Credit risk prediction with and without weights of evidence using quantitative learning models

Sei shi o, Modisane B.; Go ende , Seshni
A icle
C edi isk p edic ion wi h and wi hou weigh s o
e idence using quan i a i e lea ning models
Cogen Economics & Finance
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C edi isk p edic ion wi h and wi hou weigh s o
e idence using quan i a i e lea ning models
Modisane B. Sei shi o & Seshni Go ende
To ci e his a icle: Modisane B. Sei shi o & Seshni Go ende (2024) C edi isk p edic ion wi h
and wi hou weigh s o e idence using quan i a i e lea ning models, Cogen Economics &
Finance, 12:1, 2338971, DOI: 10.1080/23322039.2024.2338971
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ECONOMETRICS | RESEARCH ARTICLE
C edi isk p edic ion wi h and wi hou weigh s o e idence using
quan i a i e lea ning models
Modisane B. Sei shi o
a,b
and Seshni Go ende
c
a
Cen e o Business Ma hema ics and In o ma ics, No h-Wes Uni e si y, Po che s oom, Sou h A ica;
b
Na ional Ins i u e
o Theo e ical and Compu a ional Sciences (NITheCS), S ellenbosch, Sou h A ica;
c
Depa men o Decision Sciences,
Uni e si y o Sou h A ica, P e o ia, Sou h A ica
ABSTRACT
The c edi isk assessmen p ocess is necessa y o main aining inancial s abili y, cos
and ime e iciency, model pe o mance accu acy, compa abili y analysis and u u e busi-
ness implica ions in he comme cial banking sec o . By accu a ely p edic ing c edi isk,
highly egula ed banks can make in o med lending decisions and minimize po en ial
inancial losses. The pu pose o his pape is o assess he powe o con en ional p edic -
i e s a is ical models wi h and wi hou ans o ming he ea u es o gain be e insigh s
in o cus ome ’s c edi wo hiness. The indings o he p edic ed pe o mance o he logis-
ics eg ession model a e compa ed o he pe o mance esul s o machine lea ning mod-
els o c edi isk assessmen using comme cial banking c edi egis y da a. Each model
has i s s eng hs and weaknesses, and whe e one model lacks, ano he pe o ms be e .
The a icle e eals ha simple c edi isk assessmen echniques deli e ed ou s anding
pe o mance while consuming less p ocessing powe and ha e gi en insigh s in o he
mos con ibu ing ea u e ca ego ies. Imp o ing a con en ional p edic i e s a is ical
model using some o he ea u e ans o ma ions educes he o e all model pe o mance,
speci ically o c edi egis y da a. The logis ics eg ession model ou pe o med all mod-
els wi h he highes F1, accu acy, Jacca d Index and AUC alues, espec i ely.
IMPACT STATEMENT
Financial ins i u ions, speci ically banks ha e ques ioned whe he ans o ma ions
using Weigh s o E idence (WoE) ha e been signi ican in quan i ying he ela ionship
be ween ca ego ical independen a iables o a ious ypes o c edi da a. This s udy
p o ides insigh s when conside ing he usage o ea u e ans o ma ion o c edi isk
modelling in comme cial banking. The ans o ma ion echnique is pa icula ly use ul
in si ua ions whe e s a is ical p edic i e modelling echniques a e employed. The
esul s e ealed ha no only can he logis ic eg ession models pe o m simila ly o
he machine lea ning models bu can also ou pe o m hem. The bes pe o mance is
a ibu ed o he simplici y, in e p e abili y, and access o unde s anding ea u es o
indi idual clien s wi hin a po olio o c edi p oduc s. The logis ic eg ession model
wi hou ans o ma ion u ned ou o pe o m he bes ou o he i e machine lea n-
ing models. Conside ing he business impac , enhancing he logis ic eg ession model
by using a WoE ans o ma ion did no imp o e he model's pe o mance o comme -
cial banking da a conside ed. Howe e , he ans o ma ion did p o ide insigh s
ega ding each binned ca ego ical independen a iable. The e o e, ou indings in
his a icle con ibu e owa ds assis ing banks in managing he impac and in e p e -
abili y o each binned ea u e ca ego y on he disc imina o y powe o c edi sco ing.
ARTICLE HISTORY
Recei ed 14 Augus 2023
Re ised 26 Ma ch 2024
Accep ed 1 Ap il 2024
KEYWORDS
C edi isk; logis ic
eg ession; machine
lea ning; model isk;
pa ame e es ima ion;
p obabili y o de aul ;
weigh s o e idence;
op imisa ion
JEL
C12; C35; C52; C53; D81; G32
REVIEWING EDITOR
Xibin Zhang, Monash
Uni e si y, Aus alia
SUBJECTS
S a is ics & P obabili y;
Reliabili y & Risk Analysis;
Tes ing; Finance; C edi &
C edi Ins i u ions; Business,
Managemen and
Accoun ing
1. In oduc ion
A quan i a i e model is a sys em o a iables, gi en a se o assump ions, and is based on s a is ical and
ma hema ical heo ies. Financial ins i u ions such as banks a e o en equi ed o ese e unds o isk
a ising om inadequa e quan i a i e models (Hull & Suo, 2002). A pa icula isk ha is c i ical in he
CONTACT Modisane B. Sei shi o [email p o ec ed],[email p o ec ed] Cen e o Business Ma hema ics and
In o ma ics, No h-Wes Uni e si y, Po che s oom Campus, P i a e Bag X6001, Po che s oom, 2520, Sou h A ica.
ß2024 The Au ho (s). Published by In o ma UK Limi ed, ading as Taylo & F ancis G oup.
This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/licenses/by/4.0/), which
pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. The e ms on which his a icle has been
published allow he pos ing o he Accep ed Manusc ip in a eposi o y by he au ho (s) o wi h hei consen .
COGENT ECONOMICS & FINANCE
2024, VOL. 12, NO. 1, 2338971
h ps://doi.o g/10.1080/23322039.2024.2338971
a ea o comme cial banking is c edi isk. C edi isk is cen ed a ound he de aul e en , which is he
e en ha a deb o is unable o mee he legal obliga ion pe aining ules o he deb con ac (Zhang,
2009). To unde s and and educe he isk a ising om c edi , cus ome beha iou has o be analysed in
ad ance. The global inancial c isis ha began in 2007 has led o he e-e alua ion o pas me hods in
c edi isk managemen o minimise isk-loss and alloca e esou ces app op ia ely (Ma
ce inskien_
e e al.,
2014). Banks a e inc easingly de o ing esou ces o e ec i ely use he con inuously g owing c edi egis-
y da a o ope a e mo e e icien ly, p o ide insigh s o he u u e, boos inancial decision-making and
de elop a compe i i e ad an age o e businesses. Mo eo e , an impo an and di icul p ocess o
banks is e alua ing he model’s accu acy in p edic ing c edi isk. A quan i a i e model can ne e be
one hund ed pe cen accu a e. Howe e , e alua ing pe o mance can allow o he imp o emen o o e-
cas ing accu acy and assis he banks in managing c edi isk much be e .
Se e al s udies ha e explo ed he use o di e en models and echniques o c edi sco ing. Yap e al.
(2011) explo ed he use o weigh s o e idence (WoE) o C edi Sco eca d Models, Logis ic Reg ession
and Decision T ees in assessing c edi sco ing. Acco ding o Weed (2005), he weigh o e idence (WOE)
is an in e p e a i e echnique o isk assessmen . In c edi isk assessmen , WOE is known as a measu e
o ela i e isk, gi ing insigh s in o cha ac e is ics o ea u e binning le el. The measu e depends on
whe he he alue o he a ge a iable is a good isk o a bad isk. Yang e al. (2015) ocused on a
Logis ic Reg ession model using WoE applied o a c edi isk da ase . The s udy has shown ha Logis ic
Reg ession wi h WoE is a good model, wi h he Pe cen age Co ec ly Classi ied goodness-o - i measu e
used o e alua e pe o mance. Xia e al. (2017) p oposed a sequen ial ensemble c edi sco ing model
based on an XGBoos g adien boos ing machine, oge he wi h Bayesian hype -pa ame e op imisa ion.
The au ho ’s ou come was o show ha he p oposed me hod ou pe o ms baseline models using accu -
acy, e o a e, a ea unde he cu e H measu e (AUC-H) and B ie sco e. Chen e al. (2020) cons uc ed a
mixed c edi sco ing model wi h WoE and Logis ic Reg ession on a la ge c edi da ase o 100 000 obse -
a ions. Upon analysing he coe icien alues o each model, he au ho s e ealed ha he hyb id
model ou pe o med he adi ional model. Neh ebecka (2018) compa ed WoE applied o bo h Logis ic
Reg ession and Suppo Vec o Machines (SVM) models on c edi isk da a. The Logis ic Reg ession
model wi h WOE ans o ma ion p oduced he bes accu acy measu e among he models. Howe e , he
models wi hou ans o ma ion we e no assessed. While Wang e al. (2020) assessed i e di e en
machine lea ning models o c edi sco ing. All hese s udies e alua ed he pe o mance o hese models
using di e en me ics such as accu acy, a ea unde he cu e, and GINI s a is ics. Mos o he s udies
showed ha Logis ic Reg ession wi h WoE is a good model o c edi sco ing.
In addi ion, Pe sson (2021) showed ha using WoE wi h Logis ic Reg ession dec eased he disc imin-
a o y powe o c edi sco ing models, while he ea u e selec ion echnique In o ma ion Value (IV) did
no p o ide any bene i o e using backwa d selec ion echniques. Howe e , he esul s we e di e en
when applied o he SVM models in bo h WoE and IV whe e ce ain me ics p o ed ha hese me hods
imp o ed he pe o mance o he models. O e all, hese pape s p o ide a use ul o e iew o he di e -
en models and echniques used in c edi sco ing esea ch.
The pu pose o his s udy is o de e mine whe he machine lea ning models will ou pe o m adi ional
s a is ical lea ning models when applied o c edi isk. Many di e en echniques ha e been used o model
c edi isk a ising om adi ional s a is ical lea ning o machine lea ning and a i icial in elligence. I has
been shown ha adi ional echniques such as Logis ic Reg ession p oduce poo e accu acy measu es
han hose o a i icial in elligence and machine lea ning (Kuma e al., 2021). Adap ing adi ional echni-
ques can be use ul so ha he modelling is simple ye e icien and compa a i e o he pe o mance o
machine lea ning o a i icial in elligence me hods. The e ha e been ew ecen s udies on applying WoE o
hyb idise models, pa icula ly when i comes o he use o c edi egis y da a. WoE has been used o deca-
des bu s udies ha e shown ha i is no popula when i comes o modelling c edi isk (Pe sson, 2021).
The a icle uses quan i a i e lea ning models o c edi isk assessmen o se e al easons. Fi s , c edi
isk assessmen is c ucial o main aining inancial s abili y in he comme cial banking sec o . Second, by
in es iga ing he use o quan i a i e lea ning models, such as machine lea ning and s a is ical lea ning,
banks can s eamline he c edi assessmen p ocess and make i mo e e icien . Thi d, quan i a i e lea n-
ing models ha e he po en ial o p o ide mo e accu a e c edi assessmen s by analysing a wide ange
o ac o s embedded wi hin he binning o ea u es, such as employmen s a us, c edi his o y, and
2 M. B. SEITSHIRO AND S. GOVENDER
mo e. Fou h, he a icle compa es he pe o mance o di e en models, including Logis ic Reg ession
wi h and wi hou WoE, K-Nea es Neighbou s, Decision T ee, and Suppo Vec o Machines. By e alua ing
hese models, we aim o de e mine which app oach is mos e ec i e o p edic ing c edi isk. Las , he
indings o his s udy can ha e implica ions o u u e esea ch and p ac ice in he banking indus y.
Unde s anding he s eng hs and weaknesses o di e en quan i a i e lea ning models can help banks
imp o e hei c edi isk assessmen p ocesses and make mo e in o med decisions. O e all, his s udy is
impo an as i gi es insigh s in o he po en ial o quan i a i e lea ning models o enhance c edi isk
p edic ion in he comme cial banking sec o , ul ima ely con ibu ing o mo e e ec i e isk managemen
and decision-making.
In his pape mi iga ing agains model isk includes e alua ing and assessing model pe o mance
h ough goodness-o - i me hods, es ing he accu acy o pa ame e es ima ion and model selec ion c i-
e ia. This pape is aimed a cons uc ing a compa a i e analysis o di e en s a is ical and machine
lea ning me hods o classi ica ion on a c edi da ase om a comme cial bank wi h and wi hou using
he WoE analysis. The mo i a ion is o ob ain a clea e unde s anding on he limi a ions o he di e en
models as well as he da ase ’s ea u es, and o de e mine whe he machine lea ning echniques supe -
sede adi ional s a is ical echniques. This will be accomplished by employing a ious pe o mance
e alua ion me hods o de e mine he mos adequa e model. The emainde o he pape is ou lined as
ollows: Sec ion 2 discusses he me hodology; Sec ion 3 discusses he esul s; Sec ion 4 desc ibes he
model e alua ion o each me hod and las ly Sec ion 5 concludes he indings.
2. Me hodology
This sec ion p esen s he me hods used in his pape . Tha is, he ea u e selec ion, da a balancing, s a -
is ical and machine lea ning me hods and inally he me hods o model e alua ion.
2.1. Fea u e selec ion
Fea u es ep esen he p edic o a iables used in a quan i a i e model o classi y he p edic ed a iable.
Ha ing oo many, and pa icula ly i ele an ea u es can nega i ely impac model pe o mance, compu -
ing powe , model complexi y and in e p e a ion (Beniwal & A o a, 2012). Fea u e selec ion is a p ocess
whe eby unnecessa y p edic o a iables a e emo ed o ans o med so ha he inal da ase is mo e
a ibu able o he modeling p ocess and p oblem s a emen . The Chi-squa e s a is ics o ms pa o he
il e me hods and in ol es measu ing how independen one ca ego ical a iable is om ano he . I he
da ase consis s o nume ical a iables, hen hese mus be disc e ised o o m g oups o le els. The pu -
pose is o de e mine i he class a iable is independen o he ea u e a iable, in which case he ea-
u e is dis ega ded. On he con a y, i he ea u e and class a iable a e dependen , hen he ea u e is
impo an . The Chi-squa e s a is ic desc ibed by Liu e al. (2002) is gi en as
2¼X
m
i¼1X
k
j¼1
Aij −Eij
Eij

,(1)
whe e mis he numbe o le els o g oups, kis he numbe o classes, Aij is he numbe o obse a ions
in he in e al iand class jand Eij is he expec ed equency o Aij:
The la ge he Chi-squa e alue and he smalle he ela ed p- alue, he mo e impo an he ea u e is.
2.2. Da a balancing
In he eal-wo ld, da ase s a e mo e o en han no , imbalanced. In classi ica ion, an imbalanced da ase
is one in which he o ecas a iable has an une en dis ibu ion o obse a ions. In o he wo ds, one
o ecas a iable con ains mo e o less obse a ions han he al e na i e o ecas a iable(s). A c ucial
s ep in da a analysis is balancing. P oblems wi h imbalanced da a a ise when modelling because a
model’s pe o mance can be biased owa d a speci ic o ecas a iable and a ec p edic ion accu acy.
The pu pose o balancing a da ase is o ensu e ha he model accu a ely p edic s he mino i y and
COGENT ECONOMICS & FINANCE 3

majo i y class. The Syn he ic Mino i y O e -sampling Technique - Nominal me hod is an ex ension o he
Syn he ic Mino i y O e -sampling Technique (SMOTE) echnique applied o nominal ea u es only. The k-
nea es neighbou s a e compu ed using an adap ed Value Di e ence Me ic (VDM) (S an ill & Wal z,
1986). VDM conside s ea u e alue o e lapping o e all ea u e subse s and hen a gene a es dis ance
ma ix which can be used o de e mine he nea es neighbou s.
2.3. S a is ical and machine lea ning echniques
2.3.1. Logis ic eg ession
Logis ic Reg ession is a ype o adi ional s a is ical model used in classi ica ion and p edic ion. I is
widely used in c edi isk models due o i s ma hema ical lexibili y and ease o in e p e a ion
(Sa chidananda & Simha, 2006). The me hod, in con as o Linea Reg ession, does no assume ha he
dis ibu ions o cha ac e is ics in he ea u e space a e no mal. O e - i ing can be a disad an age o
model pe o mance in da ase s whe e he numbe o obse a ions a e less han he numbe o ea u es.
The concep behind Logis ic Reg ession is o ind a ela ionship be ween a dependen a iable and one
o mo e independen a iables. The independen a iables can be ca ego ical, con inuous o bo h, in
na u e. The me hod can be used as a classi ica ion echnique o p edic a dicho omous dependen a i-
able by de e mining he p obabili y ha an obse a ion belongs o a pa icula class. The unc ional
o m o his p obabili y can be exp essed as
PðyjxÞ¼ ðx,bÞ, (2)
whe e PðyjxÞis he p obabili y ha an obse a ion belongs o a class ygi en ha he obse a ion akes
on a speci ic alue x, modelled by some unc ional o m ðx,bÞ(Ko kmaz e al., 2012). The pa ame e s
o bcan be de e mined h ough maximum likelihood es ima ion on he gi en da ase . The ma hema -
ical model o he unc ional o m o Logis ic Reg ession, also known as a sigmoid unc ion wi h mul iple
independen a iables is gi en as
PðnÞ¼ eb0þb1Xn,1þb2Xn,2þ...þbkXn,k
1þeb0þb1Xn,1þb2Xn,2þ...þbkXn,k,(3)
whe e PðnÞis he p obabili y o he class ou come, Xn,iis he alue o obse a ion n o a speci ic ca -
ego y iand biis he eg ession coe icien o he model (Yang e al., 2015). Since he unc ional o m is
a p obabili y dis ibu ion, he alues o bican be de e mined using maximum likelihood es ima ion. The
logis ic eg ession model assumes ha independen a iables a e linea ly co ela ed o he log-odds
log PðnÞ
1−PðnÞo he class a iable (Tu, 1996). Secondly, no mul icollinea i y exis s be ween ea u e a iables.
Thi dly, obse a ions in he da ase a e independen . Las ly, he e a e no ou lie s in he da ase as he
model is sensi i e o la ge changes in obse ed alues.
2.3.1.1. Maximum likelihood es ima ion. Maximum Likelihood Es ima ion (MLE) is a pa ame e es ima-
ion echnique used o a Logis ic Reg ession model. The MLE is he alue ha maximises he p edic ed
p obabili y o an obse a ion belonging o a pa icula class. Re e ing o equa ion (3), he pa ame e s o
be es ima ed a e he b ec o s. The pa ame e s a e es ima ed such ha he p oduc o all p obabili ies
PðnÞis as close o 1 as possible o a gi en obse a ion o he a ge class yequal o 1. Fo he a ge
class yequal o 0, he pa ame e s a e hen es ima ed such ha he p oduc o he p obabili ies 1 −PðnÞ
is as close o 1 as possible. The p oduc o all p obabili y o PðnÞo 1 −PðnÞis called he likelihood
unc ion LðbÞ(Czepiel, 2002), which is gi en as
LðbÞ¼ Y
niny
i¼1
PðnÞ Y
niny
i¼0
ð1−PðnÞÞ ¼ Y
n
PðnÞyið1−PðnÞÞ1−yi
:(4)
To simpli y sol ing equa ion (4), he log o he unc ion is aken o ge he log-likelihood unc ion lðbÞas
lðbÞ¼ ln LðbÞ½¼
X
N
i¼1
yiln ðPðnÞÞ þ ð1−yiÞln ð1−PðnÞÞ½:(5)
4 M. B. SEITSHIRO AND S. GOVENDER
2.3.1.2. Weigh s o e idence. Weigh s o E idence (WoE) is a a iable ans o ma ion me hod ha can
be used wi h Logis ic Reg ession o imp o e he p edic i e abili y o a ea u e. WoE de e mines he p e-
dic i e powe o an independen a iable in ela ion o he a ge o dependen a iable by assigning a
weigh o each binned ca ego y in he ea u e da ase . A highe weigh is assigned o mo e ele an ca -
ego ies, and a lowe weigh is assigned o less ele an ca ego ies, sa is ying he log-odds assump ion o
Logis ic Reg ession. The WoE is gi en as
WoEi¼ln Gi
GBi
B

,(6)
whe e i ep esen s an in ege om 1 o he numbe o ca ego ies in he da ase , Giis he numbe o
obse a ions ep esen ing good isk gi en he i h ca ego y, Gis he o al numbe o obse a ions classed
as good isk, Biis he numbe o obse a ions ep esen ing bad isk gi en he i h ca ego y, and Bis he
o al numbe o obse a ions classed as bad isk. I should be no ed ha be o e using WoE, ea u e
selec ion should be pe o med o op imal pe o mance.
2.3.2. Decision ee
The Decision T ee is a supe ised lea ning me hod based on a ee s uc u e o classi ica ion and eg es-
sion. The algo i hm begins a he oo node and b anches ou o decision nodes based on ea u e a ib-
u es, using impu i y measu es such as en opy and he Gini index o de e mine he bes ea u e o
each decision. The Gini index is calcula ed as
Gini Index ¼1−X
n
i¼1
p2
i,(7)
whe e p2
iis he p obabili y o each class (Muchai & Odongo, 2014). A lowe Gini index indica es a mo e
pu e node. The classi ie can be easily unde s ood, is compu a ionally as and simila o human-based
decision-making pa e ns. I can become complex o la ge da ase s wi h many ea u es and is sensi i e
o noisy da a (Podgo elec e al., 2002).
2.3.3. K-Nea es neighbou s
K-Nea es Neighbou s (KNN) is a non-pa ame ic supe ised lea ning me hod ha uses p oximi y o p e-
dic ou comes o classi y da a. The KNN algo i hm uses a dis ance me ic, such as Euclidean dis ance, o
calcula e he simila i y be ween a sample obse a ion and i s neighbou s. A p obabili y densi y unc ion
is de eloped o es ima e he p obabili y ha a sample ea u e space belongs o a ce ain a ge class by
using he p opo ions o he a ge class de e mined by he kmos simila poin s (Henley & Hand, 1996).
The Euclidean dis ance o mula used by he KNN algo i hm is gi en as
dðx,yÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i−1
ðxi−yiÞ2
s,(8)
whe e dðx,yÞis he measu e o simila i y be ween ec o s xand y, gi en ha x¼ðx1,x2,...,xnÞand
y¼ðy1,y2,...,ynÞ:The e a e se e al o he dis ance me ics ha can be used such as Manha an,
Chebshe , So ensen, Hassana and Cosine dis ance. Howe e , he choice o dis ance me ic depends on
he na u e o he da ase used. The e ec o dis ance measu es on he pe o mance o he KNN classi ie
was comple ed by Abu Al eila e al. (2019).
KNN is bene icial in da ase s whe e he a ge a iable is poly omous and is easily in e p e able.
Howe e , i is sensi i e o imbalanced da ase s and equi es a balanced dis ibu ion on he a ge a i-
able o be e pe o mance (Hand & Henley, 1997). The dis ance me ic and he pa ame e kcan signi i-
can ly a ec he pe o mance o he KNN model, and i is up o he modelle o decide which alues o
use based on he da ase (Pa yudi, 2019).
2.3.4. Suppo ec o machines
Suppo Vec o Machines (SVM) is a supe ised lea ning echnique used o classi ica ion and eg ession
modelling. Howe e , i is mo e commonly used in classi ica ion. The SVM algo i hm is known o be
COGENT ECONOMICS & FINANCE 5
obus , accu a e and simple. A majo ad an age o he model is ha i is no p one o o e - i ing. The
pu pose o he SVM algo i hm is o ind an op imal decision bounda y called a hype plane in an n-
dimensional space, whe e nis he numbe o ea u es in he da ase , such ha he plane sepa a es he
da a poin s by a ge class. Since he e can be se e al planes o co ec ly sepa a e he da a poin s, he
maximum ma gin is calcula ed o ind he op imal hype plane. This is he maximum dis ance be ween
he suppo ec o s o each class. The suppo ec o s a e he poin s closes o he hype plane. The ea-
son he maximum dis ance is equi ed is because he suppo ec o s ep esen da a poin s ha a e he
mos di icul o classi y since hey a e close o he bounda y sepa a ing he classes. Hence, he u he
away hese poin s a e om one ano he , he mo e accu a ely he algo i hm can classi y a da a poin .
The aim o he echnique is o ind a hype plane unc ion gðxÞgi en as
gðxÞ¼wTxþb:(9)
This is so ha he he plane co ec ly sepa a es he da a poin s pe class a iable. In ma hema ical
e ms, gi en he se o da a poin s xca ego ised by wo linea ly sepa able classes y1and y2, SVM aims
o ind wand bsuch ha gðxÞis equal o 1 o he suppo ec o s belonging o class y1and −1 o he
suppo ec o s belonging o class y2(Awad e al., 2015).
2.4. Me hods o model e alua ion
2.4.1. Con usion ma ix
The Con usion Ma ix is a pe o mance e alua ion ool o s a is ical classi ica ion models pa icula ly o
supe ised lea ning. I consis s o a con ingency g id con aining in o ma ion abou ac ual and p edic ed
alues o a classi ica ion model. The ma ix allows he modelle o calcula e a ious pe o mance me ics
such as ecall, accu acy, p ecision, speci ici y and o he s (B
en
edic e al., 2021). These measu emen s a e
ma hema ically de eloped o desc ibe he pe o mance o a classi ica ion model. Fo bina y classi ica ion,
a a ge a iable can ha e a posi i e and nega i e class. Howe e , he bina y classi ica ion model may
p edic co ec o inco ec posi i e and nega i e classes. These p edic ions a e know as ue posi i e,
alse posi i e, ue nega i e and alse nega i e. All o he measu es a ising om he Con usion Ma ix
should be as high as possible o a good model. Sei shi o and Mashele (2022) p o ides ma hema ical
equa ions and desc ip ions o accu acy measu es in de ails.
2.4.2. Recei e ope a ing cha ac e is ic (ROC)
The ROC cu e is de ined as a g aph o he ecall o sensi i i y ( ue posi i e a e) e sus one minus he
speci ici y ( alse posi i e a e) and is used o e alua e he diagnos ic abili y o a classi ica ion model. The
ideal cu e would be a e ical line along he sensi i i y axis and a ho izon al line connec ing he e ical
line, pa allel o he one minus speci ici y axis. This would mean a model can accu a ely p edic obse a-
ions belonging o he posi i e class co ec ly. In eali y, models will no ollow his pa e n. An unsa is-
ac o y model would ha e a cu e lying below he diagonal do ed line. Model pe o mance will hus
imp o e i he cu e is skewed owa ds he uppe le o he g aph. The a ea unde he ROC cu e can
also be e alua ed o pe o mance. As s a ed, i he ROC cu e is skewed owa d he uppe le o he
g aph, he model pe o mance is be e han he one ha lies owa d he diagonal andom p edic o
line. The ideal a ea would hen be equal o one. The e o e, he la ge he a ea unde he cu e o he
ROC cu e, he be e he model pe o mance in p edic ing ou comes.
2.4.3. Log loss
Log loss is an accu acy me ic used o models ha de e mine he p obabili y o an obse a ion belong-
ing o a pa icula class such as Logis ic Reg ession. The me ic indica es how a away each p edic ed
p obabili y is om he ac ual class. The Log Loss is de e mined as
Log Loss ¼−
1
NX
N
i¼1X
M
j¼1
yij ln pij,(10)
6 M. B. SEITSHIRO AND S. GOVENDER
whe e Nis he numbe o obse a ions in he es se , Mis he numbe o class a iables, yij is equal
o 1 i he obse a ion ibelongs o class jand is 0 o he wise, and pij is he p edic ed p obabili y
ha he obse a ion ibelongs o class j(Agga wal e al., 2021). The lowe he log loss sco e is, he
highe a model’s accu acy will be.
2.4.4. Jacca d index
The Jacca d Index Jðy,^
yÞis an in e sec ion (y ^
y) o e union (y[^
y) a io o he numbe o co ec ly
p edic ed alues o he sum o he w ongly p edic ed alues and he o al ac ual posi i es (Eelbode
e al., 2020). The highe he Jacca d Index is, he highe he model pe o mance will be. The measu e is
gi en as
Jðy,^
yÞ¼y ^
y
y[^
y,(11)
whe e y ep esen s he ac ual alues and ^
y ep esen s he p edic ed alues.
2.5. Fu u e esea ch di ec ions in c edi isk assessmen
While Logis ic Reg ession emains a co ne s one in c edi isk assessmen due o i s in e p e abili y and
simplici y (Dumi escu e al., 2022), he ad en o machine lea ning algo i hms has p esen ed oppo uni-
ies o imp o e p edic i e accu acy (Suhadolnik e al., 2023). The indings in his pape unde sco e he
nuanced s eng hs and weaknesses o each model, highligh ing ins ances whe e one model excels o e
ano he . No ably, simple c edi isk assessmen echniques ha e demons a ed ema kable pe o mance
while consuming ewe compu a ional esou ces. Howe e , as he ield p og esses, he e exis s an
impe a i e o explo e ad anced me hodologies ha can u he enhance he obus ness o c edi isk
assessmen amewo ks.
The ounda ional De Long’s Tes (De Long e al., 1988) se es as a benchma king ool o compa e he
pe o mance o p edic i e models, c ucial o assessing he e icacy o c edi isk assessmen models.
Building upon his, ecen s udies ha e explo ed ad anced me hodologies, pa icula ly in Bayesian and
ne wo k modelling, o enhance p edic i e accu acy and eliabili y.
In Bayesian modelling, Giudici, (2001) discusses he applica ion o Bayesian da a mining echniques in
c edi sco ing, aiming o imp o e p edic i e accu acy by inco po a ing p io knowledge and upda ing
p obabili ies based on obse ed da a. In Bayesian da a mining, he s a ing poin is wi h p io belie s, col-
lec ing da a, and using a likelihood unc ion o upda e hese belie s. The pos e io dis ibu ion combines
p io knowledge and da a, allowing he modelle o es ima e model pa ame e s. This app oach is powe ul
o handling unce ain y in complex scena ios like c edi sco ing and benchma king. Addi ionally, Figini
and Giudici (2011) del e in o s a is ical me ging o a ing models, p oposing me hods o combine di e -
en models o enhanced p edic i e powe in c edi isk assessmen h ough adop ing he Bayesian ame-
wo k. The use o Bayesian me ging echniques allows o he in eg a ion o expe judgmen wi h
empi ical da a, enhancing he c edibili y and eliabili y o c edi isk assessmen s (Be na do & Smi h, 1994).
Fu he mo e, Giudici e al. (2020) in oduce ne wo k-based c edi isk models, which conside he
in e connec edness o bo owe s and lende s. These models le e age ne wo k analysis echniques o
cap u e complex ela ionships and dependencies among en i ies, he eby o e ing insigh s in o c edi
isk dynamics. Addi ionally, Chen e al. (2022) in es iga e ne wo k cen ali y e ec s in pee - o-pee lend-
ing, shedding ligh on how he cen ali y o nodes in lending ne wo ks a ec s c edi isk.
While associa ion models o web mining, as explo ed by Cas elo and Giudici (2001), may no di ec ly
apply, g aphical models can help iden i y associa ions be ween a iables like income, spending habi s,
and epaymen his o y o be e unde s and c edi wo hiness. By analysing hese associa ions, inancial
ins i u ions can make mo e in o med decisions when assessing c edi isk. Addi ionally, he use o
Bayesian in e ence echniques aids in selec ing app op ia e models o c edi isk assessmen , allowing
ins i u ions o e alua e he p obabili y o speci ic isk ac o s and make mo e accu a e p edic ions abou
c edi wo hiness.
Fu u e esea ch could le e age hese me hodologies o e ine c edi isk assessmen amewo ks u -
he . In eg a ing De Long’s es wi h Bayesian and ne wo k models p esen s an oppo uni y o enhance
COGENT ECONOMICS & FINANCE 7
dis ibu ion. Ca ego y 1 implies ha a pe son would be classi ied a bad isk mos ly because he o she
did no ha e a sa ings accoun . Ca ego y 4 had he highes WoE o 1.735 due o he la ge di e ence in
bad and good isk coun s. This would no necessa ily mean ha he ea u e was he mos impo an bu
ha in p edic ion, his ca ego y would mo e han likely mean a cus ome is a good isk.
Fo he disc e ised_du a ion ea u e, ca ego ies 1, 2 and 3 had he lowes WoE wi h alues o 0.276,
−0:144 and 0.042, espec i ely. Ca ego y 3 in pa icula , had a e y small WoE because he dis ibu ion
be ween good and bad isk we e simila . This hen mean ha hese ca ego ies would no be good p e-
dic o s o he model and lowe weigh ings we e assigned. Howe e , his can be di icul o he model
o p edic he co ec ou come i he es da ase con ain mo e o hese ca ego ies. In o he wo ds, i
he c edi du a ion was be ween 7 o 24 mon hs, hen he cus ome has oughly an equal chance o
being classi ied a good isk as he o she would be classi ied a bad isk. Ca ego y 0, which mean a c edi
du a ion o 0 o 6 mon hs, had a highe dis ibu ion o good isk han bad isk. This also mean ha he
WoE was la ge due o he di e ence. The alue o he WoE o his ca ego y was 1.981. Ca ego ies 4, 5
and 6 also had la ge WoE due o he di e ence in dis ibu ions be ween good and bad isk. An inc ease
in du a ion would mean ha he cus ome was mo e likely o be classi ied as a bad isk.
The p ope y a iable consis ed o ou di e en ca ego ies. Ca ego ies 2 and 3 had simila dis ibu-
ions be ween good and bad isk, he e o e, he WoE o each was calcula ed o be lowe . These ca ego-
ies would hen no be ega ded good classi ie s o isk in he da ase . Ca ego y 1 and 4 ca ied he
highes WoE o 0.380 and −0:479, espec i ely. These ca ego ies would hen be he be e isk classi ie s
in he da ase . The dis ibu ion also showed ha i a cus ome owned no p ope y, he o she would
mo e likely be classi ied as a good isk. On he con a y, i a cus ome owned a eal es a e, he o she
would mo e likely be classi ied a bad isk. Howe e , he e a e no la ge gaps in he dis ibu ions o ca e-
go ies 1 and 4 and his would make classi ying a cus ome mo e di icul .
The employmen _du a ion ea u e shows he dis ibu ion amongs he 5 ca ego ies. The dis ibu ion
showed ha as he employmen du a ion inc eases, he likelihood o a cus ome being classi ied as a
good isk also inc eased. This is expec ed since ha ing a longe du a ion o employmen would also mean
a cus ome is able o handle his o he inances be e in e ms o paying back c edi . Howe e , i mus be
no ed ha a cus ome can s ill be employed o longe bu be classi ied as a bad isk. The dis ibu ion
showed ha ca ego ies 4 and 5, had he highes WoE o 0.632 and 0.461, espec i ely. Ca ego ies 1, 2 and
3 ha e simila WoE and a e all nega i e in alue which indica ed ha he dis ibu ion o bad isk was
g ea e han he dis ibu ion o good isk in he employmen du a ion o 0 o 4 yea s.
The disc e ised_amoun a iable con ained 8 di e en ca ego ies. Ca ego ies 0, 1 and 6 had he lowes
WoE since he dis ibu ions be ween good and bad isk we e simila . Ca ego ies 4 and 5 had he highes
WoE o −0:996 and 1.139, espec i ely, indica ing ha hese ca ego ies a e good classi ie s o isk in he
da ase . The dis ibu ion also showed ha a c edi amoun aken o mo e han 7000DM would likely
mean a cus ome was a bad isk. Ca ego ies 2 and 3 had simila WoE o 0.480 and 0.548 which a e no
high in alue bu a e be e classi ie s o good isk han bad isk wi hin he da ase . The dis ibu ions o
his a iable indica ed ha he e was no pa e n o co ela ion o iden i ying whe he o no a cus ome
would be classi ied as a good o bad isk o c edi amoun s lowe han 7000DM.
Tdisc e ised_age a iable was encoded in o 5 ca ego ies. This ea u e does show a pa e n in classi y-
ing isk wi hin he da ase . The pa e n showed ha wi h an inc ease in age, he likelihood o a cus-
ome being classi ied as good isk also inc eased. The e was also dis ibu ion imbalance o all 5
ca ego ies be ween good and bad isk which indica ed ha his a iable would be bene icial o a classi-
ica ion model as he e a e clea e dis inc ions be ween he wo a ge ou comes. The dis ibu ion also
showed ha he highes numbe o bo h good and bad isk cus ome s we e be ween he ages o 26
and 35. This ca ego y also had he lowes WoE o −0:269 and hence i may be mo e di icul o a model
o classi y isk i a cus ome was wi hin his age b acke .
4. Model e alua ion
This sec ion will co e he e alua ion o he a ious models a e p edic ion using he es da ase . The
es da ase consis ed o 136 obse a ions o good isk and 64 obse a ions o bad isk.
14 M. B. SEITSHIRO AND S. GOVENDER

The con usion ma ix o each model was compu ed. Fo he Logis ic Reg ession model wi h WoE, he
ma ix shows ha he e we e 127 cus ome s ha we e co ec ly p edic ed as good isks ( ue posi i es),
while 47 cus ome s we e p edic ed o be good isks bu we e ac ually bad isks ( alse posi i es o ype I
e o ). 17 cus ome s we e co ec ly p edic ed as bad isks ( ue nega i es), while 9 cus ome s we e p e-
dic ed o be bad isks bu we e ac ually good isks ( alse nega i es o ype II e o ). This would hen
mean ha he model’s p ecision is lowe han i s ecall.
Re e ing o Table 2, he ecall is 93% and he p ecision is 73%. Howe e , in he cu en con ex o iden-
i ying isk, i is mo e impo an o iden i y cus ome s as being classi ied a bad isk han o alsely classi y
a cus ome who is a bad isk, as a good isk. The e o e, p ecision holds mo e signi icance han p ecision
o c edi isk. Because he Logis ic Reg ession wi h WoE places emphasis on he weigh ings o he ca ego-
ies in iden i ying a isk ou come, he model would ha e p oduced a highe ecall han p ecision. On he
con a y, iden i ying cus ome s only as ue good isks is no en i ely help ul o he bank, and would mean
he p ecision is lowe . A good model equi es a ade-o be ween ecall and p ecision. The e o e, he F1
sco e is used. This is de ined as he ha monic mean o p ecision and ecall. Fo he Logis ic Reg ession
wi h WoE, he F1 sco e is 82% which indica es he model has a good balance be ween p ecision and
ecall. In o he wo ds, he model can accu a ely cap u e good isk and co ec ly classi y he isk.
Fo he Logis ic Reg ession wi hou WoE, he ma ix shows ha he e we e 112 cus ome s ha we e
co ec ly p edic ed as good isks ( ue posi i es), while 20 cus ome s we e p edic ed o be good isks
bu we e ac ually bad isks ( alse posi i es o ype I e o ). 44 cus ome s we e co ec ly p edic ed as bad
isks ( ue nega i es), while 24 cus ome s we e p edic ed o be bad isks bu we e ac ually good isks
( alse nega i es o ype II e o ). Table 2 shows ha his model has simila p ecision and ecall alues,
85% and 82%, espec i ely. E en wi h he imbalance in he es da ase , he model could de ec a pa -
icula isk class and co ec ly classi y i . The model ga e an o e all F1 sco e o 84% which was 2%
highe han he Logis ic Reg ession wi h WoE model. The ecall o he Logis ic Reg ession model wi h
WoE is highe han wi hou WoE. This is because weigh ings a e placed highe o ca ego ies which a e
mo e ele an o a pa icula ou come. Howe e , he e s ill exis s ca ego ies ha may ha e low WoE and
hese may make up he majo i y o he obse a ions in he es da ase , ende ing he p ecision o he
WoE model lowe han he model wi hou WoE. The log loss o he model wi h WoE was also 2.072
uni s highe han he model wi hou WoE indica ing ha he la e model has be e pe o mance in
p edic ing c edi isk. The Logis ic Reg ession wi hou WoE hus has an o e all good pe o mance.
Fo he KNN model, he e we e 94 cus ome s ha we e co ec ly p edic ed as good isks ( ue posi-
i es), while 13 cus ome s we e p edic ed o be good isks bu we e ac ually bad isks ( alse posi i es o
ype I e o ). 51 cus ome s we e co ec ly p edic ed as bad isks ( ue nega i es), while 42 cus ome s
we e p edic ed o be bad isks bu we e ac ually good isks ( alse nega i es o ype II e o ). This means
ha he KNN model is be e a p edic ing good isk han bad isk. This may also be due o imbalance
in he es da ase as he e we e mo e obse a ions o good isk han bad isk and he KNN model can
be sensi i e o class imbalance since he ue pe o mance is based on a balanced aining da ase . The
p ecision o he model is much highe han he ecall, 88% and 69% espec i ely, which gi es he KNN
model ai pe o mance. In e ms o banking, he alse posi i es p oduced should be as low as possible.
This is because he cos o de aul ing is iskie han he bank no ha ing ha isk. Howe e , he ecall
should no be so low such ha he bank does no ha e many cus ome s aking c edi because p o i s
a e equi ed o be made. The model p oduced an F1 sco e o 77% as shown in Table 2 which is ai in
pe o mance o c edi isk classi ica ion o he da ase .
Fo he Decision T ee model, he e we e 83 cus ome s ha we e co ec ly p edic ed as good isks ( ue
posi i es), while only 9 cus ome s we e p edic ed o be good isks bu we e ac ually bad isks ( alse
Table 2. Classi ica ion sco es o all models.
Model P ecision Recall F1 sco e Jacca d index Accu acy AUC Log loss
Logis ic eg ession wi h WOE 0.73 0.93 0.82 0.69 0.72 0.60 9.671
Logis ic eg ession 0.85 0.82 0.84 0.72 0.78 0.76 7.599
KNN 0.88 0.69 0.77 0.63 0.73 0.74 –
Decision ee 0.90 0.61 0.73 0.57 0.69 0.73 –
SVM 0.73 0.92 0.81 0.68 0.71 0.59 –
Sou ce: Au ho ’s calcula ions.
COGENT ECONOMICS & FINANCE 15
posi i es o ype I e o ). 55 cus ome s we e co ec ly p edic ed as bad isks ( ue nega i es), while 53 cus-
ome s we e p edic ed o be bad isks bu we e ac ually good isks ( alse nega i es o ype II e o ). These
alues indica e ha he model is be e a p edic ion ue nega i es han ue posi i es and ha he p eci-
sion would be much highe han he ecall. This was indeed ue e e ing o Table 2 whe e he p ecision
is 90% and he ecall is only 61%. This model is sui able o iden i ying bad isk bu he e was s ill a la ge
numbe o alse nega i es which can be a inancial loss o he bank i he bank’s equi emen is o ha e a
inancial in low. The o e all F1 sco e was 73% which indica es he model is ai in p edic ing isk o he
pa icula da ase . Fo he SVM model, he e we e 125 cus ome s ha we e co ec ly p edic ed as good
isks ( ue posi i es), while 47 cus ome s we e p edic ed o be good isks bu we e ac ually bad isks ( alse
posi i es o ype I e o ). 17 cus ome s we e co ec ly p edic ed as bad isks ( ue nega i es), while 11 cus-
ome s we e p edic ed o be bad isks bu we e ac ually good isks ( alse nega i es o ype II e o ). These
alues indica e ha he model is be e a p edic ing ue posi i es han ue nega i es and ha he ecall
would be highe han he p ecision. This was indeed ue e e ing o Table 2 whe e he p ecision is 73%
and he call is 92%. While his model is sui able o iden i ying good isk, he e was s ill a la ge numbe o
alse posi i es which can be a isk o he bank. The o e all F1 sco e was 81% which indica es he model is
s ill good in p edic ing isk o he pa icula da ase .
Figu e 5 shows he Recei e Ope a ing Cha ac e is ic cu es o each o he 5 classi ica ion models.
An ideal cu e would be a pa allel line o he y-axis connec ing o a line pa allel o he x-axis. This ideal
line would mean he p ecision and ecall a e bo h 100%. In eali y, his is no ue and can be seen om
he a ious models. The SVM and Logis ic Reg ession wi h WoE models pe o med simila ly whe e he
models can p edic good isk well bu su e om a high numbe o alse posi i es. These models will
hen ha e simila AUC as con i med om Table 2 wi h 0.6 and 0.59 o he Logis ic Reg ession wi h WoE
model and SVM model, espec i ely. These models also ha e he lowes AUC om all 5 models. The
accu acy alues and Jacca d Index we e also simila . Howe e , hese e alua ion measu es we e no
s ic ly used o compa ing he models. Because he da ase is imbalanced, he p ecision, ecall and F1
sco e we e he mos sui able measu es o e alua ion. The Decision T ee and KNN models pe o med
simila ly AUC alues o 0.73 and 0.74, espec i ely. These models we e be e a p ecisely classi ying bad
isk, howe e , he models did p oduce a highe numbe o alse nega i es. The Logis ic Reg ession
model wi hou WoE pe o med he bes o e all om he 5 models. This s a is ical lea ning me hod bal-
anced p ecision and ecall well and p oduced he highes F1, accu acy, Jacca d Index and AUC alues o
84%, 78%, 72% and 76%, espec i ely. The Recei e Ope a ing Cha ac e is ic cu e o he model is also
ben owa d he uppe le o he g aph which is he closes o he ideal cu e.
5. Conclusion
Quan i a i e lea ning models can p o ide banks wi h he necessa y c edi assessmen by using a ious
s a is ical and machine lea ning algo i hms ha a e e icien , economical, and accu a e. Howe e , some
Figu e 5. Recei e ope a ing cha ac e is ic cu e o all i e models.
16 M. B. SEITSHIRO AND S. GOVENDER
machine lea ning models can be compu a ionally demanding and complex. S a is ical lea ning can also
p o ide simila pe o mance wi h ewe compu a ional esou ces. This a icle p o ided an analy ical com-
pa ison o 5 models namely he s a is ical lea ning models: Logis ic Reg ession wi h and wi hou ans-
o ming ea u es using WoE, and he machine lea ning models: K-Nea es Neighbou s, Decision-T ee,
and Suppo Vec o Machines. The analysis o echniques was o unde s and i he s a is ical lea ning
models could ou pe o m o pe o m simila ly o he machine lea ning models. The esul s showed ha
no only can he Logis ic Reg ession models pe o m simila ly o he machine lea ning models bu hey
can ou pe o m he models. The Logis ic Reg ession model wi hou ans o ming he ea u es pe o med
he bes ou o he 5 models. Thus, he Logis ic Reg ession model wi h WoE ans o ma ion did no
imp o e he pe o mance o he model. Howe e , his model did pe o m ela i ely simila ly o he SVM
model which equi ed mo e ime and esou ces o op imise. In he u u e, he op imal ade-o be ween
p ecision and ecall could be de e mined so ha he models can be accu a ely and ai ly e alua ed. This
also allows he modele o de e mine he sui abili y o he model o c edi isk p edic ion in comme cial
banking. Fu he mo e, he cos o misclassi ying a cus ome ’s isk p o ile could also be de e mined, while
ensu ing he e is insigh in o ma ion and in e p e abili y o he cus ome beha iou . The eby, conside -
ing he easibili y and sui abili y o a Bayesian app oach p oposed by (Giudici, 2001; Giudici & Ra ine i,
2023; James e al., 2023), in analysing indi ec dependencies be ween p edic o a iables ha make busi-
ness sense and add essing model unce ain y.
Disclosu e s a emen
No po en ial con lic o in e es was epo ed by he au ho (s).
E hics s a emen
No animal o human s udies in ol ed –all da a a e non-p op ie a y and eely a ailable om he in e ne and o he
non-p op ie a y sou ces.
Funding
The au ho s ecei ed no di ec unding o his esea ch.
Abou he au ho s
Modisane Sei shi o comple ed a PhD in Business Ma hema ics and In o ma ics (BMI) a No h-Wes Uni e si y in
2020. He is cu en ly a Senio Lec u e a he Cen e o BMI - NWU. His esea ch in e es s a e Applied S a is ics and
Quan i a i e Risk Managemen .
Seshni Go ende achie ed he Honou s BSc in Enginee ing om he Uni e si y o he Wi wa e s and, Johannesbu g,
Sou h A ica, in 2019. She also accomplished an Honou s BCom deg ee in Financial Modelling om UNISA in 2022.
Cu en ly, she is pu suing a Mas e o Comme ce (MCom) deg ee in Quan i a i e Managemen a UNISA. Wi h a p o-
essional jou ney spanning o e 4 yea s, she has gained aluable expe ience ac oss di e se sec o s including medical
and inancial adminis a ion, banking and consul ing. Seshni holds he posi ion o Quan i a i e Analys a Nedbank.
He esea ch ocus e ol es a ound enhancing he obus ness and in e p e abili y o machine lea ning wi hin he
a eas o Da a Science, Da a Enginee ing and Da a Analysis.
ORCID
Modisane B. Sei shi o h p://o cid.o g/0000-0001-9557-3714
Seshni Go ende h p://o cid.o g/0009-0002-3174-0231
Da a a ailabili y s a emen
The da a used in he pape can be p o ided on eques .
COGENT ECONOMICS & FINANCE 17
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