# R/05_STS_BINNING.R In monobin: Monotonic Binning for Credit Rating Models

#### Documented in sts.bin

```#' Four-stage monotonic binning procedure with statistical test correction
#'
#' \code{sts.bin} implements extension of the three-stage monotonic binning procedure (\code{\link{iso.bin}})
#' with final step of iterative merging of adjacent bins based on
#' statistical test.
#'
#'@seealso \code{\link{iso.bin}} for three-stage monotonic binning procedure.
#'
#'@param x Numeric vector to be binned.
#'@param y Numeric target vector (binary or continuous).
#'@param sc Numeric vector with special case elements. Default values are \code{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 \code{x} and are not defined in the \code{sc} vector, function will report the error.
#'@param sc.method Define how special cases will be treated, all together or in separate bins.
#' Possible values are \code{"together", "separately"}.
#'@param y.type Type of \code{y}, possible options are \code{"bina"} (binary) and \code{"cont"} (continuous).
#' If default value (\code{NA}) is passed, then algorithm will identify if \code{y} is 0/1 or continuous variable.
#'@param min.pct.obs Minimum percentage of observations per bin. Default is 0.05 or minimum 30 observations.
#'@param min.avg.rate Minimum \code{y} average rate. Default is 0.01 or minimum 1 bad case for y 0/1.
#'@param 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.
#'@param force.trend If the expected trend should be forced. Possible values: \code{"i"} for
#' increasing trend (\code{y} increases with increase of \code{x}), \code{"d"} for decreasing trend
#' (\code{y} decreases with decrease of \code{x}). Default value is \code{NA}.
#' If the default value is passed, then trend will be identified based on the sign of the Spearman correlation
#' coefficient between \code{x} and \code{y} on complete cases.
#'
#'@return The command \code{sts.bin} generates a list of two objects. The first object, data frame \code{summary.tbl}
#' presents a summary table of final binning, while \code{x.trans} is a vector of discretized values.
#' In case of single unique value for \code{x} or \code{y} of complete cases (cases different than special cases),
#' it will return data frame with info.
#'
#'@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
#'
#'@importFrom stats cor isoreg pt sd weighted.mean
#'@importFrom Hmisc cut2
#'@import dplyr
#'@export
sts.bin <- function(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) {
ops <- options(scipen = 20)
on.exit(options(ops))

checks.init(x = x, y = y, sc = sc, sc.method = sc.method,
y.type = y.type, force.trend = force.trend)

d <- data.frame(y, x)
d <- d[!is.na(y), ]
d.sc <- d[d\$x%in%sc, ]
d.cc <- d[!d\$x%in%sc, ]

checks.res <- checks.iter(d = d, d.cc = d.cc, y.type = y.type)
if	(checks.res[[1]] > 0) {
return(eval(parse(text = checks.res[[2]])))
}
y.check <- checks.res[[3]]

nr <- nrow(d)
min.obs <- ceiling(ifelse(nr * min.pct.obs < 30, 30, nr * min.pct.obs))
if	(y.check == "bina") {
nd <- sum(d\$y)
min.rate <- ceiling(ifelse(nd * min.avg.rate < 1, 1, nd * min.avg.rate))
} else {
min.rate <- min.avg.rate
}
ds <- iso(tbl.sc = d.sc, tbl.cc = d.cc, method = sc.method, min.obs = min.obs,
min.rate = min.rate, y.check = y.check, force.trend = force.trend)
ds.sc <- ds[ds\$type%in%"special cases", ]
ds.cc <- ds[ds\$type%in%"complete cases", ]

if	(y.check == "bina") {
ds.cc <- t2p.merge(tbl = ds.cc, sig = p.val)
} else {
ds.cc\$y.sd <- add.sd(tbl = ds.cc, x = d\$x, y = d\$y, sc = sc)
ds.cc <- ttg.merge(tbl = ds.cc, sig = p.val, ds = d.cc)
}
ds <- bind_rows(ds.sc, ds.cc)
ds <- woe.calc(tbl = ds, y.check = y.check)
sc.u <- unique(sc)
sc.g <- ds\$bin[ds\$type%in%"special cases"]
x.mins <- ds\$x.min[!ds\$bin%in%sc.u & !ds\$bin%in%"SC"]
x.maxs <- ds\$x.max[!ds\$bin%in%sc.u & !ds\$bin%in%"SC"]
x.trans <- slice.variable(x.orig = d\$x, x.lb = x.mins, x.ub = x.maxs,
sc.u = sc.u, sc.g = sc.g)
return(list(summary.tbl = ds, x.trans = x.trans))
}

#add standard deviation for ds table
add.sd <- function(tbl, x, y, sc) {
ngr <- nrow(tbl)
sd.gr <- rep(NA, ngr)
for	(i in 1:ngr) {
x.lb.l <- tbl\$x.min[i]
x.ub.l <- tbl\$x.max[i]
y.l <- y[!x%in%sc & !x%in%"SC" & x >= x.lb.l & x <= x.ub.l]
sd.gr[i] <- sd(y.l)
}
return(sd.gr)
}
#bin merging based on test of 2 proportions
t2p.merge <- function(tbl, sig) {
if	(nrow(tbl) <= 1) {
tbl\$p.val <- 99
return(tbl)
}
sts <- ifelse(sign(cor(tbl\$y.avg, tbl\$x.avg, method = "spearman")) == 1, "less", "greater")
test.exp <- "prop.test(x = c(y.sum1, y.sum2),
n = c(no1, no2), alternative = sts,
correct = FALSE)\$p.value"
tbl\$p.val <- NA
for	(i in 2:nrow(tbl)) {
y.sum1 <- tbl\$y.sum[i - 1]
y.sum2 <- tbl\$y.sum[i]
no1 <- tbl\$no[i - 1]
no2 <- tbl\$no[i]
p.val.l <- eval(parse(text = test.exp))
tbl\$p.val[i] <- p.val.l
}
tbl\$mod <- 1:nrow(tbl)
repeat {
#criteria to exit the loop
if	(all(tbl\$p.val[!is.na(tbl\$p.val)] < sig)) {break}
if	(nrow(tbl) == 1) {break}
p.max <- which.max(tbl\$p.val)[1]
tbl\$mod[(p.max -1):p.max] <- tbl\$mod[p.max]
bm <- c(as.character(tbl\$bin[p.max]), as.character(tbl\$bin[p.max - 1]))
#find previous and next bins after merging bins in previous step
if	((p.max - 2) < 1) {
bp <- NULL
} else {
bp <- as.character(tbl\$bin[p.max - 2])
}
if	((p.max + 1) > nrow(tbl)) {
bn <- NULL
} else {
bn <- as.character(tbl\$bin[p.max + 1])
}
#recalculate p-values for new group and its neighbors
if	(!is.null(bp)) {
y.sum1 <- tbl\$y.sum[tbl\$bin%in%bp]; no1 <- tbl\$no[tbl\$bin%in%bp]
y.sum2 <- sum(tbl\$y.sum[tbl\$bin%in%bm]); no2 <- sum(tbl\$no[tbl\$bin%in%bm])
p.val <- eval(parse(text = test.exp))
tbl\$p.val[tbl\$mod%in%tbl\$mod[p.max]] <- p.val
} else {
tbl\$p.val[p.max - 1] <- tbl\$p.val[p.max]
}
if	(!is.null(bn)) {
y.sum1 <- sum(tbl\$y.sum[tbl\$bin%in%bm]); no1 <- sum(tbl\$no[tbl\$bin%in%bm])
y.sum2 <- tbl\$y.sum[tbl\$bin%in%bn]; no2 <- tbl\$no[tbl\$bin%in%bn]
p.val <- eval(parse(text = test.exp))
tbl\$p.val[tbl\$mod%in%tbl\$mod[p.max + 1]] <- p.val
} else {
tbl\$p.val[p.max - 1] <- tbl\$p.val[p.max]
}
#condition for only 2 remaining groups with insignificant split
if	(is.null(bp) & is.null(bn)) {
tbl\$p.val[(p.max -1):p.max] <- 1
}
#summarize data based on group correction
tbl <- tbl %>%
group_by(mod) %>%
mutate(
y.avg = weighted.mean(y.avg, no),
x.avg = weighted.mean(x.avg, no)) %>%
summarise(
bin = paste0(bin, collapse = " + "),
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),
p.val = unique(p.val))
tbl\$p.val[1] <- NA
}
res <- as.data.frame(tbl)[, -1]
res <- res[order(res\$x.avg), ]
res\$bin <- format.bin(x.lb = res\$x.min, x.ub = res\$x.max)
res\$type <- "complete cases"
return(res)
}
#bin merging based on t test
t.test.g <- function(x1, x2, sd1, sd2, no1, no2, alternative) {
std1 <- sd1/sqrt(no1)
std2 <- sd2/sqrt(no2)
std <- sqrt(std1^2 + std2^2)
t.stat <- (x1 - x2) / std
df <-  std^4/(std1^4 / (no1 - 1) + std2^4 / (no2 - 1))
if	(alternative == "less") {
p.val <- pt(t.stat, df)
} else {
p.val <- pt(t.stat, df, lower.tail = FALSE)
}
return(p.val)
}
ttg.merge <- function(tbl, sig, ds) {
if	(nrow(tbl) == 1) {
tbl\$p.val <- 99
return(tbl)
}
sts <- ifelse(sign(cor(tbl\$y.avg, tbl\$x.avg, method = "spearman")) == 1, "less", "greater")

test.exp.init <- "t.test.g(x1 = x1, x2 = x2, sd1 = sd1, sd2 = sd2,
no1 = no1, no2 = no2, alternative = sts)"
test.exp.iter <- "t.test(x = y1, y = y2, alternative = sts)"

tbl\$p.val <- NA
for	(i in 2:nrow(tbl)) {
x1 <- tbl\$y.avg[i - 1]
x2 <- tbl\$y.avg[i]
sd1 <- tbl\$y.sd[i - 1]
sd2 <- tbl\$y.sd[i]
no1 <- tbl\$no[i - 1]
no2 <- tbl\$no[i]
p.val.l <- eval(parse(text = test.exp.init))
tbl\$p.val[i] <- p.val.l
}
tbl\$mod <- 1:nrow(tbl)
repeat {
#criteria to exit the loop
if	(all(tbl\$p.val[!is.na(tbl\$p.val)] < sig)) {break}
if	(nrow(tbl) == 1) {break}
p.max <- which.max(tbl\$p.val)[1]
tbl\$mod[(p.max -1):p.max] <- tbl\$mod[p.max]
bm <- c(as.character(tbl\$bin[p.max]), as.character(tbl\$bin[p.max - 1]))
#find previous and next bins after merging 2 in previous step
if	((p.max - 2) < 1) {
bp <- NULL
} else {
bp <- as.character(tbl\$bin[p.max - 2])
}
if	((p.max + 1) > nrow(tbl)) {
bn <- NULL
} else {
bn <- as.character(tbl\$bin[p.max + 1])
}
#recalculate p-values for new group and its neighbors
if	(!is.null(bp)) {
y1 <- ds\$y[ds\$x >= tbl\$x.min[tbl\$bin%in%bp] &
ds\$x <= tbl\$x.max[tbl\$bin%in%bp]]
y2 <- ds\$y[ds\$x >= min(tbl\$x.min[tbl\$bin%in%bm]) &
ds\$x <= max(tbl\$x.max[tbl\$bin%in%bm])]
p.val <- eval(parse(text = test.exp.iter))\$p.value
tbl\$p.val[tbl\$mod%in%tbl\$mod[p.max]] <- p.val
} else {
tbl\$p.val[p.max - 1] <- tbl\$p.val[p.max]
}
if	(!is.null(bn)) {
y1 <- ds\$y[ds\$x >= min(tbl\$x.min[tbl\$bin%in%bm]) &
ds\$x <= max(tbl\$x.max[tbl\$bin%in%bm])]
y2 <- ds\$y[ds\$x >= tbl\$x.min[tbl\$bin%in%bn] &
ds\$x <= tbl\$x.max[tbl\$bin%in%bn]]
p.val <- eval(parse(text = test.exp.iter))\$p.value
tbl\$p.val[tbl\$mod%in%tbl\$mod[p.max + 1]] <- p.val
} else {
tbl\$p.val[p.max - 1] <- tbl\$p.val[p.max]
}
#condition for only 2 remaining groups with insignificant split
if	(is.null(bp) & is.null(bn)) {
tbl\$p.val[(p.max -1):p.max] <- 1
}
#summarize data based on group correction
tbl <- tbl %>%
group_by(mod) %>%
mutate(
y.avg = weighted.mean(y.avg, no),
x.avg = weighted.mean(x.avg, no)) %>%
summarise(
bin = paste0(bin, collapse = " + "),
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),
p.val = unique(p.val))
tbl\$p.val[1] <- NA
}
res <- as.data.frame(tbl)[, -1]
res <- res[order(res\$x.avg), ]
res\$bin <- format.bin(x.lb = res\$x.min, x.ub = res\$x.max)
res\$type <- "complete cases"
return(res)
}
```

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monobin documentation built on April 18, 2022, 5:07 p.m.