bininfo
Return predictor’s bin information
Syntax
Description
returns information at bin level, such as frequencies of
“Good,” “Bad,” and bin statistics for the
predictor specified in bi
= bininfo(sc
,PredictorName
)PredictorName
.
adds optional name-value arguments.bi
= bininfo(___,Name,Value
)
[
adds optional name-value arguments.bi
,bm
]
= bininfo(sc
,PredictorName
,Name,Value
)bininfo
also optionally
returns the binning map (bm
) or bin rules in the form of a
vector of cut points for numeric predictors, or a table of category groupings
for categorical predictors.
[
returns information at bin level, such as frequencies of “Good,”
“Bad," and bin statistics for the predictor specified in
bi
,bm
,mv
]
= bininfo(sc
,PredictorName
,Name,Value
)PredictorName
using optional name-value pair arguments.
bininfo
optionally returns the binning map or bin rules
in the form of a vector of cut points for numeric predictors, or a table of
category groupings for categorical predictors. In addition, optional name-value
pair arguments mv
returns a numeric array containing the
minimum and maximum values, as set (or defined) by the user. The
mv
output argument is set to an empty array for
categorical predictors.
Examples
Display Bin Information Using Default Options
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011).
load CreditCardData
sc = creditscorecard(data);
Display bin information for the categorical predictor ResStatus
.
bi = bininfo(sc,'ResStatus')
bi=4×6 table
Bin Good Bad Odds WOE InfoValue
______________ ____ ___ ______ _________ _________
{'Home Owner'} 365 177 2.0621 0.019329 0.0001682
{'Tenant' } 307 167 1.8383 -0.095564 0.0036638
{'Other' } 131 53 2.4717 0.20049 0.0059418
{'Totals' } 803 397 2.0227 NaN 0.0097738
Display Bin Information 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,'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: {'CustID' 'CustAge' 'TmAtAddress' 'CustIncome' 'TmWBank' 'AMBalance' 'UtilRate'} CategoricalPredictors: {'ResStatus' 'EmpStatus' 'OtherCC'} BinMissingData: 0 IDVar: '' PredictorVars: {'CustID' 'CustAge' 'TmAtAddress' 'ResStatus' 'EmpStatus' 'CustIncome' 'TmWBank' 'OtherCC' 'AMBalance' 'UtilRate'} Data: [1200x12 table]
Display bin information for the numerical predictor 'CustIncome'
. When the optional name-value pair argument 'WeightsVar'
is used to specify observation (sample) weights, the bi
table contains weighted counts.
bi = bininfo(sc,'CustIncome');
bi(1:10,:)
ans=10×6 table
Bin Good Bad Odds WOE InfoValue
_________ _______ _______ _______ ________ __________
{'18000'} 0.94515 1.496 0.63179 -1.1667 0.0059198
{'19000'} 0.47588 0.80569 0.59065 -1.2341 0.0034716
{'20000'} 2.1671 1.4636 1.4806 -0.31509 0.00061392
{'21000'} 3.2522 0.88064 3.693 0.59889 0.0021303
{'22000'} 1.5438 1.2714 1.2142 -0.51346 0.0012913
{'23000'} 1.787 2.7529 0.64913 -1.1397 0.010509
{'24000'} 3.4111 2.2538 1.5135 -0.29311 0.00082663
{'25000'} 2.2333 6.1383 0.36383 -1.7186 0.042642
{'26000'} 2.1246 4.4754 0.47474 -1.4525 0.024526
{'27000'} 3.1058 3.528 0.88032 -0.83501 0.0082144
Display Bin Information Using Name-Value Arguments
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011).
load CreditCardData
sc = creditscorecard(data);
Display customized bin information for the categorical predictor ResStatus
, keeping only the WOE
column. The Weight-of-Evidence (WOE) is defined bin by bin, but there is no concept of "total WOE", therefore the last element in the 'Totals'
row is set to NaN
.
bi = bininfo(sc,'ResStatus','Statistics','WOE'); disp(bi)
Bin Good Bad WOE ______________ ____ ___ _________ {'Home Owner'} 365 177 0.019329 {'Tenant' } 307 167 -0.095564 {'Other' } 131 53 0.20049 {'Totals' } 803 397 NaN
Display customized bin information for the categorical predictor ResStatus
, keeping only the Odds
and WOE
columns, without the Totals
row.
bi = bininfo(sc,'ResStatus','Statistics',{'Odds','WOE'},'Totals','Off'); disp(bi)
Bin Good Bad Odds WOE ______________ ____ ___ ______ _________ {'Home Owner'} 365 177 2.0621 0.019329 {'Tenant' } 307 167 1.8383 -0.095564 {'Other' } 131 53 2.4717 0.20049
Display information value, entropy, Gini, and chi square statistics. For more information on these statistics, see Statistics for a Credit Scorecard.
For information value, entropy and Gini, the value reported at a bin level is the contribution of the bin to the total value. The total information value, entropy, and Gini measures are in the 'Totals'
row.
For chi square, if there are N bins, the first N-1 values in the 'Chi2'
column report pairwise chi square statistics for contiguous bins. For example, this pairwise measure is also used by the 'Merge'
algorithm in autobinning
to determine if two contiguous bins should be merged. In this example, the first value in the 'Chi2'
column (1.0331
) is the chi square statistic of bins 1 and 2 ('Home Owner'
and 'Tenant'
), and the second value in the column (2.5103
) is the chi square statistic of bins 2 and 3 ('Tenant'
and 'Other'
). There are no more pairwise chi square values to compute in this example, so the third element of the 'Chi2'
column is set to NaN
. The chi square value reported in the 'Totals'
row is the chi square statistic computed over all bins.
bi = bininfo(sc,'ResStatus','Statistics',{'InfoValue','Entropy','Gini','Chi2'}); disp(bi)
Bin Good Bad InfoValue Entropy Gini Chi2 ______________ ____ ___ _________ _______ _______ ______ {'Home Owner'} 365 177 0.0001682 0.91138 0.43984 1.0331 {'Tenant' } 307 167 0.0036638 0.93612 0.45638 2.5103 {'Other' } 131 53 0.0059418 0.86618 0.41015 NaN {'Totals' } 803 397 0.0097738 0.91422 0.44182 2.5549
Display Bin Information and Binning Map for Categorical Data
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011).
load CreditCardData
sc = creditscorecard(data);
The binning map or rules for categorical data are summarized in a "category grouping" table, returned as an optional output. By default, each category is placed in a separate bin. Here is the information for the predictor ResStatus
.
[bi,cg] = bininfo(sc,'ResStatus')
bi=4×6 table
Bin Good Bad Odds WOE InfoValue
______________ ____ ___ ______ _________ _________
{'Home Owner'} 365 177 2.0621 0.019329 0.0001682
{'Tenant' } 307 167 1.8383 -0.095564 0.0036638
{'Other' } 131 53 2.4717 0.20049 0.0059418
{'Totals' } 803 397 2.0227 NaN 0.0097738
cg=3×2 table
Category BinNumber
______________ _________
{'Home Owner'} 1
{'Tenant' } 2
{'Other' } 3
To group categories Tenant
and Other
, modify the category grouping table cg
so that the bin number for Other
is the same as the bin number for Tenant
. Then use the modifybins
function to update the scorecard.
cg.BinNumber(3) = 2; sc = modifybins(sc,'ResStatus','CatGrouping',cg);
Display the updated bin information. The bin labels have been updated and that the bin membership information is contained in the category grouping cg
.
[bi,cg] = bininfo(sc,'ResStatus')
bi=3×6 table
Bin Good Bad Odds WOE InfoValue
__________ ____ ___ ______ _________ __________
{'Group1'} 365 177 2.0621 0.019329 0.0001682
{'Group2'} 438 220 1.9909 -0.015827 0.00013772
{'Totals'} 803 397 2.0227 NaN 0.00030592
cg=3×2 table
Category BinNumber
______________ _________
{'Home Owner'} 1
{'Tenant' } 2
{'Other' } 2
Display Bin Information and Binning Map for Numeric Data
Create a creditscorecard
object using the CreditCardData.mat
file to load the data
(using a dataset from Refaat 2011).
load CreditCardData
sc = creditscorecard(data);
The predictor CustIncome
is numeric. By default, each value of the predictor is placed in a separate bin.
bi = bininfo(sc,'CustIncome')
bi=46×6 table
Bin Good Bad Odds WOE InfoValue
_________ ____ ___ _______ _________ __________
{'18000'} 2 3 0.66667 -1.1099 0.0056227
{'19000'} 1 2 0.5 -1.3976 0.0053002
{'20000'} 4 2 2 -0.011271 6.3641e-07
{'21000'} 6 3 2 -0.011271 9.5462e-07
{'22000'} 4 2 2 -0.011271 6.3641e-07
{'23000'} 4 4 1 -0.70442 0.0035885
{'24000'} 5 5 1 -0.70442 0.0044856
{'25000'} 4 9 0.44444 -1.5153 0.026805
{'26000'} 4 11 0.36364 -1.716 0.038999
{'27000'} 6 6 1 -0.70442 0.0053827
{'28000'} 13 11 1.1818 -0.53736 0.0061896
{'29000'} 11 10 1.1 -0.60911 0.0069988
{'30000'} 18 16 1.125 -0.58664 0.010493
{'31000'} 24 8 3 0.39419 0.0038382
{'32000'} 21 15 1.4 -0.36795 0.0042797
{'33000'} 35 19 1.8421 -0.093509 0.00039951
⋮
Reduce the number of bins using the autobinning
function (the modifybins
function can also be used).
sc = autobinning(sc,'CustIncome');
Display the updated bin information. The binning map or rules for numeric data are summarized as "cut points," returned as an optional output (cp
).
[bi,cp] = bininfo(sc,'CustIncome')
bi=8×6 table
Bin Good Bad Odds WOE InfoValue
_________________ ____ ___ _______ _________ __________
{'[-Inf,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
cp = 6×1
29000
33000
35000
40000
42000
47000
Manually remove the second cut point (the boundary between the second and third bins) to merge bins two and three. Use the modifybins
function to update the scorecard.
cp(2) = []; sc = modifybins(sc,'CustIncome','CutPoints',cp,'MinValue',0);
Display the updated bin information.
[bi,cp,mv] = bininfo(sc,'CustIncome')
bi=7×6 table
Bin Good Bad Odds WOE InfoValue
_________________ ____ ___ _______ _________ __________
{'[0,29000)' } 53 58 0.91379 -0.79457 0.06364
{'[29000,35000)'} 142 85 1.6706 -0.19124 0.0071274
{'[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 0.12043
cp = 5×1
29000
35000
40000
42000
47000
mv = 1×2
0 Inf
Note, it is recommended to avoid having bins with frequencies of zero because they lead to infinite or undefined (NaN
) statistics. Use the modifybins
or autobinning
functions to modify bins.
Display Bin Information for 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 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: [1200x11 table]
Display bin information for numeric data for 'CustAge'
that includes missing data in a separate bin labelled <missing>
.
bi = 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 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
disp(cg)
Category BinNumber ______________ _________ {'Tenant' } 1 {'Home Owner'} 2 {'Other' } 3
Note that the category grouping table does not include <missing>
because this is a reserved bin and users cannot interact directly with the <missing>
bin.
plotbins(sc,'ResStatus')
Input Arguments
sc
— Credit scorecard model
creditscorecard
object
Credit scorecard model, specified as a
creditscorecard
object. Use creditscorecard
to create
a creditscorecard
object.
PredictorName
— Predictor name
character vector
Predictor name, specified using a character vector containing the name
of the predictor. PredictorName
is
case-sensitive.
Data Types: char
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: bi = bininfo(sc,
PredictorName,'Statistics','WOE','Totals','On')
Statistics
— List of statistics to include for bin information
{'Odds','WOE','InfoValue'}
(default) | character vector with values 'Odds'
,
'WOE'
,
'InfoValue'
,'Entropy'
,
'Gini'
, 'Chi2'
| cell array of character vectors with values
'Odds'
, 'WOE'
,
'InfoValue'
,
'Entropy'
,'Gini'
,
'Chi2'
List of statistics to include in the bin information, specified as
the comma-separated pair consisting of 'Statistics'
and a character vector or a cell array of character vectors. For more
information, see Statistics for a Credit Scorecard. Possible values are:
'Odds'
— Odds information is the ratio of “Goods” over “Bads.”'WOE'
— Weight of Evidence. The WOE Statistic measures the deviation between the distribution of “Goods” and “Bads.”'InfoValue'
— Information value. Closely tied to the WOE, it is a statistic used to determine how strong a predictor is to use in the fitting model. It measures how strong the deviation is between the distributions of “Goods” and “Bads.” However, bins with only “Good” or only “Bad” observations do lead to an infinite Information Value. Consider modifying the bins in those cases by usingmodifybins
orautobinning
.'Entropy'
— Entropy is a measure of unpredictability contained in the bins. The more the number of “Goods” and “Bads” differ within the bins, the lower the entropy.'Gini'
— Measure of statistical dispersion or inequality within a sample of data.'Chi2'
— Measure of statistical difference and independence between groups.
Note
Avoid having bins with frequencies of zero because they lead
to infinite or undefined (NaN
) statistics.
Use modifybins
or
autobinning
to
modify bins.
Data Types: char
| cell
Totals
— Indicator to include row of totals at bottom information table
'On'
(default) | character vector with values 'On'
,
'Off'
Indicator to include a row of totals at the bottom of the
information table, specified as the comma-separated pair consisting of
'Totals'
and a character vector with values
On
or Off
.
Data Types: char
Output Arguments
bi
— Bin information
table
Bin information, returned as a table. The bin information table
contains one row per bin and a row of totals. The columns contain bin
descriptions, frequencies of “Good” and “Bad,”
and bin statistics. Avoid having bins with frequencies of zero because they
lead to infinite or undefined (NaN
) statistics. Use
modifybins
or autobinning
to modify bins.
Note
When creating the creditscorecard
object with
creditscorecard
, if
the optional name-value pair argument WeightsVar
was used to specify observation (sample) weights, then the
bi
table contains weighted counts.
bm
— Binning map or rules
vector of cut points for numeric predictors | table of category groupings for categorical predictors
Binning map or rules, returned as a vector of cut points for numeric
predictors, or a table of category groupings for categorical predictors.
For more information, see modifybins
.
mv
— Binning minimum and maximum values
numeric array
Binning minimum and maximum values (as set or defined by the user),
returned as a numeric array. The mv
output argument
is set to an empty array for categorical predictors.
More About
Statistics for a Credit Scorecard
Weight of Evidence (WOE) is a measure of the difference of the distribution of “Goods” and “Bads” within a bin.
Suppose the predictor's data takes on M possible values b1, ..., bM. For binned data, M is a small number. The response takes on two values, “Good” and “Bad.” The frequency table of the data is given by:
Good | Bad | Total | |
---|---|---|---|
b1: | n11 | n12 | n1 |
b2: | n21 | n22 | n2 |
bM: | nM1 | nM2 | nM |
Total: | nGood | nBad | nTotal |
The Weight of Evidence (WOE) is defined for each data value
bi
as
WOE(i) = log((ni1/nGood)/(ni2/nBad)).
If you define
pGood(i) = ni1/nGood, pBad(i) = ni2/nBad
then pGood
(i) is the proportion of
“Good” observations that take on the value bi
,
and similarly for pBad
(i). In other words,
pGood
(i) gives the distribution of
good observations over the M observed values of the
predictor, and similarly for pBad
(i). With
this, an equivalent formula for the WOE
is
WOE(i) = log(pGood(i)/pBad(i)).
Odds(i) = ni1 / ni2,
OddsTotal = nGood / nBad.
For each row i, you can also compute its contribution to the total Information Value, given by
InfoValue(i) = (pGood(i) - pBad(i)) * WOE(i),
and the total Information Value is simply the sum of all the
InfoValue
l(i) terms. (A
nansum
is returned to discard contributions from rows
with no observations at all.)
Likewise, for each row i, we can compute its contribution to the total Entropy, given by
Entropy(i) = -1/log(2)*(ni1/ni*log(ni1/ni)+ni2/ni*log(ni2/ni),
Entropy = sum(ni/nTotal * Entropy(i)), i = 1...M.
Chi2 is computed pairwise for each pair of bins and measures the statistical difference between two groups when splitting or merging bins and is defined as:
Chi2 = sum(sum((Aij - Eij)^2/Eij , j=1..k), i=m,m+1).
Gini ratio is a measure of the parent node, that is, of the given bins/categories prior to splitting or merging. The Gini ratio is defined as:
Gr = 1-G_hat/Gp
G_hat
is
the weighted Gini measure for the current split or
merge:G_hat = Sum((nj/N) * Gj, j=1..m).
Using bininfo
with Weights
When observation weights are defined using the optional
WeightsVar
argument when creating a
creditscorecard
object, instead of counting the rows that
are good or bad in each bin, the bininfo
function accumulates
the weight of the rows that are good or bad in each bin.
The “frequencies” reported are no longer the basic “count” of rows, but the
“cumulative weight” of the rows that are good or bad and fall in a particular
bin. Once these “weighted frequencies” are known, all other relevant statistics
(Good
, Bad
, Odds
,
WOE
, and InfoValue
) are computed with
the usual formulas. For more information, see Credit Scorecard Modeling Using Observation Weights.
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
| predictorinfo
| modifypredictor
| modifybins
| bindata
| plotbins
| fitmodel
| displaypoints
| formatpoints
| score
| setmodel
| probdefault
| validatemodel
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