope',[300 6]);
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ ______
{'CustAge' } {'[-Inf,33)' } 41.904
{'CustAge' } {'[33,37)' } 42.015
{'CustAge' } {'[37,40)' } 42.495
{'CustAge' } {'[40,46)' } 43.136
{'CustAge' } {'[46,48)' } 44.144
{'CustAge' } {'[48,58)' } 44.239
{'CustAge' } {'[58,Inf]' } 45.731
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } 42.67
{'ResStatus' } {'Home Owner' } 43.619
{'ResStatus' } {'Other' } 45.116
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } 42.399
{'EmpStatus' } {'Employed' } 44.744
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} 40.114
⋮
MinScore = 292.1401
MaxScore = 318.4355
Report Base Points Separately
This example shows how to use formatpoints
to separate the base points from the rest of the points assigned to each predictor variable. The formatpoints
name-value pair argument 'BasePoints'
serves this purpose.
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011). Use the 'IDVar'
argument in creditscorecard
to indicate that 'CustID'
contains ID information and should not be included as a predictor variable.
load CreditCardData sc = creditscorecard(data,'IDVar','CustID');
Perform automatic binning to bin for all predictors.
sc = autobinning(sc);
Fit a linear regression model using default parameters.
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
Display unscaled points for predictors retained in the fitting model and display the minimum and maximum possible unscaled scores.
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ _________
{'CustAge' } {'[-Inf,33)' } -0.15894
{'CustAge' } {'[33,37)' } -0.14036
{'CustAge' } {'[37,40)' } -0.060323
{'CustAge' } {'[40,46)' } 0.046408
{'CustAge' } {'[46,48)' } 0.21445
{'CustAge' } {'[48,58)' } 0.23039
{'CustAge' } {'[58,Inf]' } 0.479
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } -0.031252
{'ResStatus' } {'Home Owner' } 0.12696
{'ResStatus' } {'Other' } 0.37641
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } -0.076317
{'EmpStatus' } {'Employed' } 0.31449
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} -0.45716
⋮
MinScore = -1.3100
MaxScore = 3.0726
By setting the name-value pair argument BasePoints
to true, the points information table reports the base points separately in the first row. The minimum and maximum possible scores are not affected by this option.
sc = formatpoints(sc,'BasePoints',true);
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=38×3 table
Predictors Bin Points
______________ ______________ _________
{'BasePoints'} {'BasePoints'} 0.70239
{'CustAge' } {'[-Inf,33)' } -0.25928
{'CustAge' } {'[33,37)' } -0.24071
{'CustAge' } {'[37,40)' } -0.16066
{'CustAge' } {'[40,46)' } -0.053933
{'CustAge' } {'[46,48)' } 0.11411
{'CustAge' } {'[48,58)' } 0.13005
{'CustAge' } {'[58,Inf]' } 0.37866
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } -0.13159
{'ResStatus' } {'Home Owner'} 0.026616
{'ResStatus' } {'Other' } 0.27607
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } -0.17666
{'EmpStatus' } {'Employed' } 0.21415
{'EmpStatus' } {'<missing>' } NaN
⋮
MinScore = -1.3100
MaxScore = 3.0726
Round Points
This example shows how to use formatpoints
to round points. Rounding is usually applied after scaling, otherwise, if the points for a particular predictor are all in a small range, rounding could cause the rounded points for different bins to be the same. Also, rounding all the points may slightly change the minimum and maximum total points.
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011). Use the 'IDVar'
argument in creditscorecard
to indicate that 'CustID'
contains ID information and should not be included as a predictor variable.
load CreditCardData sc = creditscorecard(data,'IDVar','CustID');
Perform automatic binning to bin for all predictors.
sc = autobinning(sc);
Fit a linear regression model using default parameters.
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
Display unscaled points for predictors retained in the fitting model and display the minimum and maximum possible unscaled scores.
[PointsInfo,MinScore,MaxScore] = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ _________
{'CustAge' } {'[-Inf,33)' } -0.15894
{'CustAge' } {'[33,37)' } -0.14036
{'CustAge' } {'[37,40)' } -0.060323
{'CustAge' } {'[40,46)' } 0.046408
{'CustAge' } {'[46,48)' } 0.21445
{'CustAge' } {'[48,58)' } 0.23039
{'CustAge' } {'[58,Inf]' } 0.479
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } -0.031252
{'ResStatus' } {'Home Owner' } 0.12696
{'ResStatus' } {'Other' } 0.37641
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } -0.076317
{'EmpStatus' } {'Employed' } 0.31449
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} -0.45716
⋮
MinScore = -1.3100
MaxScore = 3.0726
Scale points, and display the points information. By default, no rounding is applied.
sc = formatpoints(sc,'WorstAndBestScores',[300 850]);
PointsInfo = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ ______
{'CustAge' } {'[-Inf,33)' } 46.396
{'CustAge' } {'[33,37)' } 48.727
{'CustAge' } {'[37,40)' } 58.772
{'CustAge' } {'[40,46)' } 72.167
{'CustAge' } {'[46,48)' } 93.256
{'CustAge' } {'[48,58)' } 95.256
{'CustAge' } {'[58,Inf]' } 126.46
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } 62.421
{'ResStatus' } {'Home Owner' } 82.276
{'ResStatus' } {'Other' } 113.58
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } 56.765
{'EmpStatus' } {'Employed' } 105.81
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} 8.9706
⋮
Use the name-value pair argument Round
to apply rounding for all points and then display the points information again.
sc = formatpoints(sc,'Round','AllPoints'); PointsInfo = displaypoints(sc)
PointsInfo=37×3 table
Predictors Bin Points
______________ ________________ ______
{'CustAge' } {'[-Inf,33)' } 46
{'CustAge' } {'[33,37)' } 49
{'CustAge' } {'[37,40)' } 59
{'CustAge' } {'[40,46)' } 72
{'CustAge' } {'[46,48)' } 93
{'CustAge' } {'[48,58)' } 95
{'CustAge' } {'[58,Inf]' } 126
{'CustAge' } {'<missing>' } NaN
{'ResStatus' } {'Tenant' } 62
{'ResStatus' } {'Home Owner' } 82
{'ResStatus' } {'Other' } 114
{'ResStatus' } {'<missing>' } NaN
{'EmpStatus' } {'Unknown' } 57
{'EmpStatus' } {'Employed' } 106
{'EmpStatus' } {'<missing>' } NaN
{'CustIncome'} {'[-Inf,29000)'} 9
⋮
Rounding and Default Probabilities
This example shows that rounding scorecard points can modify the original risk ranking of a credit scorecard. You can control rounding by using formatpoints
with the optional name-value pair argument for 'Rounding'
.
Credit scores rank customers by risk. If higher scores are given to better, less risky customers, then higher scores must correspond to lower default probabilities. When you use the name-value pair argument for 'Rounding'
, depending on the value for 'Rounding'
, the rounding behavior is:
When
'Rounding'
is set to'None'
(default option), no rounding is applied to points or scores, and the risk ranking is completely consistent with the calibrated model.When
'Rounding'
is set to'FinalScore'
, rounding is only applied to the final scores. In this case: a) Customers with different scores (different risk) may have the same rounded score. b) Customers with the same rounded score may have different default probabilities. c) Customer with higher rounded scores will always have lower default probability than customers with lower scores.When
'Rounding'
is set to'AllPoints'
, rounding is applied to all points in the scorecard (all bins, all predictors). In this case: a) Customers with different scores (different risk) may have the same rounded score, or their ranking may even be reversed (the customer with the lower original score may have a higher rounded score). b) Customers with the same rounded score may have different default probabilities. c) Customer with higher rounded scores may in some cases have higher default probabilities than customers with lower scores.
Create a creditscorecard
To demonstrate the rounding behavior, first create a creditscorecard
object.
load CreditCardData sc = creditscorecard(data,'IDVar','CustID','ResponseVar','status'); sc = autobinning(sc); sc = modifybins(sc,'CustIncome','CutPoints',20000:5000:60000); sc = fitmodel(sc);
1. Adding CustIncome, Deviance = 1487.9719, Chi2Stat = 35.469392, PValue = 2.5909009e-09 2. Adding TmWBank, Deviance = 1465.7998, Chi2Stat = 22.172089, PValue = 2.4927133e-06 3. Adding AMBalance, Deviance = 1455.206, Chi2Stat = 10.593833, PValue = 0.0011346548 4. Adding EmpStatus, Deviance = 1446.3918, Chi2Stat = 8.8142314, PValue = 0.0029889009 5. Adding CustAge, Deviance = 1440.6825, Chi2Stat = 5.709236, PValue = 0.016875883 6. Adding ResStatus, Deviance = 1436.1363, Chi2Stat = 4.5462043, PValue = 0.032991806 7. Adding OtherCC, Deviance = 1431.9546, Chi2Stat = 4.1817827, PValue = 0.040860699 Generalized linear regression model: logit(status) ~ 1 + CustAge + ResStatus + EmpStatus + CustIncome + TmWBank + OtherCC + AMBalance Distribution = Binomial Estimated Coefficients: Estimate SE tStat pValue ________ ________ ______ __________ (Intercept) 0.70247 0.064046 10.968 5.4345e-28 CustAge 0.60579 0.24405 2.4822 0.013058 ResStatus 1.4463 0.65427 2.2105 0.02707 EmpStatus 0.90501 0.29262 3.0928 0.0019828 CustIncome 0.70869 0.20535 3.4512 0.00055815 TmWBank 1.0839 0.23244 4.6631 3.1145e-06 OtherCC 1.0906 0.52936 2.0602 0.039377 AMBalance 1.0148 0.32273 3.1445 0.0016636 1200 observations, 1192 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 91.5, p-value = 6.12e-17
Apply the 'Rounding'
Options
Apply each of the three 'Rounding'
options to the creditscorecard
object.
sc = formatpoints(sc,'PointsOddsAndPDO',[500 2 50]); % No Rounding points1 = displaypoints(sc); [S1,P1] = score(sc); defProb1 = probdefault(sc); sc = formatpoints(sc,'Round','AllPoints'); % 'AllPoints' Rounding points2 = displaypoints(sc); [S2,P2] = score(sc); defProb2 = probdefault(sc); sc = formatpoints(sc,'Round','FinalScore'); % 'FinalScore' Rounding points3 = displaypoints(sc); [S3,P3] = score(sc); defProb3 = probdefault(sc);
Compare the 'Rounding'
Options
Visualize the default probabilities versus the scores.
figure hold on scatter(S1, defProb1, 'g*') scatter(S2, defProb2, 'ro') scatter(S3, defProb3, 'b+') legend('No Rounding','AllPoints','FinalScore') axis([388 394 0.695 0.705]) xlabel('Credit score') ylabel('Default probability') title('Default probabilities and Credit scores') grid
Inspect the points and total scores for each 'Rounding'
option, in table format.
ind = [208 363 694 886]; ProbDefault = defProb1(ind)
ProbDefault = 4×1
0.6997
0.6989
0.6982
0.6972
% ScoreNoRounding = S1(ind)
PointsNoRounding = P1(ind,:);
PointsNoRounding.Total = S1(ind)
PointsNoRounding=4×8 table
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance Total
_______ _________ _________ __________ _______ _______ _________ ______
52.9 61.555 58.503 24.647 51.551 50.416 89.4 388.97
67.65 61.555 58.503 24.647 51.551 75.723 49.64 389.27
54.234 61.555 58.503 24.647 51.551 75.723 63.271 389.48
52.9 92.441 58.503 24.647 61.277 50.416 49.64 389.82
% ScoreAllPoints = S2(ind)
PointsAllPoints = P2(ind,:);
PointsAllPoints.Total = S2(ind)
PointsAllPoints=4×8 table
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance Total
_______ _________ _________ __________ _______ _______ _________ _____
53 62 59 25 52 50 89 390
68 62 59 25 52 76 50 392
54 62 59 25 52 76 63 391
53 92 59 25 61 50 50 390
% ScoreFinalScore = S3(ind)
PointsFinalScore = P3(ind,:);
PointsFinalScore.Total = S3(ind)
PointsFinalScore=4×8 table
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance Total
_______ _________ _________ __________ _______ _______ _________ _____
52.9 61.555 58.503 24.647 51.551 50.416 89.4 389
67.65 61.555 58.503 24.647 51.551 75.723 49.64 389
54.234 61.555 58.503 24.647 51.551 75.723 63.271 389
52.9 92.441 58.503 24.647 61.277 50.416 49.64 390
The original creditscorecard
model, without rounding, was calibrated to the data with a logistic regression. The ranking and probabilities have a statistical foundation.
Rounding, however, effectively modifies the creditscorecard
model. When only the final score is rounded, this leads to some "ties" in rounded scores, but at least the risk ranking across scores is preserved (because if s1 <= s2, then round(s1) <= round(s2)).
However, when you round all points, a score may gain extra points by chance. For example, in the second row in the table (row 363 of original data), the points for all predictors are rounded up by almost 0.5
. The original score is 389.27
. Rounding the final score makes it 389
. However, rounding all points makes it 392
, that is three points higher than rounding the final score.
Scores for Missing or Out-of-Range Data
This example shows how to use formatpoints
to score missing or out-of-range data. When data is scored, some observations can be either missing (NaN
, or undefined
) or out of range. You will need to decide whether or not points are assigned to these cases. Use the name-value pair argument Missing
to do so.
Create a creditscorecard
object using the CreditCardData.mat
file to load the data (using a dataset from Refaat 2011). Use the 'IDVar'
argument in creditscorecard
to indicate that 'CustID'
contains ID information and should not be included as a predictor variable.
load CreditCardData sc = creditscorecard(data,'IDVar','CustID');
Perform automatic binning to bin for all predictors.
sc = autobinning(sc);
Indicate that the minimum allowed value for 'CustAge'
is zero. This makes any negative values for age invalid or out-of-range.
sc = modifybins(sc,'CustAge','MinValue',0);
Fit a linear regression model using default parameters.
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
Suppose there are missing or out of range observations in the data that you want to score. Notice that by default, the points and score assigned to the missing value is NaN
.
% Set up a data set with missing and out of range data for illustration purposes newdata = data(1:5,:); newdata.CustAge(1) = NaN; % missing newdata.CustAge(2) = -100; % invalid newdata.ResStatus(3) = missing; % missing newdata.ResStatus(4) = 'House'; % invalid disp(newdata)
CustID CustAge TmAtAddress ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance UtilRate status ______ _______ ___________ ___________ _________ __________ _______ _______ _________ ________ ______ 1 NaN 62 Tenant Unknown 50000 55 Yes 1055.9 0.22 0 2 -100 22 Home Owner Employed 52000 25 Yes 1161.6 0.24 0 3 47 30 <undefined> Employed 37000 61 No 877.23 0.29 0 4 50 75 House Employed 53000 20 Yes 157.37 0.08 0 5 68 56 Home Owner Employed 53000 14 Yes 561.84 0.11 0
[Scores,Points] = score(sc,newdata); disp(Scores)
NaN NaN NaN NaN 1.4535
disp(Points)
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance _______ _________ _________ __________ _________ ________ _________ NaN -0.031252 -0.076317 0.43693 0.39607 0.15842 -0.017472 NaN 0.12696 0.31449 0.43693 -0.033752 0.15842 -0.017472 0.21445 NaN 0.31449 0.081611 0.39607 -0.19168 -0.017472 0.23039 NaN 0.31449 0.43693 -0.044811 0.15842 0.35551 0.479 0.12696 0.31449 0.43693 -0.044811 0.15842 -0.017472
Use the name-value pair argument Missing
to replace NaN
with points corresponding to a zero Weight-of-Evidence (WOE).
sc = formatpoints(sc,'Missing','ZeroWOE'); [Scores,Points] = score(sc,newdata); disp(Scores)
0.9667 1.0859 0.8978 1.5513 1.4535
disp(Points)
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance _______ _________ _________ __________ _________ ________ _________ 0.10034 -0.031252 -0.076317 0.43693 0.39607 0.15842 -0.017472 0.10034 0.12696 0.31449 0.43693 -0.033752 0.15842 -0.017472 0.21445 0.10034 0.31449 0.081611 0.39607 -0.19168 -0.017472 0.23039 0.10034 0.31449 0.43693 -0.044811 0.15842 0.35551 0.479 0.12696 0.31449 0.43693 -0.044811 0.15842 -0.017472
Alternatively, use the name-value pair argument Missing
to replace the missing value with the minimum points for the predictors that have the missing values.
sc = formatpoints(sc,'Missing','MinPoints'); [Scores,Points] = score(sc,newdata); disp(Scores)
0.7074 0.8266 0.7662 1.4197 1.4535
disp(Points)
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance ________ _________ _________ __________ _________ ________ _________ -0.15894 -0.031252 -0.076317 0.43693 0.39607 0.15842 -0.017472 -0.15894 0.12696 0.31449 0.43693 -0.033752 0.15842 -0.017472 0.21445 -0.031252 0.31449 0.081611 0.39607 -0.19168 -0.017472 0.23039 -0.031252 0.31449 0.43693 -0.044811 0.15842 0.35551 0.479 0.12696 0.31449 0.43693 -0.044811 0.15842 -0.017472
As a third alternative, use the name-value pair argument Missing
to replace the missing value with the maximum points for the predictors that have the missing values.
sc = formatpoints(sc,'Missing','MaxPoints'); [Scores,Points] = score(sc,newdata); disp(Scores)
1.3454 1.4646 1.1739 1.8273 1.4535
disp(Points)
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance _______ _________ _________ __________ _________ ________ _________ 0.479 -0.031252 -0.076317 0.43693 0.39607 0.15842 -0.017472 0.479 0.12696 0.31449 0.43693 -0.033752 0.15842 -0.017472 0.21445 0.37641 0.31449 0.081611 0.39607 -0.19168 -0.017472 0.23039 0.37641 0.31449 0.43693 -0.044811 0.15842 0.35551 0.479 0.12696 0.31449 0.43693 -0.044811 0.15842 -0.017472
Verify that the minimum and maximum points assigned to the missing data correspond to the minimum and maximum points for the corresponding predictors. The points for 'CustAge'
are reported in the first seven rows of the points information table. For 'ResStatus'
the points are in rows 8 through 10.
PointsInfo = displaypoints(sc); PointsInfo(1:7,:)
ans=7×3 table
Predictors Bin Points
___________ ____________ _________
{'CustAge'} {'[0,33)' } -0.15894
{'CustAge'} {'[33,37)' } -0.14036
{'CustAge'} {'[37,40)' } -0.060323
{'CustAge'} {'[40,46)' } 0.046408
{'CustAge'} {'[46,48)' } 0.21445
{'CustAge'} {'[48,58)' } 0.23039
{'CustAge'} {'[58,Inf]'} 0.479
min(PointsInfo.Points(1:7))
ans = -0.1589
max(PointsInfo.Points(1:7))
ans = 0.4790
PointsInfo(8:10,:)
ans=3×3 table
Predictors Bin Points
_____________ ______________ _________
{'CustAge' } {'<missing>' } 0.479
{'ResStatus'} {'Tenant' } -0.031252
{'ResStatus'} {'Home Owner'} 0.12696
min(PointsInfo.Points(8:10))
ans = -0.0313
max(PointsInfo.Points(8:10))
ans = 0.4790
Scores for Missing or Out-of-Range Data When Using the 'BinMissingData'
Option
This example describes the assignment of points for missing data when the 'BinMissingData'
option is set to true
.
Predictors that have missing data in the training set have an explicit bin for
<missing>
with corresponding points in the final scorecard. These points are computed from the Weight-of-Evidence (WOE) value for the<missing>
bin and the logistic model coefficients. For scoring purposes, these points are assigned to missing values and to out-of-range values.Predictors with no missing data in the training set have no
<missing>
bin, therefore no WOE can be estimated from the training data. By default, the points for missing and out-of-range values are set toNaN
, and this leads to a score ofNaN
when runningscore
. For predictors that have no explicit<missing>
bin, use the name-value argument'Missing'
informatpoints
to indicate how missing data should be treated for scoring purposes.
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. Apply automatic binning.
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: [1200x11 table]
Set a minimum value of zero for CustAge
and CustIncome
. With this, any negative age or income information becomes invalid or "out-of-range". For scoring purposes, out-of-range values are given the same points as missing values.
sc = modifybins(sc,'CustAge','MinValue',0); sc = modifybins(sc,'CustIncome','MinValue',0);
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 _____________ ____ ___ ______ ________ __________ {'[0,33)' } 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')
For the 'CustAge'
and 'ResStatus'
predictors, there is missing data (NaN
s and <undefined>
) in the training data, and the binning process estimates a WOE value of -0.15787
and 0.026469
respectively for missing data in these predictors, as shown above.
For EmpStatus
and CustIncome
there is no explicit bin for missing values because the training data has no missing values for these predictors.
bi = bininfo(sc,'EmpStatus');
disp(bi)
Bin Good Bad Odds WOE InfoValue ____________ ____ ___ ______ ________ _________ {'Unknown' } 396 239 1.6569 -0.19947 0.021715 {'Employed'} 407 158 2.5759 0.2418 0.026323 {'Totals' } 803 397 2.0227 NaN 0.048038
bi = bininfo(sc,'CustIncome');
disp(bi)
Bin Good Bad Odds WOE InfoValue _________________ ____ ___ _______ _________ __________ {'[0,29000)' } 53 58 0.91379 -0.79457 0.06364 {'[29000,33000)'} 74 49 1.5102 -0.29217 0.0091366 {'[33000,35000)'} 68 36 1.8889 -0.06843 0.00041042 {'[35000,40000)'} 193 98 1.9694 -0.026696 0.00017359 {'[40000,42000)'} 68 34 2 -0.011271 1.0819e-05 {'[42000,47000)'} 164 66 2.4848 0.20579 0.0078175 {'[47000,Inf]' } 183 56 3.2679 0.47972 0.041657 {'Totals' } 803 397 2.0227 NaN 0.12285
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.
[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
Scale the scorecard points by the "points, odds, and points to double the odds (PDO)" method using the 'PointsOddsAndPDO'
argument of formatpoints
. Suppose that you want a score of 500 points to have odds of 2 (twice as likely to be good than to be bad) and that the odds double every 50 points (so that 550 points would have odds of 4).
Display the scorecard showing the scaled points for predictors retained in the fitting model.
sc = formatpoints(sc,'PointsOddsAndPDO',[500 2 50]);
PointsInfo = displaypoints(sc)
PointsInfo=38×3 table
Predictors Bin Points
_____________ ______________ ______
{'CustAge' } {'[0,33)' } 54.062
{'CustAge' } {'[33,37)' } 56.282
{'CustAge' } {'[37,40)' } 60.012
{'CustAge' } {'[40,46)' } 69.636
{'CustAge' } {'[46,48)' } 77.912
{'CustAge' } {'[48,51)' } 78.86
{'CustAge' } {'[51,58)' } 80.83
{'CustAge' } {'[58,Inf]' } 96.76
{'CustAge' } {'<missing>' } 64.984
{'ResStatus'} {'Tenant' } 62.138
{'ResStatus'} {'Home Owner'} 73.248
{'ResStatus'} {'Other' } 90.828
{'ResStatus'} {'<missing>' } 74.125
{'EmpStatus'} {'Unknown' } 58.807
{'EmpStatus'} {'Employed' } 86.937
{'EmpStatus'} {'<missing>' } NaN
⋮
Notice that points for the <missing>
bin for CustAge
and ResStatus
are explicitly shown (as 64.9836
and 74.1250
, respectively). These points are computed from the WOE value for the <missing>
bin, and the logistic model coefficients.
For predictors that have no missing data in the training set, there is no explicit <missing>
bin. By default the points are set to NaN
for missing data and they lead to a score of NaN
when running score
. For predictors that have no explicit <missing>
bin, use the name-value argument 'Missing'
in formatpoints
to indicate how missing data should be treated for scoring purposes.
For the purpose of illustration, take a few rows from the original data as test data and introduce some missing data. Also introduce some invalid, or out-of-range values. For numeric data, values below the minimum (or above the maximum) allowed are considered invalid, such as a negative value for age (recall 'MinValue'
was earlier set to 0
for CustAge
and CustIncome
). For categorical data, invalid values are categories not explicitly included in the scorecard, for example, a residential status not previously mapped to scorecard categories, such as "House", or a meaningless string such as "abc123".
tdata = dataMissing(11:18,mdl.PredictorNames); % Keep only the predictors retained in the model % Set some missing values tdata.CustAge(1) = NaN; tdata.ResStatus(2) = missing; tdata.EmpStatus(3) = missing; tdata.CustIncome(4) = NaN; % Set some invalid values tdata.CustAge(5) = -100; tdata.ResStatus(6) = 'House'; tdata.EmpStatus(7) = 'Freelancer'; tdata.CustIncome(8) = -1; disp(tdata)
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance _______ ___________ ___________ __________ _______ _______ _________ NaN Tenant Unknown 34000 44 Yes 119.8 48 <undefined> Unknown 44000 14 Yes 403.62 65 Home Owner <undefined> 48000 6 No 111.88 44 Other Unknown NaN 35 No 436.41 -100 Other Employed 46000 16 Yes 162.21 33 House Employed 36000 36 Yes 845.02 39 Tenant Freelancer 34000 40 Yes 756.26 24 Home Owner Employed -1 19 Yes 449.61
Score the new data and see how points are assigned for missing CustAge
and ResStatus
, because we have an explicit bin with points for <missing>
. However, for EmpStatus
and CustIncome
the score
function sets the points to NaN
.
[Scores,Points] = score(sc,tdata); disp(Scores)
481.2231 520.8353 NaN NaN 551.7922 487.9588 NaN NaN
disp(Points)
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance _______ _________ _________ __________ _______ _______ _________ 64.984 62.138 58.807 67.893 61.858 75.622 89.922 78.86 74.125 58.807 82.439 61.061 75.622 89.922 96.76 73.248 NaN 96.969 51.132 50.914 89.922 69.636 90.828 58.807 NaN 61.858 50.914 89.922 64.984 90.828 86.937 82.439 61.061 75.622 89.922 56.282 74.125 86.937 70.107 61.858 75.622 63.028 60.012 62.138 NaN 67.893 61.858 75.622 63.028 54.062 73.248 86.937 NaN 61.061 75.622 89.922
Use the name-value argument 'Missing'
in formatpoints
to choose how to assign points to missing values for predictors that do not have an explicit <missing>
bin. In this example, use the 'MinPoints'
option for the 'Missing'
argument. The minimum points for EmpStatus
in the scorecard displayed above are 58.8072
, and for CustIncome
the minimum points are 29.3753
.
sc = formatpoints(sc,'Missing','MinPoints'); [Scores,Points] = score(sc,tdata); disp(Scores)
481.2231 520.8353 517.7532 451.3405 551.7922 487.9588 449.3577 470.2267
disp(Points)
CustAge ResStatus EmpStatus CustIncome TmWBank OtherCC AMBalance _______ _________ _________ __________ _______ _______ _________ 64.984 62.138 58.807 67.893 61.858 75.622 89.922 78.86 74.125 58.807 82.439 61.061 75.622 89.922 96.76 73.248 58.807 96.969 51.132 50.914 89.922 69.636 90.828 58.807 29.375 61.858 50.914 89.922 64.984 90.828 86.937 82.439 61.061 75.622 89.922 56.282 74.125 86.937 70.107 61.858 75.622 63.028 60.012 62.138 58.807 67.893 61.858 75.622 63.028 54.062 73.248 86.937 29.375 61.061 75.622 89.922
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 =
formatpoints(sc,'BasePoints',true,'Round','AllPoints','WorstAndBestScores',[100,
700])
Note
ShiftAndSlope
, PointsOddsAndPDO
,
and WorstAndBestScores
are scaling methods and you can
use only one of these name-value pair arguments at one time. The other three
name-value pair arguments (BasePoints
,
Missing
, and Round
) are not
scaling methods and can be used together or with any one of the three
scaling methods.
BasePoints
— Indicator for separating base points
false
(default) | logical scalar
Indicator for separating base points, specified as the
comma-separated pair consisting of 'BasePoints'
and a
logical scalar. If true
, the scorecard explicitly
separates base points. If false
, the base points are
spread across all variables in the creditscorecard
object.
Data Types: char
Missing
— Indicator for points assigned to missing or out-of-range information when scoring
NoScore
(default) | character vector with values NoScore
,
ZeroWOE
, MinPoints
, and
MaxPoints
Indicator for points assigned to missing or out-of-range
information when scoring, specified as the comma-separated pair
consisting of 'Missing'
and a character vector with a
value for NoScore
, ZeroWOE
,
MinPoints
, or MaxPoints
,
where:
NoScore
— Missing and out-of-range data do not get points assigned and points are set toNaN
. Also, the total score is set toNaN
.ZeroWOE
— Missing or out-of-range data get assigned a zero Weight-of-Evidence (WOE) value.MinPoints
— Missing or out-of-range data get the minimum possible points for that predictor. This penalizes the score if higher scores are better.MaxPoints
— Missing or out-of-range data get the maximum possible points for that predictor. This penalizes the score if lower scores are better.Note
When using the
creditscorecard
name-value argument'BinMissingData'
with a value oftrue
, missing data for numeric and categorical predictors is binned in a separate bin labeled<missing>
. The<missing>
bin only contains missing values for a predictor and does not contain invalid or out-of-range values for a predictor.
Data Types: char
Round
— Indicator whether to round points or scores
'None'
(default) | character vector with values'AllPoints'
,
'FinalScore'
Indicator whether to round points or scores, specified as the
comma-separated pair consisting of 'Round'
and a
character vector with values 'AllPoints'
,
'FinalScore'
or 'None'
, where:
None
— No rounding is applied.AllPoints
— Apply rounding to each predictor's points before adding up the total score.FinalScore
— Round the final score only (rounding is applied after all points are added up).
For more information and an example of using the
'Round'
name-value pair argument, see Rounding and Default Probabilities.
Data Types: char
ShiftAndSlope
— Indicator for shift and slope scaling parameters
[0,1]
(default) | numeric array with two elements
[Shift,Slope]
Indicator for shift and slope scaling parameters for the credit
scorecard, specified as the comma-separated pair consisting of
'ShiftAndSlope'
and a numeric array with two
elements [Shift, Slope]
. Slope
cannot be zero. The ShiftAndSlope
values are used
scale the scoring model.
Note
ShiftAndSlope
,
PointsOddsAndPDO
, and
WorstAndBestScores
are scaling methods
and you can use only one of these name-value pair arguments at
one time. The other three name-value pair arguments
(BasePoints
,
Missing
, and
Round
) are not scaling methods and can be
used together or with any one of the three scaling
methods.
To remove a previous scaling and revert to unscaled scores,
set ShiftAndSlope
to[0,1]
.
Data Types: double
PointsOddsAndPDO
— Indicator for target points for given odds and double odds level
numeric array with three elements
[Points,Odds,PDO]
Indicator for target points (Points
) for a
given odds level (Odds
) and the desired number of
points to double the odds (PDO
), specified as the
comma-separated pair consisting of 'PointsOddsAndPDO'
and a numeric array with three elements
[Points,Odds,PDO]
. Odds
must
be a positive number. The PointsOddsAndPDO
values
are used to find scaling parameters for the scoring model.
Note
The points to double the odds (PDO
) may be
positive or negative, depending on whether higher scores mean
lower risk, or vice versa.
ShiftAndSlope
,
PointsOddsAndPDO
, and
WorstAndBestScores
are scaling methods
and you can use only one of these name-value pair arguments at
one time. The other three name-value pair arguments
(BasePoints
,
Missing
, and
Round
) are not scaling methods and can be
used together or with any one of the three scaling
methods.
To remove a previous scaling and revert to unscaled scores,
set ShiftAndSlope
to[0,1]
.
Data Types: double
WorstAndBestScores
— Indicator for worst (highest risk) and best (lowest risk) scores in scorecard
numeric array with two elements
[WorstScore,BestScore]
Indicator for worst (highest risk) and best (lowest risk) scores
in the scorecard, specified as the comma-separated pair consisting of
'WorstAndBestScores'
and a numeric array with two
elements [WorstScore,BestScore]
.
WorstScore
and BestScore
must
be different values. These WorstAndBestScores
values are used to find scaling parameters for the scoring model.
Note
WorstScore
means the riskiest score, and
its value could be lower or higher than the ‘best’ score. In
other words, the ‘minimum’ score may be the ‘worst‘ score or the
'best' score, depending on the desired scoring scale.
ShiftAndSlope
,
PointsOddsAndPDO
, and
WorstAndBestScores
are scaling methods
and you can use only one of these name-value pair arguments at
one time. The other three name-value pair arguments
(BasePoints
,
Missing
, and
Round
) are not scaling methods and can be
used together or with any one of the three scaling
methods.
To remove a previous scaling and revert to unscaled scores,
set ShiftAndSlope
to[0,1]
.
Data Types: double
Output Arguments
sc
— Credit scorecard model
creditscorecard
object
Credit scorecard model returned as an updated
creditscorecard
object. For more information on
using the creditscorecard
object, see creditscorecard
.
Algorithms
The score of an individual i is given by the formula
Score(i) = Shift + Slope*(b0 + b1*WOE1(i) + b2*WOE2(i)+ ... +bp*WOEp(i))
where bj is the coefficient of the jth
variable in the model, and WOEj(i) is the Weight
of Evidence (WOE) value for the ith individual corresponding to the
jth model variable. Shift
and
Slope
are scaling constants further discussed below. The scaling
constant can be controlled with formatpoints
.
If the data for individual i is in the i-th
row of a given dataset, to compute a score, the
data(i,j) is binned using existing binning
maps, and converted into a corresponding Weight of Evidence value
WOE
j(i). Using the
model coefficients, the unscaled score is computed
as
s = b0 + b1*WOE1(i) + ... +bp*WOEp(i).
For simplicity, assume in the description above that the j-th variable in the model is the j-th column in the data input, although, in general, the order of variables in a given dataset does not have to match the order of variables in the model, and the dataset could have additional variables that are not used in the model.
The formatting options can be controlled using formatpoints
.
When the base points are reported separately (see the formatpoints
parameter BasePoints
), the base points are given
by
Base Points = Shift + Slope*b0,
Points_ji = Slope*(bj*WOEj(i))).
By default, the base points are not reported separately, in which case
Points_ji = (Shift + Slope*b0)/p + Slope*(bj*WOEj(i)),
By default, no rounding is applied to the points by the score
function (Round
is None
). If
Round
is set to AllPoints
using
formatpoints
, then the points for individual i
for variable j are given
by
points if rounding is 'AllPoints': round( Points_ji )
Round
is
set to FinalScore
using formatpoints
, then the
points per predictor are not rounded, and only the final score is
roundedscore if rounding is 'FinalScore': round(Score(i)).
Regarding the scaling parameters, the Shift
parameter, and the
Slope
parameter can be set directly with the
ShiftAndSlope
parameter of formatpoints
.
Alternatively, you can use the formatpoints
parameter for
WorstAndBestScores
. In this case, the parameters
Shift
and Slope
are found internally by
solving the
system
Shift + Slope*smin = WorstScore, Shift + Slope*smax = BestScore,
WorstScore
and BestScore
are the first and
second elements in the formatpoints
parameter for
WorstAndBestScores
and smin and
smax are the minimum and maximum possible unscaled
scores:smin = b0 + min(b1*WOE1) + ... +min(bp*WOEp), smax = b0 + max(b1*WOE1) + ... +max(bp*WOEp).
A third alternative to scale scores is the PointsOddsAndPDO
parameter in formatpoints
. In this case, assume that the unscaled
score s gives the log-odds for a row, and the
Shift
and Slope
parameters are found by
solving the following
system
Points = Shift + Slope*log(Odds) Points + PDO = Shift + Slope*log(2*Odds)
Points
, Odds
, and PDO
("points to double the odds") are the first, second, and third elements in the
PointsOddsAndPDO
parameter.Whenever a given dataset has a missing or out-of-range value data
(i,j), the points for predictor
j, for individual i, are set to
NaN
by default, which results in a missing score for that row (a
NaN
score). Using the Missing
parameter for
formatpoints
, you can modify this behavior and set the
corresponding Weight-of-Evidence (WOE) value to zero, or set the points to the minimum
points, or the maximum points for that predictor.
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
creditscorecard
| autobinning
| bininfo
| predictorinfo
| modifypredictor
| plotbins
| modifybins
| bindata
| fitmodel
| displaypoints
| score
| setmodel
| probdefault
| validatemodel
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