Title: Monotonic Binning for Credit Rating Models
Version: 0.2.4
Maintainer: Andrija Djurovic <djandrija@gmail.com>
Description: Performs monotonic binning of numeric risk factor in credit rating models (PD, LGD, EAD) development. All functions handle both binary and continuous target variable. Functions that use isotonic regression in the first stage of binning process have an additional feature for correction of minimum percentage of observations and minimum target rate per bin. Additionally, monotonic trend can be identified based on raw data or, if known in advance, forced by functions' argument. Missing values and other possible special values are treated separately from so-called complete cases.
License: GPL (≥ 3)
URL: https://github.com/andrija-djurovic/monobin
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.1.1
Depends: dplyr, Hmisc, R (≥ 2.10)
NeedsCompilation: no
Packaged: 2022-07-21 09:00:36 UTC; adjurovic
Author: Andrija Djurovic [aut, cre]
Repository: CRAN
Date/Publication: 2022-07-21 09:30:08 UTC

Monotonic binning based on maximum cumulative target rate (MAPA)

Description

cum.bin implements monotonic binning based on maximum cumulative target rate. This algorithm is known as MAPA (Monotone Adjacent Pooling Algorithm).

Usage

cum.bin(
  x,
  y,
  sc = c(NA, NaN, Inf, -Inf),
  sc.method = "together",
  g = 15,
  y.type = NA,
  force.trend = NA
)

Arguments

x

Numeric vector to be binned.

y

Numeric target vector (binary or continuous).

sc

Numeric vector with special case elements. Default values are c(NA, NaN, Inf, -Inf). Recommendation is to keep the default values always and add new ones if needed. Otherwise, if these values exist in x and are not defined in the sc vector, function will report the error.

sc.method

Define how special cases will be treated, all together or in separate bins. Possible values are "together", "separately".

g

Number of starting groups. Default is 15.

y.type

Type of y, possible options are "bina" (binary) and "cont" (continuous). If default value (NA) is passed, then algorithm will identify if y is 0/1 or continuous variable.

force.trend

If the expected trend should be forced. Possible values: "i" for increasing trend (y increases with increase of x), "d" for decreasing trend (y decreases with decrease of x). Default value is NA. If the default value is passed, then trend will be identified based on the sign of the Spearman correlation coefficient between x and y on complete cases.

Value

The command cum.bin generates a list of two objects. The first object, data frame summary.tbl presents a summary table of final binning, while x.trans is a vector of discretized values. In case of single unique value for x or y in complete cases (cases different than special cases), it will return data frame with info.

Examples

suppressMessages(library(monobin))
data(gcd)
amount.bin <- cum.bin(x = gcd$amount, y = gcd$qual)
amount.bin[[1]]
gcd$amount.bin <- amount.bin[[2]]
gcd %>% group_by(amount.bin) %>% summarise(n = n(), y.avg = mean(qual))
#increase default number of groups (g = 20)
amount.bin.1 <- cum.bin(x = gcd$amount, y = gcd$qual, g = 20)
amount.bin.1[[1]]
#force trend to decreasing
cum.bin(x = gcd$amount, y = gcd$qual, g = 20, force.trend = "d")[[1]]

Excerpt from German Credit Data

Description

The German Credit Data contains data on 20 variables and the classification whether an applicant is considered a Good or a Bad credit risk for 1000 loan applicants. Only 3 numeric variables are extracted (Duration of Credit (month), Credit Amount and Age (years)) along with good/bad indicator (Creditability) and renamed as: qual (Creditability), maturity (Duration of Credit (month)), age (Age (years)), amount (Credit Amount).

Usage

gcd

Format

An object of class data.frame with 1000 rows and 4 columns.

Source

https://online.stat.psu.edu/stat857/node/215/

Three-stage monotonic binning procedure

Description

iso.bin implements three-stage monotonic binning procedure. The first stage is isotonic regression used to achieve the monotonicity, while the remaining two stages are possible corrections for minimum percentage of observations and target rate.

Usage

iso.bin(
  x,
  y,
  sc = c(NA, NaN, Inf, -Inf),
  sc.method = "together",
  y.type = NA,
  min.pct.obs = 0.05,
  min.avg.rate = 0.01,
  force.trend = NA
)

Arguments

x

Numeric vector to be binned.

y

Numeric target vector (binary or continuous).

sc

Numeric vector with special case elements. Default values are c(NA, NaN, Inf, -Inf). Recommendation is to keep the default values always and add new ones if needed. Otherwise, if these values exist in x and are not defined in the sc vector, function will report the error.

sc.method

Define how special cases will be treated, all together or in separate bins. Possible values are "together", "separately".

y.type

Type of y, possible options are "bina" (binary) and "cont" (continuous). If default value (NA) is passed, then algorithm will identify if y is 0/1 or continuous variable.

min.pct.obs

Minimum percentage of observations per bin. Default is 0.05 or minimum 30 observations.

min.avg.rate

Minimum y average rate. Default is 0.01 or minimum 1 bad case for y 0/1.

force.trend

If the expected trend should be forced. Possible values: "i" for increasing trend (y increases with increase of x), "d" for decreasing trend (y decreases with decrease of x). Default value is NA. If the default value is passed, then trend will be identified based on the sign of the Spearman correlation coefficient between x and y on complete cases.

Details

The corrections of isotonic regression results present an important step in credit rating model development. The minimum percentage of observation is capped to minimum 30 observations per bin, while target rate for binary target is capped to 1 bad case.

Value

The command iso.bin generates a list of two objects. The first object, data frame summary.tbl presents a summary table of final binning, while x.trans is a vector of discretized values. In case of single unique value for x or y of complete cases (cases different than special cases), it will return data frame with info.

Examples

suppressMessages(library(monobin))
data(gcd)
age.bin <- iso.bin(x = gcd$age, y = gcd$qual)
age.bin[[1]]
table(age.bin[[2]])
# force increasing trend
iso.bin(x = gcd$age, y = gcd$qual, force.trend = "i")[[1]]

#stage by stage example
#inputs
x <- gcd$age		#risk factor
y <- gcd$qual	#binary dependent variable
min.pct.obs <- 0.05	#minimum percentage of observations per bin
min.avg.rate <- 0.01	#minimum percentage of defaults per bin
#stage 1: isotonic regression
db <- data.frame(x, y)
db <- db[order(db$x), ]
cc.sign <- sign(cor(db$y, db$x, method = "spearman", use = "complete.obs"))
iso.r <- isoreg(x = db$x, y = cc.sign * db$y)
db$y.hat <- iso.r$yf
db.s0 <- db %>%
	   group_by(bin = y.hat) %>%
	   summarise(no = n(),
			 y.sum = sum(y),
			 y.avg = mean(y),
			 x.avg = mean(x),
			 x.min = min(x),
			 x.max = max(x))
db.s0 
#stage 2: merging based on minimum percentage of observations
db.s1 <- db.s0
thr.no <- ceiling(ifelse(nrow(db) * min.pct.obs < 30, 30, nrow(db) * min.pct.obs))
thr.no #threshold for minimum number of observations per bin
repeat {
		 if	(nrow(db.s1) == 1) {break}
		 values <- db.s1[, "no"]
		 if	(all(values >= thr.no)) {break}
		 gap <- min(which(values < thr.no))
		 if	(gap == nrow(db.s1)) {
			db.s1$bin[(gap - 1):gap] <- db.s1$bin[(gap - 1)]
			} else {
			db.s1$bin[gap:(gap + 1)] <- db.s1$bin[gap + 1]
			}	
		 db.s1 <- db.s1 %>%
			    group_by(bin) %>%
			    mutate(
				y.avg = weighted.mean(y.avg, no),
				x.avg = weighted.mean(x.avg, no)) %>% 
			    summarise(
				no = sum(no),
				y.sum = sum(y.sum),
				y.avg = unique(y.avg),
				x.avg = unique(x.avg),
				x.min = min(x.min),
				x.max = max(x.max))
		} 
db.s1
#stage 3: merging based on minimum percentage of bad cases
db.s2 <- db.s1
thr.nb <- ceiling(ifelse(nrow(db) * min.avg.rate < 1, 1, nrow(db) * min.avg.rate))
thr.nb #threshold for minimum number of observations per bin
#already each bin has more bad cases than selected threshold hence no need for further merging
all(db.s2$y.sum > thr.nb)
#final result
db.s2
#result of the iso.bin function (formatting and certain metrics has been added)
iso.bin(x = gcd$age, y = gcd$qual)[[1]]

Monotonic binning driven by decision tree

Description

mdt.bin implements monotonic binning driven by decision tree. As a splitting metric for continuous target algorithm uses sum of squared errors, while for the binary target Gini index is used.

Usage

mdt.bin(
  x,
  y,
  g = 50,
  sc = c(NA, NaN, Inf, -Inf),
  sc.method = "together",
  y.type = NA,
  min.pct.obs = 0.05,
  min.avg.rate = 0.01,
  force.trend = NA
)

Arguments

x

Numeric vector to be binned.

y

Numeric target vector (binary or continuous).

g

Number of splitting groups for each node. Default is 50.

sc

Numeric vector with special case elements. Default values are c(NA, NaN, Inf, -Inf). Recommendation is to keep the default values always and add new ones if needed. Otherwise, if these values exist in x and are not defined in the sc vector, function will report the error.

sc.method

Define how special cases will be treated, all together or in separate bins. Possible values are "together", "separately".

y.type

Type of y, possible options are "bina" (binary) and "cont" (continuous). If default value (NA) is passed, then algorithm will identify if y is 0/1 or continuous variable.

min.pct.obs

Minimum percentage of observations per bin. Default is 0.05 or minimum 30 observations.

min.avg.rate

Minimum y average rate. Default is 0.01 or minimum 1 bad case for y 0/1.

force.trend

If the expected trend should be forced. Possible values: "i" for increasing trend (y increases with increase of x), "d" for decreasing trend (y decreases with decrease of x). Default value is NA. If the default value is passed, then trend will be identified based on the sign of the Spearman correlation coefficient between x and y on complete cases.

Value

The command mdt.bin generates a list of two objects. The first object, data frame summary.tbl presents a summary table of final binning, while x.trans is a vector of discretized values. In case of single unique value for x or y in complete cases (cases different than special cases), it will return data frame with info.

Examples

suppressMessages(library(monobin))
data(gcd)
amt.bin <- mdt.bin(x = gcd$amount, y = gcd$qual)
amt.bin[[1]]
table(amt.bin[[2]])
#force decreasing trend
mdt.bin(x = gcd$amount, y = gcd$qual, force.trend = "d")[[1]]

Four-stage monotonic binning procedure including regression with nested dummies

Description

ndr.bin implements extension of three-stage monotonic binning procedure (iso.bin) with step of regression with nested dummies as fourth stage. The first stage is isotonic regression used to achieve the monotonicity. The next two stages are possible corrections for minimum percentage of observations and target rate, while the last regression stage is used to identify statistically significant cut points.

Usage

ndr.bin(
  x,
  y,
  sc = c(NA, NaN, Inf, -Inf),
  sc.method = "together",
  y.type = NA,
  min.pct.obs = 0.05,
  min.avg.rate = 0.01,
  p.val = 0.05,
  force.trend = NA
)

Arguments

x

Numeric vector to be binned.

y

Numeric target vector (binary or continuous).

sc

Numeric vector with special case elements. Default values are c(NA, NaN, Inf, -Inf). Recommendation is to keep the default values always and add new ones if needed. Otherwise, if these values exist in x and are not defined in the sc vector, function will report the error.

sc.method

Define how special cases will be treated, all together or separately. Possible values are "together", "separately".

y.type

Type of y, possible options are "bina" (binary) and "cont" (continuous). If default value is passed, then algorithm will identify if y is 0/1 or continuous variable.

min.pct.obs

Minimum percentage of observations per bin. Default is 0.05 or 30 observations.

min.avg.rate

Minimum y average rate. Default is 0.05 or 30 observations.

p.val

Threshold for p-value of regression coefficients. Default is 0.05. For a binary target binary logistic regression is estimated, whereas for a continuous target, linear regression is used.

force.trend

If the expected trend should be forced. Possible values: "i" for increasing trend (y increases with increase of x), "d" for decreasing trend (y decreases with decrease of x). Default value is NA. If the default value is passed, then trend will be identified based on the sign of the Spearman correlation coefficient between x and y on complete cases.

Value

The command ndr.bin generates a list of two objects. The first object, data frame summary.tbl presents a summary table of final binning, while x.trans is a vector of discretized values. In case of single unique value for x or y of complete cases (cases different than special cases), it will return data frame with info.

See Also

iso.bin for three-stage monotonic binning procedure.

Examples

suppressMessages(library(monobin))
data(gcd)
age.bin <- ndr.bin(x = gcd$age, y = gcd$qual)
age.bin[[1]]
table(age.bin[[2]])
#linear regression example
amount.bin <- ndr.bin(x = gcd$amount, y = gcd$qual, y.type = "cont", p.val = 0.05)
#create nested dummies
db.reg <- gcd[, c("qual", "amount")]
db.reg$amount.bin <- amount.bin[[2]]
amt.s <- db.reg %>% 
      group_by(amount.bin) %>% 
      summarise(qual.mean = mean(qual),
		    amt.min = min(amount))
mins <- amt.s$amt.min
for (i in 2:length(mins)) {
	 level.l <- mins[i]
 nd <- ifelse(db.reg$amount < level.l, 0, 1)
 db.reg <- cbind.data.frame(db.reg, nd)
 names(db.reg)[ncol(db.reg)] <- paste0("dv_", i)
 }
reg.f <- paste0("qual ~ dv_2 + dv_3")
lrm <- lm(as.formula(reg.f), data = db.reg)
lr.coef <- data.frame(summary(lrm)$coefficients)
lr.coef
cumsum(lr.coef$Estimate)
#check
as.data.frame(amt.s)
diff(amt.s$qual.mean)

Monotonic binning based on percentiles

Description

pct.bin implements percentile-based monotonic binning by the iterative discretization.

Usage

pct.bin(
  x,
  y,
  sc = c(NA, NaN, Inf, -Inf),
  sc.method = "together",
  g = 15,
  y.type = NA,
  woe.trend = TRUE,
  force.trend = NA
)

Arguments

x

Numeric vector to be binned.

y

Numeric target vector (binary or continuous).

sc

Numeric vector with special case elements. Default values are c(NA, NaN, Inf, -Inf). Recommendation is to keep the default values always and add new ones if needed. Otherwise, if these values exist in x and are not defined in the sc list some statistics cannot be calculated properly.

sc.method

Define how special cases will be treated, all together or in separate bins. Possible values are "together", "separately".

g

Number of starting groups. Default is 15.

y.type

Type of y, possible options are "bina" (binary) and "cont" (continuous). If default value is passed, then algorithm will identify if y is 0/1 or continuous variable.

woe.trend

Applied only for a continuous target (y) as weights of evidence (WoE) trend check. Default is TRUE.

force.trend

If the expected trend should be forced. Possible values: "i" for increasing trend (y increases with increase of x), "d" for decreasing trend (y decreases with decrease of x). Default value is NA. If the default value is passed, algorithm will stop if perfect negative or positive correlation (Spearman) is achieved between average y and average x per bin. Otherwise, it will stop only if the forced trend is achieved.

Value

The command pct.bin generates a list of two objects. The first object, data frame summary.tbl presents a summary table of final binning, while x.trans is a vector of discretized values. In case of single unique value for x or y of complete cases (cases different than special cases), it will return data frame with info.

Examples

suppressMessages(library(monobin))
data(gcd)
#binary target
mat.bin <- pct.bin(x = gcd$maturity, y = gcd$qual)
mat.bin[[1]]
table(mat.bin[[2]])
#continuous target, separate groups for special cases
set.seed(123)
gcd$age.d <- gcd$age
gcd$age.d[sample(1:nrow(gcd), 10)] <- NA
gcd$age.d[sample(1:nrow(gcd), 3)] <- 9999999999
age.d.bin <- pct.bin(x = gcd$age.d, 
			   	y = gcd$qual, 
			   	sc = c(NA, NaN, Inf, -Inf, 9999999999), 
			  	sc.method = "separately",
			   	force.trend = "d")
age.d.bin[[1]]
gcd$age.d.bin <- age.d.bin[[2]]
gcd %>% group_by(age.d.bin) %>% summarise(n = n(), y.avg = mean(qual))

Four-stage monotonic binning procedure with statistical test correction

Description

sts.bin implements extension of the three-stage monotonic binning procedure (iso.bin) with final step of iterative merging of adjacent bins based on statistical test.

Usage

sts.bin(
  x,
  y,
  sc = c(NA, NaN, Inf, -Inf),
  sc.method = "together",
  y.type = NA,
  min.pct.obs = 0.05,
  min.avg.rate = 0.01,
  p.val = 0.05,
  force.trend = NA
)

Arguments

x

Numeric vector to be binned.

y

Numeric target vector (binary or continuous).

sc

Numeric vector with special case elements. Default values are c(NA, NaN, Inf, -Inf). Recommendation is to keep the default values always and add new ones if needed. Otherwise, if these values exist in x and are not defined in the sc vector, function will report the error.

sc.method

Define how special cases will be treated, all together or in separate bins. Possible values are "together", "separately".

y.type

Type of y, possible options are "bina" (binary) and "cont" (continuous). If default value (NA) is passed, then algorithm will identify if y is 0/1 or continuous variable.

min.pct.obs

Minimum percentage of observations per bin. Default is 0.05 or minimum 30 observations.

min.avg.rate

Minimum y average rate. Default is 0.01 or minimum 1 bad case for y 0/1.

p.val

Threshold for p-value of statistical test. Default is 0.05. For binary target test of two proportion is applied, while for continuous two samples independent t-test.

force.trend

If the expected trend should be forced. Possible values: "i" for increasing trend (y increases with increase of x), "d" for decreasing trend (y decreases with decrease of x). Default value is NA. If the default value is passed, then trend will be identified based on the sign of the Spearman correlation coefficient between x and y on complete cases.

Value

The command sts.bin generates a list of two objects. The first object, data frame summary.tbl presents a summary table of final binning, while x.trans is a vector of discretized values. In case of single unique value for x or y of complete cases (cases different than special cases), it will return data frame with info.

See Also

iso.bin for three-stage monotonic binning procedure.

Examples

suppressMessages(library(monobin))
data(gcd)
#binary target
maturity.bin <- sts.bin(x = gcd$maturity, y = gcd$qual)
maturity.bin[[1]]
tapply(gcd$qual, maturity.bin[[2]], function(x) c(length(x), sum(x), mean(x)))
prop.test(x = c(sum(gcd$qual[maturity.bin[[2]]%in%"01 (-Inf,8)"]), 
	       sum(gcd$qual[maturity.bin[[2]]%in%"02 [8,16)"])), 
       n = c(length(gcd$qual[maturity.bin[[2]]%in%"01 (-Inf,8)"]),
	       length(gcd$qual[maturity.bin[[2]]%in%"02 [8,16)"])), 
       alternative = "less", 
       correct = FALSE)$p.value
#continuous target
age.bin <- sts.bin(x = gcd$age, y = gcd$qual, y.type = "cont")
age.bin[[1]]
t.test(x = gcd$qual[age.bin[[2]]%in%"01 (-Inf,26)"], 
    y = gcd$qual[age.bin[[2]]%in%"02 [26,35)"],
    alternative = "greater")$p.value

Four-stage monotonic binning procedure with WoE threshold

Description

woe.bin implements extension of the three-stage monotonic binning procedure (iso.bin) with weights of evidence (WoE) threshold. The first stage is isotonic regression used to achieve the monotonicity. The next two stages are possible corrections for minimum percentage of observations and target rate, while the last stage is iterative merging of bins until WoE threshold is exceeded.

Usage

woe.bin(
  x,
  y,
  sc = c(NA, NaN, Inf, -Inf),
  sc.method = "together",
  y.type = NA,
  min.pct.obs = 0.05,
  min.avg.rate = 0.01,
  woe.gap = 0.1,
  force.trend = NA
)

Arguments

x

Numeric vector to be binned.

y

Numeric target vector (binary or continuous).

sc

Numeric vector with special case elements. Default values are c(NA, NaN, Inf, -Inf). Recommendation is to keep the default values always and add new ones if needed. Otherwise, if these values exist in x and are not defined in the sc vector, function will report the error.

sc.method

Define how special cases will be treated, all together or in separate bins. Possible values are "together", "separately".

y.type

Type of y, possible options are "bina" (binary) and "cont" (continuous). If default value (NA) is passed, then algorithm will identify if y is 0/1 or continuous variable.

min.pct.obs

Minimum percentage of observations per bin. Default is 0.05 or minimum 30 observations.

min.avg.rate

Minimum y average rate. Default is 0.01 or minimum 1 bad case for y 0/1.

woe.gap

Minimum WoE gap between bins. Default is 0.1.

force.trend

If the expected trend should be forced. Possible values: "i" for increasing trend (y increases with increase of x), "d" for decreasing trend (y decreases with decrease of x). Default value is NA. If the default value is passed, then trend will be identified based on the sign of the Spearman correlation coefficient between x and y on complete cases.

Value

The command woe.bin generates a list of two objects. The first object, data frame summary.tbl presents a summary table of final binning, while x.trans is a vector of discretized values. In case of single unique value for x or y of complete cases (cases different than special cases), it will return data frame with info.

See Also

iso.bin for three-stage monotonic binning procedure.

Examples

suppressMessages(library(monobin))
data(gcd)
amount.bin <- woe.bin(x = gcd$amount, y = gcd$qual)
amount.bin[[1]]
diff(amount.bin[[1]]$woe)
tapply(gcd$amount, amount.bin[[2]], function(x) c(length(x), mean(x)))
woe.bin(x = gcd$maturity, y = gcd$qual)[[1]]
woe.bin(x = gcd$maturity, y = gcd$qual, woe.gap = 0.5)[[1]]