Application of bayesian additive regression trees in the development of credit scoring models in Brazil

Brito Filho, Daniel Alves de; Artes, Rinaldo

doi:10.1590/0103-6513.20170110

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Research Article • Prod. 28 • 2018 • https://doi.org/10.1590/0103-6513.20170110 copy

Application of bayesian additive regression trees in the development of credit scoring models in Brazil

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Paper aims

This paper presents a comparison of the performances of the Bayesian additive regression trees (BART), Random Forest (RF) and the logistic regression model (LRM) for the development of credit scoring models.

Originality

It is not usual the use of BART methodology for the analysis of credit scoring data. The database was provided by Serasa-Experian with information regarding direct retail consumer credit operations. The use of credit bureau variables is not usual in academic papers.

Research method

Several models were adjusted and their performances were compared by using regular methods.

Main findings

The analysis confirms the superiority of the BART model over the LRM for the analyzed data. RF was superior to LRM only for the balanced sample. The best-adjusted BART model was superior to RF.

Implications for theory and practice

The paper suggests that the use of BART or RF may bring better results for credit scoring modelling.

Keywords
Credit; Machine learning; Logistic regression; BART; Random Forest

	Config. 1	Config. 2	Config. 3
$α$	0.50	0.95	0.95
$β$	2.00	2.00	0.10
A priori probability of trees with
1 terminal node	0.500	0.050	0.050
2 terminal nodes	0.383	0.552	0.012
3 terminal nodes	0.098	0.275	0.004
4 terminal nodes	0.017	0.092	0.002
≥ 5 terminal nodes	0.003	0.031	0.932

Customer Types	Full Sample		Development Samples				Validation Sample
	Full Sample		Unbalanced		Balanced		Validation Sample
	N	%	N	%	N	%	N	%
GOOD	9,319	90	6,522	90	727	50	2,797	90
BAD	1,037	10	727	10	727	50	310	10
Total	10,356	100	7,249	100	1,454	100	3,107	100

Model	Basis	KS %	AUC %	Gini %
Balanced	Development	35.90	73.96	47.91
Balanced	Validation	31.99	68.85	37.69
Unbalanced	Development	35.56	73.03	46.07
Unbalanced	Validation	33.84	69.45	38.90

Model	Basis	% of variables used in random selection	KS %	AUC %	Gini %
Balanced	Development	10	46.63	80.43	60.86
		25	52.27	82.98	65.95
		50	54.88	84.16	68.32
		100	56.40	84.77	69.54
	Validation	10	32.14	69.99	39.99
		25	32.99	70.35	40.71
		50	32.33	70.36	40.71
		100	31.94	69.93	39.85
Unbalanced	Development	10	49.90	81.54	63.08
		25	59.62	86.45	72.89
		50	60.21	87.05	74.10
		100	60.82	87.42	74.83
	Validation	10	33.24	70.31	40.61
		25	32.39	69.79	39.58
		50	32.07	69.40	38.80
		100	31.03	68.81	37.61

Model	(m) Number of trees	(z) *Prior of the interval of E(yx)**	KS %	AUC %	Gini %
Balanced	50	1	32.99	70.91	41.81
	50	2	34.24	71.02	42.04
	50	3	33.81	70.92	41.84
	50	5	30.50	69.44	38.89
	200	1	33.71	70.88	41.76
	200	2	33.96	70.73	41.47
	200	3	33.31	70.10	40.21
	200	5	28.64	68.34	36.67
Unbalanced	50	1	32.41	70.68	41.37
	50	2	34.70	70.91	41.82
	50	3	34.89	71.33	42.67
	50	5	34.81	71.60	43.20
	200	1	34.45	70.55	41.11
	200	2	34.99	71.09	42.17
	200	3	35.06	71.25	42.50
	200	5	34.63	71.52	43.04

Sample	Hypotheses	Test
		Delong		Bootstrap
		z	p	z	p
Balanced	H₀: Log. Reg. = R. Forest	-1.958	0.050	-1.934	0.053
	H₀: Default BART = R. Forests	-1.246	0.213	-1.246	0.213
	H₀: Default BART = Log. Reg.	-3.322	0.001	-3.332	0.001
Unbalanced	H₀: Logistic Reg. = R. Forest	-0.922	0.356	-0.967	0.334
	H₀: BART = R. Forests	-2.028	0.043	-2.004	0.045
	H₀: BART = Logistic Regression	-2.869	0.004	-2.788	0.005
	H₀: Default BART = R. Forest	-0.884	0.376	-0.907	0.365
	H₀: Default BART = Log. Reg.	-1.977	0.048	-1.958	0.050

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