SBA Bank Loan Data Analysis Report
Andrew Heneghan
10/16/2022
Introduction
The U.S. Small Business Administration (SBA) collected historical data between 1987 and 2014 of loans guaranteed to some degree by the SBA. The variable FranchiseCode was used as a stratification variable to determine which of three types of random samples, simple, systematic, and stratified, would perform the best in an analysis of this data. Those observations that had franchise codes were divided into categories based off the first 2 digits of the code. Some categories were deleted due to small sizes or an absence of a franchise code, finalizing a study population. One of each kind of random sample, simple, systematic, and stratified, was created with 5000 observations. The default rates of each sample were used in a comparative performance analysis to determine which was best to use for the analysis. The systematic random sample performed better than the simple and stratified random samples, leading me to believe the systematic random sample is the best type to use for the analysis of this data.
Data
I used a U.S. Small Business Administration (SBA) dataset for my analysis, which uses data between the years of 1987 and 2014. I used three different kinds of samples for my analysis. I used a simple random sample, a systematic random sample, and a stratified random sample, each using a total of 5000 observations of loans guaranteed to some degree by the SBA. Of the 27 variables in the dataset, I decided to use the FranchiseCode variable as my stratification variable for the stratified random sample. Most of the observations did not have a franchise code, which limited the population I could use, which I believe helped the study. Even though most observations didn’t have a franchise code, the number that did made it easier for me to find an appropriate sample size. I wanted to determine which of the three samples was best for this analysis.
loan01 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational01.csv", header = TRUE)[, -1]
loan02 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational02.csv", header = TRUE)[, -1]
loan03 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational03.csv", header = TRUE)[, -1]
loan04 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational04.csv", header = TRUE)[, -1]
loan05 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational05.csv", header = TRUE)[, -1]
loan06 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational06.csv", header = TRUE)[, -1]
loan07 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational07.csv", header = TRUE)[, -1]
loan08 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational08.csv", header = TRUE)[, -1]
loan09 = read.csv("https://pengdsci.github.io/datasets/w06-SBAnational09.csv", header = TRUE)[, -1]
bankLoan = rbind(loan01, loan02, loan03, loan04, loan05, loan06, loan07, loan08, loan09)Methods
After choosing FranchiseCode as my stratification variable, I will divide the codes into categories by their first two digits to make the data more manageable. I will then find the loan default rates by franchise code and delete categories that are unclassified or not large enough to be used via the inclusion rule. This will define the study population. After finding the population, I will run the three different types of samples listed above, each composed of 5000 observations. Using their default rates, I will run a comparative performance analysis on the three samples to determine which one is the best to use for this analysis.
Analysis
franchise =as.character(bankLoan$FranchiseCode) # make a character vector
franchise.2.digits = substr(bankLoan$FranchiseCode, 1, 2) # extract the first two digits of the NAICS code
bankLoan$FranchiseCode2Digit = franchise.2.digits # add the above two-digit variable the loan data
FranchiseCode2Digit0 = bankLoan$FranchiseCode2Digit # extract the 2-digit NAICS
FranchiseCode2Digit = bankLoan$FranchiseCode2Digit # extract the 2-digit NAICS-copy
bankLoan$strFranchiseCode = FranchiseCode2Digit
del.categories = c("0", "1", "11", "12", "14", "27", "3", "86", "87", "92", "94", "95", "96", "97", "98", "99") # categories to be deleted in the original population
del.obs.status = !(bankLoan$strFranchiseCode %in% del.categories) # deletion status. ! negation operator
study.pop = bankLoan[del.obs.status,] # excluding the categories
knitr::kable(t(table(study.pop$strFranchiseCode)))| 10 | 13 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 88 | 89 | 90 | 91 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2548 | 328 | 746 | 667 | 1571 | 320 | 434 | 779 | 1827 | 776 | 314 | 827 | 908 | 567 | 231 | 538 | 300 | 288 | 177 | 305 | 978 | 1098 | 512 | 244 | 849 | 546 | 231 | 408 | 388 | 480 | 328 | 694 | 370 | 236 | 537 | 407 | 1707 | 283 | 1374 | 700 | 411 | 476 | 682 | 246 | 203 | 218 | 359 | 710 | 336 | 389 | 679 | 927 | 736 | 1010 | 2688 | 273 | 577 | 257 | 489 | 735 | 377 | 795 | 276 | 493 | 3658 | 1247 | 632 | 858 | 268 | 338 | 745 | 191 | 312 | 626 | 607 | 297 |
I made FranchiseCode a stratification variable and divided the observation codes into categories by their first two digits. After checking the distributions of the 2-digit codes, I found the loan default rates by franchise code and deleted any categories that were unclassified or not large enough to be used via the inclusion rule. Doing this, I was able to define a study population to draw three different kinds of random samples from. Each sample was composed of 5000 loan observations.
Simple Random Sample
study.pop$sampling.frame = 1:length(study.pop$GrAppv) # sampling list
# checking the sampling list variable
sampled.list = sample(1:length(study.pop$GrAppv), 5000) # sampling the list
SRS.sample = study.pop[sampled.list,] # extract the sampling units (observations)
## dimension check
dimension.SRS = dim(SRS.sample)
names(dimension.SRS) = c("Size", "Var.count")
knitr::kable(t(dimension.SRS)) # checking the sample size| Size | Var.count |
|---|---|
| 5000 | 30 |
For the simple random sample, I randomly chose a sample of 5000 loans guaranteed to some degree by the SBA. I defined a sampling list and then added it to the study population.
Systematic Random Sample
jump.size = dim(study.pop)[1]%/%5000 # find the jump size in the systematic sampling
rand.starting.pt=sample(1:jump.size,1) # find the random starting value
sampling.id = seq(rand.starting.pt, dim(study.pop)[1], jump.size) # sampling IDs
sys.sample=study.pop[sampling.id,] # extract the sampling units of systematic samples
sys.Sample.dim = dim(sys.sample)
names(sys.Sample.dim) = c("Size", "Var.count")
knitr::kable(t(sys.Sample.dim))| Size | Var.count |
|---|---|
| 5095 | 30 |
For the systematic random sample, I used a jump size to randomly chose a sample of 5000 loans guaranteed to some degree by the SBA at a regular interval.
Because the jump size involves rounding error and the population is large, the actual systematic sample size is slightly different from the target size. In this report, I used the integer part of the actual jump size. The actual systematic sampling size is slightly bigger than the target size. We can take away some records random from the systematic sample to make the size to be equal to the target size.
Stratified Random Sample
freq.table = table(study.pop$strFranchiseCode) # frequency table of strFranchiseCode
rel.freq = freq.table/sum(freq.table) # relative frequency
strata.size = round(rel.freq*5000) # strata size allocation
strata.names=names(strata.size) # extract strFranchiseCode names for accuracy checking
strata.sample = study.pop[1,] # create a reference data frame
strata.sample$add.id = 1 # add a temporary ID to because in the loop
# i =2 # testing a single iteration
for (i in 1:length(strata.names)){
ith.strata.names = strata.names[i] # extract data frame names
ith.strata.size = strata.size[i] # allocated stratum size
# The following code identifies observations to be selected
ith.sampling.id = which(study.pop$strFranchiseCode==ith.strata.names)
ith.strata = study.pop[ith.sampling.id,] # i-th stratified population
ith.strata$add.id = 1:dim(ith.strata)[1] # add sampling list/frame
# The following code generates a subset of random ID
ith.sampling.id = sample(1:dim(ith.strata)[1], ith.strata.size)
## Create a selection status
ith.sample =ith.strata[ith.strata$add.id %in%ith.sampling.id,]
## dim(ith.sample) $ check the sample
strata.sample = rbind(strata.sample, ith.sample) # stack all data frame!
}
# dim(strata.sample)
strat.sample.final = strata.sample[-1,] # drop the temporary stratum ID
knitr::kable(t(strata.size)) # makes a table of stratified data| 10 | 13 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 88 | 89 | 90 | 91 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 250 | 32 | 73 | 65 | 154 | 31 | 43 | 76 | 179 | 76 | 31 | 81 | 89 | 56 | 23 | 53 | 29 | 28 | 17 | 30 | 96 | 108 | 50 | 24 | 83 | 54 | 23 | 40 | 38 | 47 | 32 | 68 | 36 | 23 | 53 | 40 | 168 | 28 | 135 | 69 | 40 | 47 | 67 | 24 | 20 | 21 | 35 | 70 | 33 | 38 | 67 | 91 | 72 | 99 | 264 | 27 | 57 | 25 | 48 | 72 | 37 | 78 | 27 | 48 | 359 | 122 | 62 | 84 | 26 | 33 | 73 | 19 | 31 | 61 | 60 | 29 |
For the stratified sample, I used FranchiseCode as the stratification variable. Even though most observations didn’t have a franchise code, the number that did made it easier for me to find an appropriate sample size. A SRS was taken from each FranchiseCode stratum. I separated the different codes by their first two numbers and deleted the categories that were either too small or represented no franchise. Not many observations were able to be used since they didn’t have a franchise code. This made the population smaller and easier to sample from.
Results
Using the default rates of the three samples, I ran the comparative performance analysis on the three samples to determine which one is the best to use for this analysis.
x.table = table(bankLoan$strFranchiseCode, bankLoan$MIS_Status)
no.lab = x.table[,1] # first column consists of unknown default label
default = x.table[,2]
no.default = x.table[,3]
default.rate = round(100*default/(default+no.default),1)
default.status.rate = cbind(no.lab = no.lab,
default = default,
no.default = no.default,
default.rate=default.rate)
x.table = table(SRS.sample$strFranchiseCode, SRS.sample$MIS_Status)
no.lab.srs = x.table[,1] # first column consists of unknown default label
default.srs = x.table[,2]
no.default.srs = x.table[,3]
default.rate.srs = round(100*default.srs/(default.srs+no.default.srs),1)
##
franchise.code = names(default.rate.srs) # extract NSICS code
default.rate.pop = default.rate[franchise.code]
# cbind(industry.code,industry.name)
SRS.pop.rates = cbind(default.rate.pop,default.rate.srs)
x.table = table(sys.sample$strFranchiseCode, sys.sample$MIS_Status)
no.lab.sys = x.table[,1] # first column consists of unknown default label
default.sys = x.table[,2]
no.default.sys = x.table[,3]
default.rate.sys = round(100*default.sys/(default.sys+no.default.sys),1)
sys.SRS.pop.rates = cbind(default.rate.pop, default.rate.srs, default.rate.sys)
x.table = table(strat.sample.final$strFranchiseCode, strat.sample.final$MIS_Status)
no.lab.str = x.table[,1] # first column consists of unknown default label
default.str = x.table[,2]
no.default.str = x.table[,3]
default.rate.str = round(100*default.str/(default.str+no.default.str),1)
str.SRS.pop.rates = cbind(default.rate.pop, default.rate.srs, default.rate.sys, default.rate.str)
knitr::kable(str.SRS.pop.rates, caption="Comparison of franchise-specific default rates between population, SRS, Systematic Sample, and Stratified Samples.")| default.rate.pop | default.rate.srs | default.rate.sys | default.rate.str | |
|---|---|---|---|---|
| 10 | 15.8 | 14.9 | 12.8 | 16.4 |
| 13 | 22.3 | 33.3 | 22.6 | 31.2 |
| 15 | 16.9 | 10.4 | 18.3 | 16.4 |
| 16 | 10.0 | 17.4 | 5.6 | 10.8 |
| 17 | 21.1 | 18.6 | 22.2 | 24.7 |
| 18 | 15.0 | 14.3 | 17.2 | 22.6 |
| 19 | 15.4 | 11.9 | 12.0 | 20.9 |
| 20 | 23.6 | 21.9 | 19.0 | 22.4 |
| 21 | 9.3 | 8.9 | 10.8 | 13.4 |
| 22 | 7.6 | 7.4 | 3.7 | 7.9 |
| 23 | 15.3 | 13.0 | 11.5 | 29.0 |
| 24 | 14.7 | 22.6 | 13.6 | 21.2 |
| 25 | 10.1 | 12.5 | 7.2 | 3.4 |
| 26 | 13.1 | 13.8 | 14.9 | 8.9 |
| 28 | 32.0 | 35.0 | 38.1 | 21.7 |
| 29 | 16.7 | 22.2 | 17.5 | 22.6 |
| 30 | 17.7 | 27.9 | 22.6 | 24.1 |
| 31 | 24.3 | 27.3 | 22.2 | 28.6 |
| 32 | 22.6 | 15.0 | 33.3 | 23.5 |
| 33 | 17.7 | 25.0 | 23.3 | 26.7 |
| 34 | 21.4 | 19.6 | 11.8 | 26.0 |
| 35 | 14.9 | 16.1 | 18.0 | 15.7 |
| 36 | 9.0 | 11.1 | 7.0 | 10.0 |
| 37 | 11.5 | 17.9 | 13.6 | 16.7 |
| 38 | 7.2 | 6.1 | 5.3 | 9.6 |
| 39 | 16.8 | 15.0 | 18.0 | 13.0 |
| 40 | 19.9 | 35.0 | 15.0 | 13.0 |
| 41 | 13.2 | 10.0 | 9.5 | 15.0 |
| 42 | 10.1 | 15.4 | 5.3 | 7.9 |
| 43 | 12.1 | 2.3 | 9.8 | 6.4 |
| 44 | 25.0 | 8.6 | 21.6 | 31.2 |
| 45 | 13.1 | 13.2 | 20.7 | 8.8 |
| 46 | 18.6 | 21.6 | 19.2 | 22.2 |
| 47 | 19.5 | 16.7 | 12.5 | 17.4 |
| 48 | 12.7 | 12.2 | 12.0 | 7.5 |
| 49 | 16.5 | 19.5 | 22.5 | 17.5 |
| 50 | 12.9 | 11.8 | 13.4 | 10.7 |
| 51 | 11.8 | 19.2 | 4.5 | 11.5 |
| 52 | 22.1 | 19.4 | 20.0 | 13.3 |
| 53 | 16.0 | 24.6 | 19.2 | 17.4 |
| 54 | 14.8 | 25.0 | 18.4 | 17.5 |
| 55 | 17.0 | 15.7 | 22.6 | 12.8 |
| 56 | 14.4 | 16.9 | 10.1 | 17.9 |
| 57 | 9.3 | 4.5 | 12.5 | 8.3 |
| 58 | 33.0 | 17.6 | 29.4 | 35.0 |
| 59 | 25.2 | 36.8 | 20.8 | 19.0 |
| 60 | 15.9 | 29.0 | 21.2 | 14.3 |
| 61 | 13.4 | 14.7 | 9.2 | 15.7 |
| 62 | 13.4 | 11.9 | 13.6 | 18.2 |
| 63 | 26.0 | 25.0 | 20.8 | 21.1 |
| 64 | 23.7 | 20.0 | 27.7 | 22.4 |
| 65 | 21.3 | 24.7 | 23.9 | 17.6 |
| 66 | 16.0 | 13.9 | 13.6 | 16.7 |
| 67 | 6.5 | 4.6 | 3.0 | 5.1 |
| 68 | 22.7 | 26.4 | 21.4 | 23.5 |
| 69 | 15.0 | 11.5 | 13.3 | 29.6 |
| 70 | 18.0 | 15.8 | 19.0 | 21.1 |
| 71 | 21.4 | 13.0 | 31.0 | 24.0 |
| 72 | 16.0 | 16.3 | 17.0 | 16.7 |
| 73 | 10.2 | 12.3 | 10.0 | 13.9 |
| 74 | 14.3 | 13.2 | 7.1 | 18.9 |
| 75 | 14.5 | 16.9 | 12.5 | 12.8 |
| 76 | 14.1 | 21.4 | 18.9 | 14.8 |
| 77 | 12.0 | 11.1 | 16.3 | 14.6 |
| 78 | 5.7 | 5.4 | 5.5 | 4.5 |
| 79 | 11.2 | 10.0 | 7.8 | 12.4 |
| 80 | 19.5 | 19.3 | 13.1 | 22.6 |
| 81 | 17.1 | 16.5 | 23.4 | 17.9 |
| 82 | 13.1 | 13.0 | 7.7 | 19.2 |
| 83 | 12.7 | 8.3 | 14.7 | 15.2 |
| 84 | 12.2 | 5.5 | 12.0 | 11.0 |
| 85 | 12.6 | 5.6 | 14.3 | 10.5 |
| 88 | 11.5 | 6.2 | 11.1 | 6.5 |
| 89 | 24.6 | 28.6 | 30.4 | 26.2 |
| 90 | 14.2 | 12.2 | 14.5 | 18.3 |
| 91 | 14.8 | 7.4 | 13.8 | 17.2 |
n=length(default.rate.pop)
plot(NULL, xlim=c(0,n), ylim=c(0, 50),
xlab="Franchise Code",
ylab ="Default Rates (Percentage)", axes=FALSE) # empty plot
# Light gray background
rect(par("usr")[1], par("usr")[3],
par("usr")[2], par("usr")[4],
col = "white")
# Add white grid
grid(nx = NULL, ny = NULL,
col = "white", lwd = 1)
title("Comparison of Franchise-specific Default Rates Based on Random Samples")
points(1:n, as.vector(default.rate.pop), pch=16, col="gold3", cex = 0.8)
lines(1:n, as.vector(default.rate.pop), lty=1, col="gold3", cex = 0.8)
#
points(1:n, as.vector(default.rate.srs), pch=17, col="darkorange1", cex = 0.8)
lines(1:n, as.vector(default.rate.srs), lty=2, col="darkorange1", cex = 0.8)
#
points(1:n, as.vector(default.rate.sys), pch=19, col="navyblue", cex = 0.8)
lines(1:n, as.vector(default.rate.sys), lty=3, col="navyblue", cex = 0.8)
#
points(1:n, as.vector(default.rate.str), pch=20, col="magenta", cex = 0.8)
lines(1:n, as.vector(default.rate.str), lty=4, col="magenta", cex = 0.8)
#
axis(1,at=1:n, label=franchise.code)
axis(2, las = 2)
#
clr = c("yellow","darkorange1","navyblue","magenta")
rowMax=apply(str.SRS.pop.rates, 1, max) # max default rate in each franchise
#segments(1:n, rep(0,n), 1:n, rowMax, lty=2, col="lightgray", lwd = 0.5)
legend(58, 50, c("Population", "Simple Random Sampling", "Systematic Sampling", "Stratified Sampling"), lty=rep(1,4), col=clr, pch=c(16,17,19,20), cex=0.6, bty="n")
After running a performance analysis on three different random samples, I found the systematic random sample to have performed better compared to the simple and stratified random samples. Therefore, I believe the systematic random sample is the best type of sample to use for the analysis of the SBA data.
Conclusion
Using the SBA dataset of loans and FranchiseCode as a stratification variable, I was able to determine which of the three samples, simple, systematic, and stratified, would have the best performance in a data analysis. A sample of 5000 observations was taken for each of the three samples. Examining the default rates of the three samples showed that the systematic random sample was best to use for this data analysis. Yet, many of the observations were not actually used in the analysis since they didn’t have a franchise code. I wonder, however, if the performance analysis of the three random samples would have turned out different if more of the loan observations in the dataset had actual franchise codes to use.
Appendix
x.table = table(bankLoan$strFranchiseCode, bankLoan$MIS_Status)
no.lab = x.table[,1] # first column consists of unknown default label
default = x.table[,2]
no.default = x.table[,3]
default.rate = round(100*default/(default+no.default),1)
default.status.rate = cbind(no.lab = no.lab,
default = default,
no.default = no.default,
default.rate=default.rate)
knitr::kable(default.status.rate, caption = "Population size, default counts, and population default rates")| no.lab | default | no.default | default.rate | |
|---|---|---|---|---|
| 0 | 795 | 71175 | 136865 | 34.2 |
| 1 | 1159 | 78523 | 558872 | 12.3 |
| 10 | 0 | 402 | 2146 | 15.8 |
| 11 | 0 | 5 | 50 | 9.1 |
| 12 | 0 | 3 | 12 | 20.0 |
| 13 | 0 | 73 | 255 | 22.3 |
| 14 | 0 | 11 | 80 | 12.1 |
| 15 | 1 | 126 | 619 | 16.9 |
| 16 | 0 | 67 | 600 | 10.0 |
| 17 | 0 | 332 | 1239 | 21.1 |
| 18 | 0 | 48 | 272 | 15.0 |
| 19 | 0 | 67 | 367 | 15.4 |
| 20 | 0 | 184 | 595 | 23.6 |
| 21 | 3 | 169 | 1655 | 9.3 |
| 22 | 0 | 59 | 717 | 7.6 |
| 23 | 0 | 48 | 266 | 15.3 |
| 24 | 3 | 121 | 703 | 14.7 |
| 25 | 0 | 92 | 816 | 10.1 |
| 26 | 0 | 74 | 493 | 13.1 |
| 27 | 0 | 21 | 70 | 23.1 |
| 28 | 0 | 74 | 157 | 32.0 |
| 29 | 0 | 90 | 448 | 16.7 |
| 3 | 0 | 3 | 9 | 25.0 |
| 30 | 1 | 53 | 246 | 17.7 |
| 31 | 0 | 70 | 218 | 24.3 |
| 32 | 0 | 40 | 137 | 22.6 |
| 33 | 0 | 54 | 251 | 17.7 |
| 34 | 0 | 209 | 769 | 21.4 |
| 35 | 0 | 164 | 934 | 14.9 |
| 36 | 2 | 46 | 464 | 9.0 |
| 37 | 0 | 28 | 216 | 11.5 |
| 38 | 0 | 61 | 788 | 7.2 |
| 39 | 0 | 92 | 454 | 16.8 |
| 40 | 0 | 46 | 185 | 19.9 |
| 41 | 0 | 54 | 354 | 13.2 |
| 42 | 3 | 39 | 346 | 10.1 |
| 43 | 0 | 58 | 422 | 12.1 |
| 44 | 0 | 82 | 246 | 25.0 |
| 45 | 0 | 91 | 603 | 13.1 |
| 46 | 0 | 69 | 301 | 18.6 |
| 47 | 0 | 46 | 190 | 19.5 |
| 48 | 1 | 68 | 468 | 12.7 |
| 49 | 0 | 67 | 340 | 16.5 |
| 50 | 0 | 221 | 1486 | 12.9 |
| 51 | 20 | 31 | 232 | 11.8 |
| 52 | 0 | 303 | 1071 | 22.1 |
| 53 | 0 | 112 | 588 | 16.0 |
| 54 | 0 | 61 | 350 | 14.8 |
| 55 | 0 | 81 | 395 | 17.0 |
| 56 | 1 | 98 | 583 | 14.4 |
| 57 | 0 | 23 | 223 | 9.3 |
| 58 | 0 | 67 | 136 | 33.0 |
| 59 | 0 | 55 | 163 | 25.2 |
| 60 | 0 | 57 | 302 | 15.9 |
| 61 | 0 | 95 | 615 | 13.4 |
| 62 | 0 | 45 | 291 | 13.4 |
| 63 | 0 | 101 | 288 | 26.0 |
| 64 | 1 | 161 | 517 | 23.7 |
| 65 | 1 | 197 | 729 | 21.3 |
| 66 | 0 | 118 | 618 | 16.0 |
| 67 | 0 | 66 | 944 | 6.5 |
| 68 | 1 | 609 | 2078 | 22.7 |
| 69 | 0 | 41 | 232 | 15.0 |
| 70 | 0 | 104 | 473 | 18.0 |
| 71 | 0 | 55 | 202 | 21.4 |
| 72 | 0 | 78 | 411 | 16.0 |
| 73 | 1 | 75 | 659 | 10.2 |
| 74 | 0 | 54 | 323 | 14.3 |
| 75 | 1 | 115 | 679 | 14.5 |
| 76 | 0 | 39 | 237 | 14.1 |
| 77 | 0 | 59 | 434 | 12.0 |
| 78 | 0 | 209 | 3449 | 5.7 |
| 79 | 2 | 140 | 1105 | 11.2 |
| 80 | 0 | 123 | 509 | 19.5 |
| 81 | 0 | 147 | 711 | 17.1 |
| 82 | 0 | 35 | 233 | 13.1 |
| 83 | 0 | 43 | 295 | 12.7 |
| 84 | 0 | 91 | 654 | 12.2 |
| 85 | 0 | 24 | 167 | 12.6 |
| 86 | 0 | 15 | 67 | 18.3 |
| 87 | 0 | 8 | 45 | 15.1 |
| 88 | 0 | 36 | 276 | 11.5 |
| 89 | 0 | 154 | 472 | 24.6 |
| 90 | 1 | 86 | 520 | 14.2 |
| 91 | 0 | 44 | 253 | 14.8 |
| 92 | 0 | 13 | 72 | 15.3 |
| 94 | 0 | 35 | 33 | 51.5 |
| 95 | 0 | 6 | 57 | 9.5 |
| 96 | 0 | 1 | 17 | 5.6 |
| 97 | 0 | 10 | 38 | 20.8 |
| 98 | 0 | 13 | 138 | 8.6 |
| 99 | 0 | 0 | 1 | 0.0 |
I made this table to calculate default rates across the franchises. I decided to use the population-level franchise-specific rates as a reference and compare them with the sample-level default rates. This table also includes the category of loans with no franchise code.
x.table = table(sys.sample$strFranchiseCode, sys.sample$MIS_Status)
no.lab.sys = x.table[,1] # first column consists of unknown default label
default.sys = x.table[,2]
no.default.sys = x.table[,3]
default.rate.sys = round(100*default.sys/(default.sys+no.default.sys),1)
sys.SRS.pop.rates = cbind(default.rate.pop, default.rate.srs, default.rate.sys)
knitr::kable(sys.SRS.pop.rates, caption="Comparison of industry-specific default rates between population, SRS, and Systematic Sample.")| default.rate.pop | default.rate.srs | default.rate.sys | |
|---|---|---|---|
| 10 | 15.8 | 14.9 | 12.8 |
| 13 | 22.3 | 33.3 | 22.6 |
| 15 | 16.9 | 10.4 | 18.3 |
| 16 | 10.0 | 17.4 | 5.6 |
| 17 | 21.1 | 18.6 | 22.2 |
| 18 | 15.0 | 14.3 | 17.2 |
| 19 | 15.4 | 11.9 | 12.0 |
| 20 | 23.6 | 21.9 | 19.0 |
| 21 | 9.3 | 8.9 | 10.8 |
| 22 | 7.6 | 7.4 | 3.7 |
| 23 | 15.3 | 13.0 | 11.5 |
| 24 | 14.7 | 22.6 | 13.6 |
| 25 | 10.1 | 12.5 | 7.2 |
| 26 | 13.1 | 13.8 | 14.9 |
| 28 | 32.0 | 35.0 | 38.1 |
| 29 | 16.7 | 22.2 | 17.5 |
| 30 | 17.7 | 27.9 | 22.6 |
| 31 | 24.3 | 27.3 | 22.2 |
| 32 | 22.6 | 15.0 | 33.3 |
| 33 | 17.7 | 25.0 | 23.3 |
| 34 | 21.4 | 19.6 | 11.8 |
| 35 | 14.9 | 16.1 | 18.0 |
| 36 | 9.0 | 11.1 | 7.0 |
| 37 | 11.5 | 17.9 | 13.6 |
| 38 | 7.2 | 6.1 | 5.3 |
| 39 | 16.8 | 15.0 | 18.0 |
| 40 | 19.9 | 35.0 | 15.0 |
| 41 | 13.2 | 10.0 | 9.5 |
| 42 | 10.1 | 15.4 | 5.3 |
| 43 | 12.1 | 2.3 | 9.8 |
| 44 | 25.0 | 8.6 | 21.6 |
| 45 | 13.1 | 13.2 | 20.7 |
| 46 | 18.6 | 21.6 | 19.2 |
| 47 | 19.5 | 16.7 | 12.5 |
| 48 | 12.7 | 12.2 | 12.0 |
| 49 | 16.5 | 19.5 | 22.5 |
| 50 | 12.9 | 11.8 | 13.4 |
| 51 | 11.8 | 19.2 | 4.5 |
| 52 | 22.1 | 19.4 | 20.0 |
| 53 | 16.0 | 24.6 | 19.2 |
| 54 | 14.8 | 25.0 | 18.4 |
| 55 | 17.0 | 15.7 | 22.6 |
| 56 | 14.4 | 16.9 | 10.1 |
| 57 | 9.3 | 4.5 | 12.5 |
| 58 | 33.0 | 17.6 | 29.4 |
| 59 | 25.2 | 36.8 | 20.8 |
| 60 | 15.9 | 29.0 | 21.2 |
| 61 | 13.4 | 14.7 | 9.2 |
| 62 | 13.4 | 11.9 | 13.6 |
| 63 | 26.0 | 25.0 | 20.8 |
| 64 | 23.7 | 20.0 | 27.7 |
| 65 | 21.3 | 24.7 | 23.9 |
| 66 | 16.0 | 13.9 | 13.6 |
| 67 | 6.5 | 4.6 | 3.0 |
| 68 | 22.7 | 26.4 | 21.4 |
| 69 | 15.0 | 11.5 | 13.3 |
| 70 | 18.0 | 15.8 | 19.0 |
| 71 | 21.4 | 13.0 | 31.0 |
| 72 | 16.0 | 16.3 | 17.0 |
| 73 | 10.2 | 12.3 | 10.0 |
| 74 | 14.3 | 13.2 | 7.1 |
| 75 | 14.5 | 16.9 | 12.5 |
| 76 | 14.1 | 21.4 | 18.9 |
| 77 | 12.0 | 11.1 | 16.3 |
| 78 | 5.7 | 5.4 | 5.5 |
| 79 | 11.2 | 10.0 | 7.8 |
| 80 | 19.5 | 19.3 | 13.1 |
| 81 | 17.1 | 16.5 | 23.4 |
| 82 | 13.1 | 13.0 | 7.7 |
| 83 | 12.7 | 8.3 | 14.7 |
| 84 | 12.2 | 5.5 | 12.0 |
| 85 | 12.6 | 5.6 | 14.3 |
| 88 | 11.5 | 6.2 | 11.1 |
| 89 | 24.6 | 28.6 | 30.4 |
| 90 | 14.2 | 12.2 | 14.5 |
| 91 | 14.8 | 7.4 | 13.8 |
Before I created the table comparing default rates for all the samples, I made a table excluding the stratified random sample to compare the other two samples first. It turned out that the systematic sample performed much better compared to the simple random sample.