Data Mining - Decision Tree Classification
Datamanz:
- 1 Introduction
- 2 Import Libraries and Dataset
- 3 Preprocessing and Exploratory Analysis
- 4 Statistical Significance Tests
- 5 Building the First Decision Tree
- 6 With the obtained tree, provide a brief explanation of the rules derived and any points of interest. One element to consider, for example, is how many observations fall under each rule.
- 7 Once you have a valid model, proceed to perform a goodness-of-fit analysis on the test set and the confusion matrix. Do you consider this model sufficiently good to be used? Justify your answer by considering all possible types of error.
- 8 Using a similar approach to the previous points and considering the same variables, enrich the exercise by fitting complementary decision tree models. Is the new approach better than the original? Justify your answer.
- 9 What alternatives remain after not being fully convinced with our analyses?
- 10 Summary of Main Findings Across All Models
- 11 Final Conclusions
- 12 Final Conclusion
- 13 References
1 Introduction
The purpose of this project is to apply data mining techniques to the German Credit dataset in order to explore patterns and build predictive models. The focus is on decision tree classification, evaluating its performance, and interpreting the results in the context of credit risk assessment.
The analysis follows a structured process: importing and preprocessing the dataset, conducting exploratory data analysis, building classification models (Decision Tree and Random Forest), and evaluating their predictive accuracy.
This work is part of the Datamanz project, which emphasizes the application of statistical learning methods and reproducible research practices using R.
2 Import Libraries and Dataset
This code block ensures that all the necessary packages for data analysis and visualization are installed and loaded into the R environment. Conditional installation is applied so that only missing packages are installed. The libraries included provide tools for clustering, advanced graphics, statistical analysis, machine learning, and data manipulation.
if (!require('C50')) install.packages('C50')## Cargando paquete requerido: C50## Warning: package 'C50' was built under R version 4.4.3library(C50)
if (!require('gridExtra')) install.packages('gridExtra')## Cargando paquete requerido: gridExtralibrary(gridExtra)
if (!require('grid')) install.packages('grid')## Cargando paquete requerido: gridlibrary(grid)
if (!require('ggpubr')) install.packages('ggpubr')## Cargando paquete requerido: ggpubr## Cargando paquete requerido: ggplot2library(ggpubr)
if (!require('cluster')) install.packages('cluster')## Cargando paquete requerido: clusterlibrary(cluster)
if (!require('Stat2Data')) install.packages('Stat2Data')## Cargando paquete requerido: Stat2Datalibrary(Stat2Data)
if (!require('dplyr')) install.packages('dplyr')## Cargando paquete requerido: dplyr##
## Adjuntando el paquete: 'dplyr'## The following object is masked from 'package:gridExtra':
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## combine## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(dplyr)
if (!require('ggplot2')) install.packages("ggplot2")
library(ggplot2)
if (!require('factoextra')) install.packages("factoextra")## Cargando paquete requerido: factoextra## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(factoextra)
if (!require('NbClust')) install.packages("NbClust")## Cargando paquete requerido: NbClustlibrary(NbClust)
if (!require('dbscan')) install.packages('dbscan')## Cargando paquete requerido: dbscan##
## Adjuntando el paquete: 'dbscan'## The following object is masked from 'package:stats':
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## as.dendrogramlibrary(dbscan)
if (!require('tidyr')) install.packages('tidyr')## Cargando paquete requerido: tidyrlibrary(tidyr)
if (!require('factoextra')) install.packages('factoextra')
library(factoextra)
if (!require('corrplot')) install.packages('corrplot')## Cargando paquete requerido: corrplot## corrplot 0.95 loadedlibrary(corrplot)
if (!require('psych')) install.packages('psych')## Cargando paquete requerido: psych##
## Adjuntando el paquete: 'psych'## The following objects are masked from 'package:ggplot2':
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## %+%, alphalibrary(psych)
if (!require('DescTools')) install.packages('DescTools')## Cargando paquete requerido: DescTools## Warning: package 'DescTools' was built under R version 4.4.3##
## Adjuntando el paquete: 'DescTools'## The following objects are masked from 'package:psych':
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## AUC, ICC, SDlibrary(DescTools)
if (!require('rpart')) install.packages('rpart')## Cargando paquete requerido: rpartlibrary(rpart)
if (!require('rpart.plot')) install.packages('rpart.plot')## Cargando paquete requerido: rpart.plot## Warning: package 'rpart.plot' was built under R version 4.4.3library(rpart.plot)
if (!require('DiagrammeR')) install.packages('DiagrammeR')## Cargando paquete requerido: DiagrammeR## Warning: package 'DiagrammeR' was built under R version 4.4.3library(DiagrammeR)
if (!require('randomForest')) install.packages('randomForest')## Cargando paquete requerido: randomForest## Warning: package 'randomForest' was built under R version 4.4.3## randomForest 4.7-1.2## Type rfNews() to see new features/changes/bug fixes.##
## Adjuntando el paquete: 'randomForest'## The following object is masked from 'package:psych':
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## outlier## The following object is masked from 'package:dplyr':
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## combine## The following object is masked from 'package:ggplot2':
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## margin## The following object is masked from 'package:gridExtra':
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## combinelibrary(randomForest)
if (!require('caret')) install.packages('caret')## Cargando paquete requerido: caret## Warning: package 'caret' was built under R version 4.4.3## Cargando paquete requerido: lattice##
## Adjuntando el paquete: 'caret'## The following objects are masked from 'package:DescTools':
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## MAE, RMSElibrary(caret)
if (!require('e1071')) install.packages('e1071')## Cargando paquete requerido: e1071## Warning: package 'e1071' was built under R version 4.4.3library(e1071)
if (!require('pROC')) install.packages('pROC')## Cargando paquete requerido: pROC## Warning: package 'pROC' was built under R version 4.4.3## Type 'citation("pROC")' for a citation.##
## Adjuntando el paquete: 'pROC'## The following objects are masked from 'package:stats':
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## cov, smooth, varlibrary(pROC)Next, the German Credit dataset is loaded from a CSV file and stored in the object dfcredit. This data frame will be used throughout the project for preprocessing, exploratory analysis, and predictive modeling.
dfcredit <- read.csv("C:/Users/Manuel/Desktop/credit.csv")3 Preprocessing and Exploratory Analysis
- At this stage, it is important to gain a clear understanding of the dataset before proceeding with further analysis. Take note of any observations or surprising findings in the data.
The head(dfcredit) command displays the first rows of
the data frame dfcredit. This provides a quick overview of
the loaded dataset, helping to understand its structure and
contents.
head(dfcredit)## checking_balance months_loan_duration credit_history purpose amount
## 1 < 0 DM 6 critical radio/tv 1169
## 2 1 - 200 DM 48 repaid radio/tv 5951
## 3 unknown 12 critical education 2096
## 4 < 0 DM 42 repaid furniture 7882
## 5 < 0 DM 24 delayed car (new) 4870
## 6 unknown 36 repaid education 9055
## savings_balance employment_length installment_rate personal_status
## 1 unknown > 7 yrs 4 single male
## 2 < 100 DM 1 - 4 yrs 2 female
## 3 < 100 DM 4 - 7 yrs 2 single male
## 4 < 100 DM 4 - 7 yrs 2 single male
## 5 < 100 DM 1 - 4 yrs 3 single male
## 6 unknown 1 - 4 yrs 2 single male
## other_debtors residence_history property age installment_plan
## 1 none 4 real estate 67 none
## 2 none 2 real estate 22 none
## 3 none 3 real estate 49 none
## 4 guarantor 4 building society savings 45 none
## 5 none 4 unknown/none 53 none
## 6 none 4 unknown/none 35 none
## housing existing_credits default dependents telephone foreign_worker
## 1 own 2 1 1 yes yes
## 2 own 1 2 1 none yes
## 3 own 1 1 2 none yes
## 4 for free 1 1 2 none yes
## 5 for free 2 2 2 none yes
## 6 for free 1 1 2 yes yes
## job
## 1 skilled employee
## 2 skilled employee
## 3 unskilled resident
## 4 skilled employee
## 5 skilled employee
## 6 unskilled residentThe str(dfcredit) command shows the internal structure of the data frame dfcredit. It provides details such as the type of object, the number of observations and variables, data types, and sample values for each column.
str(dfcredit)## 'data.frame': 1000 obs. of 21 variables:
## $ checking_balance : chr "< 0 DM" "1 - 200 DM" "unknown" "< 0 DM" ...
## $ months_loan_duration: int 6 48 12 42 24 36 24 36 12 30 ...
## $ credit_history : chr "critical" "repaid" "critical" "repaid" ...
## $ purpose : chr "radio/tv" "radio/tv" "education" "furniture" ...
## $ amount : int 1169 5951 2096 7882 4870 9055 2835 6948 3059 5234 ...
## $ savings_balance : chr "unknown" "< 100 DM" "< 100 DM" "< 100 DM" ...
## $ employment_length : chr "> 7 yrs" "1 - 4 yrs" "4 - 7 yrs" "4 - 7 yrs" ...
## $ installment_rate : int 4 2 2 2 3 2 3 2 2 4 ...
## $ personal_status : chr "single male" "female" "single male" "single male" ...
## $ other_debtors : chr "none" "none" "none" "guarantor" ...
## $ residence_history : int 4 2 3 4 4 4 4 2 4 2 ...
## $ property : chr "real estate" "real estate" "real estate" "building society savings" ...
## $ age : int 67 22 49 45 53 35 53 35 61 28 ...
## $ installment_plan : chr "none" "none" "none" "none" ...
## $ housing : chr "own" "own" "own" "for free" ...
## $ existing_credits : int 2 1 1 1 2 1 1 1 1 2 ...
## $ default : int 1 2 1 1 2 1 1 1 1 2 ...
## $ dependents : int 1 1 2 2 2 2 1 1 1 1 ...
## $ telephone : chr "yes" "none" "none" "none" ...
## $ foreign_worker : chr "yes" "yes" "yes" "yes" ...
## $ job : chr "skilled employee" "skilled employee" "unskilled resident" "skilled employee" ...Next, we provide a short description of the variables:
- checking_balance Indicates the customer’s current account
balance, categorized into ranges such as “< 0 DM”, “1 - 200 DM”, and
“unknown”.
- months_loan_duration Represents the duration of the loan in
months (numeric).
- credit_history Describes the customer’s credit history with
categories such as “critical”, “repaid”, and “delayed”.
- purpose Indicates the purpose of the loan, with categories
such as “radio/tv”, “furniture”, “education”, and others.
- amount Represents the requested loan amount
(numeric).
- savings_balance Shows the customer’s savings account
balance, categorized into ranges such as “< 100 DM”, “500 - 1000 DM”,
and “unknown”.
- employment_length Indicates the customer’s length of
employment, with categories such as “< 1 yr”, “1 - 4 yrs”, “4 - 7
yrs”, and “> 7 yrs”.
- age Represents the customer’s age in years (numeric).
- housing Shows the customer’s housing situation, with
categories such as “own”, “rent”, and “for free”.
- existing_credits Indicates the number of existing credits
held by the customer (numeric).
- foreign_worker Indicates whether the customer is a foreign
worker, with values such as “yes” or “no”.
- telephone Reflects whether the customer has a registered
telephone line, with values “yes” or “none”.
- job Describes the type of employment, with categories such
as “skilled employee”, “unskilled resident”, and “management”.
- installment_rate Monthly loan installment rate expressed as
a percentage of the customer’s income.
- personal_status Marital or personal status of the
customer.
- other_debtors Information about other debtors or
guarantors.
- residence_history The number of years the customer has
lived at the current residence.
- property Type of property owned by the customer.
- installment_plan Indicates whether the customer has an
installment plan for the loan.
- dependents Number of dependents supported by the
customer.
- default Indicates whether the customer has defaulted on the
loan, with values:
- 1: No default (“compliant”)
- 2: Default (“non-compliant”)
- 1: No default (“compliant”)
The summary(dfcredit) command generates a statistical summary of the dataset, including minimum, maximum, median, quartiles, and frequency counts for categorical variables. This helps identify unusual values and provides insight into the distribution of the data.
summary(dfcredit)## checking_balance months_loan_duration credit_history purpose
## Length:1000 Min. : 4.0 Length:1000 Length:1000
## Class :character 1st Qu.:12.0 Class :character Class :character
## Mode :character Median :18.0 Mode :character Mode :character
## Mean :20.9
## 3rd Qu.:24.0
## Max. :72.0
## amount savings_balance employment_length installment_rate
## Min. : 250 Length:1000 Length:1000 Min. :1.000
## 1st Qu.: 1366 Class :character Class :character 1st Qu.:2.000
## Median : 2320 Mode :character Mode :character Median :3.000
## Mean : 3271 Mean :2.973
## 3rd Qu.: 3972 3rd Qu.:4.000
## Max. :18424 Max. :4.000
## personal_status other_debtors residence_history property
## Length:1000 Length:1000 Min. :1.000 Length:1000
## Class :character Class :character 1st Qu.:2.000 Class :character
## Mode :character Mode :character Median :3.000 Mode :character
## Mean :2.845
## 3rd Qu.:4.000
## Max. :4.000
## age installment_plan housing existing_credits
## Min. :19.00 Length:1000 Length:1000 Min. :1.000
## 1st Qu.:27.00 Class :character Class :character 1st Qu.:1.000
## Median :33.00 Mode :character Mode :character Median :1.000
## Mean :35.55 Mean :1.407
## 3rd Qu.:42.00 3rd Qu.:2.000
## Max. :75.00 Max. :4.000
## default dependents telephone foreign_worker
## Min. :1.0 Min. :1.000 Length:1000 Length:1000
## 1st Qu.:1.0 1st Qu.:1.000 Class :character Class :character
## Median :1.0 Median :1.000 Mode :character Mode :character
## Mean :1.3 Mean :1.155
## 3rd Qu.:2.0 3rd Qu.:1.000
## Max. :2.0 Max. :2.000
## job
## Length:1000
## Class :character
## Mode :character
##
##
## The following commands provide further insights:
lapply(dfcredit, unique): Applies the unique function to each column of the data frame, returning a list of unique values for every variable.
sapply(dfcredit, function(x) length(unique(x))): Calculates the number of unique values in each column, returning a vector of counts.
sapply(dfcredit, class): Returns the data type (class) of each column, providing an overview of how variables are stored.
lapply(dfcredit, unique)## $checking_balance
## [1] "< 0 DM" "1 - 200 DM" "unknown" "> 200 DM"
##
## $months_loan_duration
## [1] 6 48 12 42 24 36 30 15 9 10 7 60 18 45 11 27 8 54 20 14 33 21 16 4 47
## [26] 13 22 39 28 5 26 72 40
##
## $credit_history
## [1] "critical" "repaid" "delayed"
## [4] "fully repaid" "fully repaid this bank"
##
## $purpose
## [1] "radio/tv" "education" "furniture"
## [4] "car (new)" "car (used)" "business"
## [7] "domestic appliances" "repairs" "others"
## [10] "retraining"
##
## $amount
## [1] 1169 5951 2096 7882 4870 9055 2835 6948 3059 5234 1295 4308
## [13] 1567 1199 1403 1282 2424 8072 12579 3430 2134 2647 2241 1804
## [25] 2069 1374 426 409 2415 6836 1913 4020 5866 1264 1474 4746
## [37] 6110 2100 1225 458 2333 1158 6204 6187 6143 1393 2299 1352
## [49] 7228 2073 5965 1262 3378 2225 783 6468 9566 1961 6229 1391
## [61] 1537 1953 14421 3181 5190 2171 1007 1819 2394 8133 730 1164
## [73] 5954 1977 1526 3965 4771 9436 3832 5943 1213 1568 1755 2315
## [85] 1412 12612 2249 1108 618 1409 797 3617 1318 15945 2012 2622
## [97] 2337 7057 1469 2323 932 1919 2445 11938 6458 6078 7721 1410
## [109] 1449 392 6260 7855 1680 3578 7174 2132 4281 2366 1835 3868
## [121] 1768 781 1924 2121 701 639 1860 3499 8487 6887 2708 1984
## [133] 10144 1240 8613 766 2728 1881 709 4795 3416 2462 2288 3566
## [145] 860 682 5371 1582 1346 5848 7758 6967 1288 339 3512 1898
## [157] 2872 1055 7308 909 2978 1131 1577 3972 1935 950 763 2064
## [169] 1414 3414 7485 2577 338 1963 571 9572 4455 1647 3777 884
## [181] 1360 5129 1175 674 3244 4591 3844 3915 2108 3031 1501 1382
## [193] 951 2760 4297 936 1168 5117 902 1495 10623 1424 6568 1413
## [205] 3074 3835 5293 1908 3342 3104 3913 3021 1364 625 1200 707
## [217] 4657 2613 10961 7865 1478 3149 4210 2507 2141 866 1544 1823
## [229] 14555 2767 1291 2522 915 1595 4605 1185 3447 1258 717 1204
## [241] 1925 433 666 2251 2150 4151 2030 7418 2684 2149 3812 1154
## [253] 1657 1603 5302 2748 1231 802 6304 1533 8978 999 2662 1402
## [265] 12169 3060 11998 2697 2404 4611 1901 3368 1574 1445 1520 3878
## [277] 10722 4788 7582 1092 1024 1076 9398 6419 4796 7629 9960 4675
## [289] 1287 2515 2745 672 3804 1344 1038 10127 1543 4811 727 1237
## [301] 276 5381 5511 3749 685 1494 2746 708 4351 3643 4249 1938
## [313] 2910 2659 1028 3398 5801 1525 4473 1068 6615 1864 7408 11590
## [325] 4110 3384 2101 1275 4169 1521 5743 3599 3213 4439 3949 1459
## [337] 882 3758 1743 1136 1236 959 3229 6199 1246 2331 4463 776
## [349] 2406 1239 3399 2247 1766 2473 1542 3850 3650 3446 3001 3079
## [361] 6070 2146 13756 14782 7685 2320 846 14318 362 2212 12976 1283
## [373] 1330 4272 2238 1126 7374 2326 1820 983 3249 1957 11760 2578
## [385] 2348 1223 1516 1473 1887 8648 2899 2039 2197 1053 3235 939
## [397] 1967 7253 2292 1597 1381 5842 2579 8471 2782 1042 3186 2028
## [409] 958 1591 2762 2779 2743 1149 1313 1190 3448 11328 1872 2058
## [421] 2136 1484 660 3394 609 1884 1620 2629 719 5096 1244 1842
## [433] 2576 1512 11054 518 2759 2670 4817 2679 3905 3386 343 4594
## [445] 3620 1721 3017 754 1950 2924 1659 7238 2764 4679 3092 448
## [457] 654 1238 1245 3114 2569 5152 1037 3573 1201 3622 960 1163
## [469] 1209 3077 3757 1418 3518 1934 8318 368 2122 2996 9034 1585
## [481] 1301 1323 3123 5493 1216 1207 1309 2360 6850 8588 759 4686
## [493] 2687 585 2255 1361 7127 1203 700 5507 3190 7119 3488 1113
## [505] 7966 1532 1503 2302 662 2273 2631 1311 3105 2319 3612 7763
## [517] 3049 1534 2032 6350 2864 1255 1333 2022 1552 626 8858 996
## [529] 1750 6999 1995 1331 2278 5003 3552 1928 2964 1546 683 12389
## [541] 4712 1553 1372 3979 6758 3234 5433 806 1082 2788 2930 1927
## [553] 2820 937 1056 3124 1388 2384 2133 2799 1289 1217 2246 385
## [565] 1965 1572 2718 1358 931 1442 4241 2775 3863 2329 918 1837
## [577] 3349 2828 4526 2671 2051 1300 741 3357 3632 1808 12204 9157
## [589] 3676 3441 640 3652 1530 3914 1858 2600 1979 2116 1437 4042
## [601] 3660 1444 1980 1355 1376 15653 1493 4370 750 1308 4623 1851
## [613] 1880 7980 4583 1386 947 684 7476 1922 2303 8086 2346 3973
## [625] 888 10222 4221 6361 1297 900 1050 1047 6314 3496 3609 4843
## [637] 4139 5742 10366 2080 2580 4530 5150 5595 1453 1538 2279 5103
## [649] 9857 6527 1347 2862 2753 3651 975 2896 4716 2284 1103 926
## [661] 1800 1905 1123 6331 1377 2503 2528 5324 6560 2969 1206 2118
## [673] 629 1198 2476 1138 14027 7596 1505 3148 6148 1337 1228 790
## [685] 2570 250 1316 1882 6416 6403 1987 760 2603 3380 3990 11560
## [697] 4380 6761 4280 2325 1048 3160 2483 14179 1797 2511 1274 5248
## [709] 3029 428 976 841 5771 1555 1285 1299 1271 691 5045 2124
## [721] 2214 12680 2463 1155 3108 2901 1655 2812 8065 3275 2223 1480
## [733] 1371 3535 3509 5711 3872 4933 1940 836 1941 2675 2751 6224
## [745] 5998 1188 6313 1221 2892 3062 2301 7511 1549 1795 7472 9271
## [757] 590 930 9283 1778 907 484 9629 3051 3931 7432 1338 1554
## [769] 15857 1345 1101 3016 2712 731 3780 1602 3966 4165 8335 6681
## [781] 2375 11816 5084 2327 886 601 2957 2611 5179 2993 1943 1559
## [793] 3422 3976 1249 2235 1471 10875 894 3343 3959 3577 5804 2169
## [805] 2439 2210 2221 2389 3331 7409 652 7678 1343 874 3590 1322
## [817] 3595 1422 6742 7814 9277 2181 1098 4057 795 2825 15672 6614
## [829] 7824 2442 1829 5800 8947 2606 1592 2186 4153 2625 3485 10477
## [841] 1278 1107 3763 3711 3594 3195 4454 4736 2991 2142 3161 18424
## [853] 2848 14896 2359 3345 1817 12749 1366 2002 6872 697 1049 10297
## [865] 1867 1747 1670 1224 522 1498 745 2063 6288 6842 3527 929
## [877] 1455 1845 8358 2859 3621 2145 4113 10974 1893 3656 4006 3069
## [889] 1740 2353 3556 2397 454 1715 2520 3568 7166 3939 1514 7393
## [901] 1193 7297 2831 753 2427 2538 8386 4844 2923 8229 1433 6289
## [913] 6579 3565 1569 1936 2390 1736 3857 804 4576
##
## $savings_balance
## [1] "unknown" "< 100 DM" "501 - 1000 DM" "> 1000 DM"
## [5] "101 - 500 DM"
##
## $employment_length
## [1] "> 7 yrs" "1 - 4 yrs" "4 - 7 yrs" "unemployed" "0 - 1 yrs"
##
## $installment_rate
## [1] 4 2 3 1
##
## $personal_status
## [1] "single male" "female" "divorced male" "married male"
##
## $other_debtors
## [1] "none" "guarantor" "co-applicant"
##
## $residence_history
## [1] 4 2 3 1
##
## $property
## [1] "real estate" "building society savings"
## [3] "unknown/none" "other"
##
## $age
## [1] 67 22 49 45 53 35 61 28 25 24 60 32 44 31 48 26 36 39 42 34 63 27 30 57 33
## [26] 37 58 23 29 52 50 46 51 41 40 66 47 56 54 20 21 38 70 65 74 68 43 55 64 75
## [51] 19 62 59
##
## $installment_plan
## [1] "none" "bank" "stores"
##
## $housing
## [1] "own" "for free" "rent"
##
## $existing_credits
## [1] 2 1 3 4
##
## $default
## [1] 1 2
##
## $dependents
## [1] 1 2
##
## $telephone
## [1] "yes" "none"
##
## $foreign_worker
## [1] "yes" "no"
##
## $job
## [1] "skilled employee" "unskilled resident"
## [3] "mangement self-employed" "unemployed non-resident"sapply(dfcredit, function(x) length(unique(x)))## checking_balance months_loan_duration credit_history
## 4 33 5
## purpose amount savings_balance
## 10 921 5
## employment_length installment_rate personal_status
## 5 4 4
## other_debtors residence_history property
## 3 4 4
## age installment_plan housing
## 53 3 3
## existing_credits default dependents
## 4 2 2
## telephone foreign_worker job
## 2 2 4sapply(dfcredit, class)## checking_balance months_loan_duration credit_history
## "character" "integer" "character"
## purpose amount savings_balance
## "character" "integer" "character"
## employment_length installment_rate personal_status
## "character" "integer" "character"
## other_debtors residence_history property
## "character" "integer" "character"
## age installment_plan housing
## "integer" "character" "character"
## existing_credits default dependents
## "integer" "integer" "integer"
## telephone foreign_worker job
## "character" "character" "character"As observed, the results from these functions are not very informative in their current form, since many columns are not yet properly categorized. Therefore, it is both logical and practical to transform the categorical variables into factors. This facilitates working with categorical data, optimizes statistical analysis, and allows the use of specialized visualization tools.
Reference Nº1
The following transformation converts all character-type columns in dfcredit into factors:
dfcredit <- dfcredit %>%
mutate(across(where(is.character), factor))
str(dfcredit)## 'data.frame': 1000 obs. of 21 variables:
## $ checking_balance : Factor w/ 4 levels "< 0 DM","> 200 DM",..: 1 3 4 1 1 4 4 3 4 3 ...
## $ months_loan_duration: int 6 48 12 42 24 36 24 36 12 30 ...
## $ credit_history : Factor w/ 5 levels "critical","delayed",..: 1 5 1 5 2 5 5 5 5 1 ...
## $ purpose : Factor w/ 10 levels "business","car (new)",..: 8 8 5 6 2 5 6 3 8 2 ...
## $ amount : int 1169 5951 2096 7882 4870 9055 2835 6948 3059 5234 ...
## $ savings_balance : Factor w/ 5 levels "< 100 DM","> 1000 DM",..: 5 1 1 1 1 5 4 1 2 1 ...
## $ employment_length : Factor w/ 5 levels "> 7 yrs","0 - 1 yrs",..: 1 3 4 4 3 3 1 3 4 5 ...
## $ installment_rate : int 4 2 2 2 3 2 3 2 2 4 ...
## $ personal_status : Factor w/ 4 levels "divorced male",..: 4 2 4 4 4 4 4 4 1 3 ...
## $ other_debtors : Factor w/ 3 levels "co-applicant",..: 3 3 3 2 3 3 3 3 3 3 ...
## $ residence_history : int 4 2 3 4 4 4 4 2 4 2 ...
## $ property : Factor w/ 4 levels "building society savings",..: 3 3 3 1 4 4 1 2 3 2 ...
## $ age : int 67 22 49 45 53 35 53 35 61 28 ...
## $ installment_plan : Factor w/ 3 levels "bank","none",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ housing : Factor w/ 3 levels "for free","own",..: 2 2 2 1 1 1 2 3 2 2 ...
## $ existing_credits : int 2 1 1 1 2 1 1 1 1 2 ...
## $ default : int 1 2 1 1 2 1 1 1 1 2 ...
## $ dependents : int 1 1 2 2 2 2 1 1 1 1 ...
## $ telephone : Factor w/ 2 levels "none","yes": 2 1 1 1 1 2 1 2 1 1 ...
## $ foreign_worker : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
## $ job : Factor w/ 4 levels "mangement self-employed",..: 2 2 4 2 2 4 2 1 4 1 ...This transformation ensures that categorical variables are correctly encoded, preparing the dataset for subsequent modeling and analysis.
summary(dfcredit)## checking_balance months_loan_duration credit_history
## < 0 DM :274 Min. : 4.0 critical :293
## > 200 DM : 63 1st Qu.:12.0 delayed : 88
## 1 - 200 DM:269 Median :18.0 fully repaid : 40
## unknown :394 Mean :20.9 fully repaid this bank: 49
## 3rd Qu.:24.0 repaid :530
## Max. :72.0
##
## purpose amount savings_balance employment_length
## radio/tv :280 Min. : 250 < 100 DM :603 > 7 yrs :253
## car (new) :234 1st Qu.: 1366 > 1000 DM : 48 0 - 1 yrs :172
## furniture :181 Median : 2320 101 - 500 DM :103 1 - 4 yrs :339
## car (used):103 Mean : 3271 501 - 1000 DM: 63 4 - 7 yrs :174
## business : 97 3rd Qu.: 3972 unknown :183 unemployed: 62
## education : 50 Max. :18424
## (Other) : 55
## installment_rate personal_status other_debtors residence_history
## Min. :1.000 divorced male: 50 co-applicant: 41 Min. :1.000
## 1st Qu.:2.000 female :310 guarantor : 52 1st Qu.:2.000
## Median :3.000 married male : 92 none :907 Median :3.000
## Mean :2.973 single male :548 Mean :2.845
## 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :4.000 Max. :4.000
##
## property age installment_plan housing
## building society savings:232 Min. :19.00 bank :139 for free:108
## other :332 1st Qu.:27.00 none :814 own :713
## real estate :282 Median :33.00 stores: 47 rent :179
## unknown/none :154 Mean :35.55
## 3rd Qu.:42.00
## Max. :75.00
##
## existing_credits default dependents telephone foreign_worker
## Min. :1.000 Min. :1.0 Min. :1.000 none:596 no : 37
## 1st Qu.:1.000 1st Qu.:1.0 1st Qu.:1.000 yes :404 yes:963
## Median :1.000 Median :1.0 Median :1.000
## Mean :1.407 Mean :1.3 Mean :1.155
## 3rd Qu.:2.000 3rd Qu.:2.0 3rd Qu.:1.000
## Max. :4.000 Max. :2.0 Max. :2.000
##
## job
## mangement self-employed:148
## skilled employee :630
## unemployed non-resident: 22
## unskilled resident :200
##
##
## - Initial Observations
Low balances in accounts (checking_balance and
savings_balance)
Most customers have less than 100 DM in savings (603 cases) or unknown
balances (183).
For current accounts, 274 customers are negative (< 0 DM), while 394
have missing or unknown values.
Moderate loan amounts
The average loan amount is 3,271 DM, with a median of 2,320 and values
ranging from 250 to 18,424.
While small to moderate loans dominate, there are large loans exceeding
10,000 DM.
Loan purposes focused on consumer goods
The most common purposes are radio/TV (280), car (new) (234), and
furniture (181), showing high demand for basic consumption.
Less frequent categories include business (97) and education (50),
indicating lower use for productive activities.
Credit history with frequent problems
293 customers have a critical credit history, representing a significant
proportion of credit risk.
Only 40 customers have fully repaid loans, suggesting general repayment
difficulties.
Target variable (default) and prediction of
non-compliance
The variable default takes values 1 and 2, corresponding to two
classes: compliant (1) and non-compliant (2).
The analysis is oriented toward predicting the probability of default to
support credit decisions.
Average customer age
The average age is 35.55 years, with a median of 33 and a wide range
from 19 to 75 years.
Most customers fall into the young adult group, with 75% under 42 years
old.
Foreign workers and lack of registered telephone
The vast majority are foreign workers (yes: 963 vs. no: 37), reflecting
a highly mobile clientele.
Additionally, 596 customers do not have a registered telephone, making
direct contact difficult and increasing operational risks.
- Data Cleaning
To consolidate these initial observations, it is essential to confirm that the dataset has a solid structure and is valuable for analysis. A key step in ensuring data quality is verifying the absence of erroneous or inconsistent values that could bias results.
The logical first step is to check for empty values, missing values, or entries marked as NA (Not Available), as these represent gaps in information that could affect calculations and subsequent models. Detecting and properly handling these values is critical to ensuring analytical precision and avoiding errors in interpretation or prediction.
missing_values <- is.na(dfcredit) | dfcredit == "" | dfcredit == "NA"
missing_values_count <- colSums(missing_values)
print(missing_values_count)## checking_balance months_loan_duration credit_history
## 0 0 0
## purpose amount savings_balance
## 0 0 0
## employment_length installment_rate personal_status
## 0 0 0
## other_debtors residence_history property
## 0 0 0
## age installment_plan housing
## 0 0 0
## existing_credits default dependents
## 0 0 0
## telephone foreign_worker job
## 0 0 0This code combines multiple conditions to detect missing values. It evaluates whether data are NA, empty cells (““), or explicitly marked as”NA” in text format. Then, colSums counts how many missing values exist in each column of the data frame, providing a clear summary of the dataset’s state.
Based on this analysis, we can determine whether missing values exist that require treatment, either through imputation, removal, or another method. This step ensures that the dataset meets the quality standards required for reliable analysis and accurate results.
As seen from the execution, the dataset does not contain missing values. This means there are no NA records, empty cells, or explicit “NA” text. This is highly positive, as it guarantees that the dataset is complete and does not require further preprocessing to handle missing values.
The absence of missing values allows us to proceed with the analysis without implementing imputation techniques, row/column removal, or other strategies for handling incomplete data. This not only simplifies the workflow but also ensures that the results are not biased due to missing information.
Having a clean dataset with no missing values provides a strong foundation for statistical analysis, exploratory research, and predictive modeling, maximizing both the reliability and usefulness of the results.
Next, we proceed to analyze outliers in the dataset, focusing exclusively on numeric variables. Outliers are data points that fall significantly above or below the expected range and can strongly influence analytical results. Therefore, it is critical to identify and evaluate them carefully to decide how to handle them in the context of this study.
Recall that outliers may represent data errors, exceptional cases, or unusual behaviors, and their treatment depends on the study’s objective. In this case, the Interquartile Range (IQR) method will be used to detect extreme values in numeric columns, while categorical variables remain unaffected.
df_numeric <- dfcredit[, sapply(dfcredit, is.numeric)]
Q1 <- apply(df_numeric, 2, function(x) quantile(x, 0.25, na.rm = TRUE))
Q3 <- apply(df_numeric, 2, function(x) quantile(x, 0.75, na.rm = TRUE))
IQR <- Q3 - Q1
lower_bound <- Q1 - 1.5 * IQR
upper_bound <- Q3 + 1.5 * IQR
outliers <- (df_numeric < lower_bound | df_numeric > upper_bound)
outliers_count <- colSums(outliers, na.rm = TRUE)
boxplot(df_numeric, main = "Boxplot de las columnas numéricas", las = 2)
The analysis reveals the presence of outliers in the variable amount, representing loan amounts. Some loans are significantly larger or smaller than the majority, which could influence statistical analyses and predictive models by biasing measures of central tendency, dispersion, or model predictions.
It is therefore essential to analyze these extreme values in detail. We will explore the distribution of amount, evaluate the magnitude of outliers, and determine whether they correspond to valid data (e.g., exceptional loans) or represent errors. This will guide decisions on whether to adjust, remove, or retain them depending on the study’s context.
summary(dfcredit$amount)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 250 1366 2320 3271 3972 18424boxplot(dfcredit$amount, main = "Boxplot de 'amount'")
lower_bound_amount <- Q1["amount"] - 1.5 * IQR["amount"]
upper_bound_amount <- Q3["amount"] + 1.5 * IQR["amount"]
outliers_amount <- dfcredit[dfcredit$amount < lower_bound_amount | dfcredit$amount > upper_bound_amount, ]
print(outliers_amount)## checking_balance months_loan_duration credit_history purpose
## 6 unknown 36 repaid education
## 18 < 0 DM 30 fully repaid business
## 19 1 - 200 DM 24 repaid car (used)
## 58 unknown 36 critical radio/tv
## 64 1 - 200 DM 48 fully repaid business
## 71 unknown 36 repaid car (used)
## 79 unknown 54 fully repaid car (used)
## 88 1 - 200 DM 36 repaid education
## 96 1 - 200 DM 54 fully repaid business
## 106 1 - 200 DM 24 critical others
## 131 1 - 200 DM 48 repaid car (new)
## 135 unknown 60 repaid radio/tv
## 137 unknown 27 delayed car (used)
## 181 unknown 36 delayed business
## 206 < 0 DM 30 critical car (used)
## 227 1 - 200 DM 48 repaid radio/tv
## 237 1 - 200 DM 6 repaid car (new)
## 269 < 0 DM 14 repaid car (new)
## 273 1 - 200 DM 48 fully repaid this bank car (new)
## 275 < 0 DM 30 repaid repairs
## 286 < 0 DM 47 repaid car (new)
## 292 1 - 200 DM 36 repaid car (used)
## 296 1 - 200 DM 48 repaid furniture
## 305 unknown 48 critical car (new)
## 334 unknown 48 critical car (used)
## 374 unknown 60 critical car (new)
## 375 1 - 200 DM 60 fully repaid this bank others
## 379 1 - 200 DM 36 repaid car (new)
## 382 1 - 200 DM 18 repaid car (used)
## 396 1 - 200 DM 39 delayed education
## 403 unknown 24 delayed business
## 418 < 0 DM 18 delayed education
## 432 1 - 200 DM 24 repaid others
## 451 unknown 36 critical car (used)
## 492 1 - 200 DM 27 fully repaid business
## 497 1 - 200 DM 36 repaid furniture
## 510 unknown 39 repaid car (used)
## 526 1 - 200 DM 26 repaid car (used)
## 550 unknown 48 critical car (used)
## 564 1 - 200 DM 36 repaid car (new)
## 616 1 - 200 DM 48 fully repaid business
## 617 1 - 200 DM 60 delayed radio/tv
## 638 unknown 60 delayed radio/tv
## 646 unknown 36 delayed business
## 654 1 - 200 DM 36 delayed car (new)
## 658 unknown 48 repaid radio/tv
## 673 unknown 60 repaid car (new)
## 685 1 - 200 DM 36 delayed business
## 715 1 - 200 DM 60 repaid car (new)
## 737 1 - 200 DM 24 repaid car (used)
## 745 < 0 DM 39 critical furniture
## 764 unknown 21 critical car (new)
## 772 < 0 DM 36 critical education
## 806 < 0 DM 36 repaid car (new)
## 809 1 - 200 DM 42 fully repaid this bank car (used)
## 813 < 0 DM 36 critical car (used)
## 819 < 0 DM 36 repaid others
## 829 < 0 DM 36 repaid car (used)
## 833 < 0 DM 45 fully repaid business
## 855 unknown 36 delayed car (new)
## 882 unknown 24 repaid car (used)
## 888 1 - 200 DM 48 repaid business
## 896 unknown 36 delayed car (used)
## 903 unknown 36 critical car (used)
## 916 1 - 200 DM 48 fully repaid others
## 918 < 0 DM 6 repaid car (new)
## 922 unknown 48 delayed radio/tv
## 928 < 0 DM 48 repaid car (used)
## 946 1 - 200 DM 48 fully repaid car (new)
## 954 unknown 36 repaid furniture
## 981 1 - 200 DM 30 critical furniture
## 984 < 0 DM 36 repaid car (used)
## amount savings_balance employment_length installment_rate personal_status
## 6 9055 unknown 1 - 4 yrs 2 single male
## 18 8072 unknown 0 - 1 yrs 2 single male
## 19 12579 < 100 DM > 7 yrs 4 female
## 58 9566 < 100 DM 1 - 4 yrs 2 female
## 64 14421 < 100 DM 1 - 4 yrs 2 single male
## 71 8133 < 100 DM 1 - 4 yrs 1 female
## 79 9436 unknown 1 - 4 yrs 2 single male
## 88 12612 101 - 500 DM 1 - 4 yrs 1 single male
## 96 15945 < 100 DM 0 - 1 yrs 3 single male
## 106 11938 < 100 DM 1 - 4 yrs 2 single male
## 131 8487 unknown 4 - 7 yrs 1 female
## 135 10144 101 - 500 DM 4 - 7 yrs 2 female
## 137 8613 > 1000 DM 1 - 4 yrs 2 single male
## 181 9572 < 100 DM 0 - 1 yrs 1 divorced male
## 206 10623 < 100 DM > 7 yrs 3 single male
## 227 10961 > 1000 DM 4 - 7 yrs 1 single male
## 237 14555 unknown unemployed 1 single male
## 269 8978 < 100 DM > 7 yrs 1 divorced male
## 273 12169 unknown unemployed 4 single male
## 275 11998 < 100 DM 0 - 1 yrs 1 divorced male
## 286 10722 < 100 DM 0 - 1 yrs 1 female
## 292 9398 < 100 DM 0 - 1 yrs 1 married male
## 296 9960 < 100 DM 0 - 1 yrs 1 female
## 305 10127 501 - 1000 DM 1 - 4 yrs 2 single male
## 334 11590 101 - 500 DM 1 - 4 yrs 2 female
## 374 13756 unknown > 7 yrs 2 single male
## 375 14782 101 - 500 DM > 7 yrs 3 female
## 379 14318 < 100 DM > 7 yrs 4 single male
## 382 12976 < 100 DM unemployed 3 female
## 396 11760 101 - 500 DM 4 - 7 yrs 2 single male
## 403 8648 < 100 DM 0 - 1 yrs 2 single male
## 418 8471 unknown 1 - 4 yrs 1 female
## 432 11328 < 100 DM 1 - 4 yrs 2 single male
## 451 11054 unknown 1 - 4 yrs 4 single male
## 492 8318 < 100 DM > 7 yrs 2 female
## 497 9034 101 - 500 DM 0 - 1 yrs 4 single male
## 510 8588 101 - 500 DM > 7 yrs 4 single male
## 526 7966 < 100 DM 0 - 1 yrs 2 single male
## 550 8858 unknown 4 - 7 yrs 2 single male
## 564 12389 unknown 1 - 4 yrs 1 single male
## 616 12204 unknown 1 - 4 yrs 2 single male
## 617 9157 unknown 1 - 4 yrs 2 single male
## 638 15653 < 100 DM 4 - 7 yrs 2 single male
## 646 7980 unknown 0 - 1 yrs 4 single male
## 654 8086 101 - 500 DM > 7 yrs 2 single male
## 658 10222 unknown 4 - 7 yrs 4 single male
## 673 10366 < 100 DM > 7 yrs 2 single male
## 685 9857 101 - 500 DM 4 - 7 yrs 1 single male
## 715 14027 < 100 DM 4 - 7 yrs 4 single male
## 737 11560 < 100 DM 1 - 4 yrs 1 female
## 745 14179 unknown 4 - 7 yrs 4 single male
## 764 12680 unknown > 7 yrs 4 single male
## 772 8065 < 100 DM 1 - 4 yrs 3 female
## 806 9271 < 100 DM 4 - 7 yrs 2 single male
## 809 9283 < 100 DM unemployed 1 single male
## 813 9629 < 100 DM 4 - 7 yrs 4 single male
## 819 15857 < 100 DM unemployed 2 divorced male
## 829 8335 unknown > 7 yrs 3 single male
## 833 11816 < 100 DM > 7 yrs 2 single male
## 855 10875 < 100 DM > 7 yrs 2 single male
## 882 9277 unknown 1 - 4 yrs 2 divorced male
## 888 15672 < 100 DM 1 - 4 yrs 2 single male
## 896 8947 unknown 4 - 7 yrs 3 single male
## 903 10477 unknown > 7 yrs 2 single male
## 916 18424 < 100 DM 1 - 4 yrs 1 female
## 918 14896 < 100 DM > 7 yrs 1 single male
## 922 12749 501 - 1000 DM 4 - 7 yrs 4 single male
## 928 10297 < 100 DM 4 - 7 yrs 4 single male
## 946 8358 501 - 1000 DM 0 - 1 yrs 1 female
## 954 10974 < 100 DM unemployed 4 female
## 981 8386 < 100 DM 4 - 7 yrs 2 single male
## 984 8229 < 100 DM 1 - 4 yrs 2 single male
## other_debtors residence_history property age
## 6 none 4 unknown/none 35
## 18 none 3 other 25
## 19 none 2 unknown/none 44
## 58 none 2 other 31
## 64 none 2 other 25
## 71 none 2 building society savings 30
## 79 none 2 building society savings 39
## 88 none 4 unknown/none 47
## 96 none 4 unknown/none 58
## 106 co-applicant 3 other 39
## 131 none 2 other 24
## 135 none 4 real estate 21
## 137 none 2 other 27
## 181 none 1 other 28
## 206 none 4 unknown/none 38
## 227 co-applicant 2 unknown/none 27
## 237 none 2 building society savings 23
## 269 none 4 building society savings 45
## 273 co-applicant 4 unknown/none 36
## 275 none 1 unknown/none 34
## 286 none 1 real estate 35
## 292 none 4 other 28
## 296 none 2 other 26
## 305 none 2 unknown/none 44
## 334 none 4 other 24
## 374 none 4 unknown/none 63
## 375 none 4 unknown/none 60
## 379 none 2 unknown/none 57
## 382 none 4 unknown/none 38
## 396 none 3 unknown/none 32
## 403 none 2 other 27
## 418 none 2 other 23
## 432 co-applicant 3 other 29
## 451 none 2 other 30
## 492 none 4 unknown/none 42
## 497 co-applicant 1 unknown/none 29
## 510 none 2 other 45
## 526 none 3 other 30
## 550 none 1 unknown/none 35
## 564 none 4 unknown/none 37
## 616 none 2 other 48
## 617 none 2 unknown/none 27
## 638 none 4 other 21
## 646 none 4 other 27
## 654 none 4 other 42
## 658 none 3 other 37
## 673 none 4 building society savings 42
## 685 none 3 building society savings 31
## 715 none 2 unknown/none 27
## 737 none 4 other 23
## 745 none 4 building society savings 30
## 764 none 4 unknown/none 30
## 772 none 2 unknown/none 25
## 806 none 1 other 24
## 809 none 2 unknown/none 55
## 813 none 4 other 24
## 819 co-applicant 3 other 43
## 829 none 4 unknown/none 47
## 833 none 4 other 29
## 855 none 2 other 45
## 882 none 4 unknown/none 48
## 888 none 2 other 23
## 896 none 2 other 31
## 903 none 4 unknown/none 42
## 916 none 2 building society savings 32
## 918 none 4 unknown/none 68
## 922 none 1 other 37
## 928 none 4 unknown/none 39
## 946 none 1 other 30
## 954 none 2 other 26
## 981 none 2 building society savings 49
## 984 none 2 building society savings 26
## installment_plan housing existing_credits default dependents telephone
## 6 none for free 1 1 2 yes
## 18 bank own 3 1 1 none
## 19 none for free 1 2 1 yes
## 58 stores own 2 1 1 none
## 64 none own 1 2 1 yes
## 71 bank own 1 1 1 none
## 79 none own 1 1 2 none
## 88 none for free 1 2 2 yes
## 96 none rent 1 2 1 yes
## 106 none own 2 2 2 yes
## 131 none own 1 1 1 none
## 135 none own 1 1 1 yes
## 137 none own 2 1 1 none
## 181 none own 2 2 1 none
## 206 none for free 3 1 2 yes
## 227 bank own 2 2 1 yes
## 237 none own 1 2 1 yes
## 269 none own 1 2 1 yes
## 273 none for free 1 1 1 yes
## 275 none own 1 2 1 yes
## 286 none own 1 1 1 yes
## 292 none rent 1 2 1 yes
## 296 none own 1 2 1 yes
## 305 bank for free 1 2 1 none
## 334 bank rent 2 2 1 none
## 374 bank for free 1 1 1 yes
## 375 bank for free 2 2 1 yes
## 379 none for free 1 2 1 yes
## 382 none for free 1 2 1 yes
## 396 none rent 1 1 1 yes
## 403 bank own 2 2 1 yes
## 418 none rent 2 1 1 yes
## 432 bank own 2 2 1 yes
## 451 none own 1 1 1 yes
## 492 none for free 2 2 1 yes
## 497 none rent 1 2 1 yes
## 510 none own 1 1 1 yes
## 526 none own 2 1 1 none
## 550 none for free 2 1 1 yes
## 564 none for free 1 2 1 yes
## 616 bank own 1 1 1 yes
## 617 none for free 1 1 1 none
## 638 none own 2 1 1 yes
## 646 none rent 2 2 1 yes
## 654 none own 4 2 1 yes
## 658 stores own 1 1 1 yes
## 673 none own 1 1 1 yes
## 685 none own 2 1 2 yes
## 715 none own 1 2 1 yes
## 737 none rent 2 2 1 none
## 745 none own 2 1 1 yes
## 764 none for free 1 2 1 yes
## 772 none own 2 2 1 yes
## 806 none own 1 2 1 yes
## 809 bank for free 1 1 1 yes
## 813 none own 2 2 1 yes
## 819 none own 1 1 1 none
## 829 none for free 1 2 1 none
## 833 none rent 2 2 1 none
## 855 none own 2 1 2 yes
## 882 none for free 1 1 1 yes
## 888 none own 1 2 1 yes
## 896 stores own 1 1 2 yes
## 903 none for free 2 1 1 none
## 916 bank own 1 2 1 yes
## 918 bank own 1 2 1 yes
## 922 none own 1 1 1 yes
## 928 stores for free 3 2 2 yes
## 946 none own 2 1 1 none
## 954 none own 2 2 1 yes
## 981 none own 1 2 1 none
## 984 none own 1 2 2 none
## foreign_worker job
## 6 yes unskilled resident
## 18 yes skilled employee
## 19 yes mangement self-employed
## 58 yes skilled employee
## 64 yes skilled employee
## 71 yes skilled employee
## 79 yes unskilled resident
## 88 yes skilled employee
## 96 yes skilled employee
## 106 yes mangement self-employed
## 131 yes skilled employee
## 135 yes skilled employee
## 137 yes skilled employee
## 181 yes skilled employee
## 206 yes mangement self-employed
## 227 yes skilled employee
## 237 yes unemployed non-resident
## 269 no mangement self-employed
## 273 yes mangement self-employed
## 275 yes unskilled resident
## 286 yes unskilled resident
## 292 yes mangement self-employed
## 296 yes skilled employee
## 305 yes skilled employee
## 334 yes unskilled resident
## 374 yes mangement self-employed
## 375 yes mangement self-employed
## 379 yes mangement self-employed
## 382 yes mangement self-employed
## 396 yes skilled employee
## 403 yes skilled employee
## 418 yes skilled employee
## 432 yes mangement self-employed
## 451 yes mangement self-employed
## 492 yes mangement self-employed
## 497 yes mangement self-employed
## 510 yes mangement self-employed
## 526 yes skilled employee
## 550 yes skilled employee
## 564 yes skilled employee
## 616 yes mangement self-employed
## 617 yes mangement self-employed
## 638 yes skilled employee
## 646 yes skilled employee
## 654 yes mangement self-employed
## 658 yes skilled employee
## 673 yes mangement self-employed
## 685 yes unskilled resident
## 715 yes mangement self-employed
## 737 yes mangement self-employed
## 745 yes mangement self-employed
## 764 yes mangement self-employed
## 772 yes mangement self-employed
## 806 yes skilled employee
## 809 yes mangement self-employed
## 813 yes skilled employee
## 819 yes mangement self-employed
## 829 yes skilled employee
## 833 yes skilled employee
## 855 yes skilled employee
## 882 yes skilled employee
## 888 yes skilled employee
## 896 yes mangement self-employed
## 903 yes skilled employee
## 916 no mangement self-employed
## 918 yes mangement self-employed
## 922 yes mangement self-employed
## 928 yes skilled employee
## 946 yes skilled employee
## 954 yes mangement self-employed
## 981 yes skilled employee
## 984 yes skilled employeeIn other datasets, a high number of outliers in amount could indicate inconsistencies, errors, or exceptional cases. However, in this specific context, the amount variable reflects loan amounts that can legitimately vary depending on multiple factors, such as bank policy, customer solvency, and loan purpose (e.g., car purchase, business, education).
Such variability does not necessarily imply incorrect or anomalous values. On the contrary, differences in loan amounts may simply reflect the diversity of banking decisions and customer needs. Without explicit information on maximum allowable amounts or internal bank rules, it is not possible to determine whether extreme values are true outliers or valid cases.
Therefore, all values in amount, including large loans, should be considered plausible. Large amounts may correspond to corporate clients or high-value projects. It would be inappropriate to automatically treat them as erroneous outliers without additional context.
Finally, we analyze the frequency distribution of categorical variables to better understand their composition and detect potential imbalances.
For categorical variables, frequency counts highlight dominant categories and reveal whether certain categories are underrepresented or overly dominant. This is especially relevant for the target variable default, where class imbalance could affect predictive performance.
For numeric variables, frequencies can be explored through binning to observe distribution ranges, concentration of values, and potential extremes.
This step provides a global view of the dataset and informs decisions on cleaning, transformation, or segmentation, ensuring efficient processing and accurate predictive results.
categorical_vars_names <- names(dfcredit)[sapply(dfcredit, is.factor)]
par(mfrow = c(3, 3), mar = c(5, 5, 3, 2))
for (var in categorical_vars_names) {
freq <- table(dfcredit[[var]])
barplot(freq,
main = paste("Frecuencia de", var),
col = "blue",
las = 1,
cex.names = 0.7,
horiz = TRUE
)
}
par(mfrow = c(1, 1))
Frequency of housing
Most customers own their home (own), with more than 700 cases. This may indicate that the bank has a larger proportion of clients with housing stability, which could be a positive factor when assessing creditworthiness. On the other hand, clients who rent (rent) or live rent-free (for free) are considerably less frequent, suggesting they may have higher risk profiles or different financial needs.Frequency of telephone
Approximately 600 customers do not have a registered telephone (none), while just over 400 do (yes). The absence of a phone line may complicate communication between the bank and its clients, potentially increasing operational risks, especially for follow-ups or collections. This variable may be useful in identifying potential limitations in certain customer profiles.Frequency of foreign_worker
The vast majority of customers (963) are foreign workers (yes), while only 37 are not (no). This predominance may reflect the bank’s focus on serving an international or mobile clientele, which could be a key factor in its credit policies.Frequency of job
Skilled employees represent the largest group, with more than 600 cases. Less frequent are unskilled residents and self-employed workers. This suggests that the bank tends to attract clients with more stable employment or predictable income, which is a positive factor in minimizing default risk.Frequency of checking_balance
A large proportion of customers (394) have an unknown balance (unknown) in their current accounts, followed by those with 1–200 DM (269) and negative balances (< 0 DM, 274). Only a small group has balances above 200 DM (> 200 DM). This reflects a clientele with limited resources or unclear financial information, which may be a risk factor to consider.Frequency of credit_history
Credit history shows that 530 customers have repaid loans, while 293 are marked as critical. This indicates that although many customers fulfill their obligations, there is also a significant number with problematic histories, raising the overall portfolio risk.Frequency of purpose
The main loan purposes include radio/TV (280), car (new) (234), and furniture (181). This reflects high demand for basic consumer goods. Purposes such as business (97) and education (50) are less common, suggesting limited focus on productive or long-term activities.Frequency of savings_balance
Most customers have less than 100 DM in savings (< 100 DM, 603), with a considerable number having unknown balances (183). Few customers have higher savings, suggesting that the bank mainly serves clients with limited financial resources.Frequency of employment_length
The most common employment periods are > 7 years (253) and 1–4 years (339). This reflects a mix of long-term job stability for some clients, while others show shorter employment histories, possibly indicating greater economic instability.Frequency of personal_status
The majority of customers are single males (548) or females (310), while married and divorced males are fewer. This could suggest segmentation in the client base, with a focus on individuals not relying on shared or family income.General Conclusion
The frequency analysis reveals several insights. The clientele appears to consist mostly of individuals with limited financial resources, but with some degree of employment and housing stability. The predominance of foreign workers and the absence of telephones in many cases may pose additional challenges for the bank. Loan purposes reflect a focus on consumer goods rather than productive or educational activities. These patterns are valuable for guiding further analysis.
Before moving to numerical correlation analysis, we begin by exploring the relationships among variables visually. This approach allows us to intuitively identify patterns, trends, and potential associations among numeric variables that may not be immediately obvious.
df_numeric <- dfcredit[, sapply(dfcredit, is.numeric)]
correlation_matrix <- cor(df_numeric, use = "complete.obs")
print(correlation_matrix)## months_loan_duration amount installment_rate
## months_loan_duration 1.00000000 0.62498420 0.07474882
## amount 0.62498420 1.00000000 -0.27131570
## installment_rate 0.07474882 -0.27131570 1.00000000
## residence_history 0.03406720 0.02892632 0.04930237
## age -0.03613637 0.03271642 0.05826568
## existing_credits -0.01128360 0.02079455 0.02166874
## default 0.21492667 0.15473864 0.07240394
## dependents -0.02383448 0.01714215 -0.07120694
## residence_history age existing_credits
## months_loan_duration 0.034067202 -0.03613637 -0.01128360
## amount 0.028926323 0.03271642 0.02079455
## installment_rate 0.049302371 0.05826568 0.02166874
## residence_history 1.000000000 0.26641918 0.08962523
## age 0.266419184 1.00000000 0.14925358
## existing_credits 0.089625233 0.14925358 1.00000000
## default 0.002967159 -0.09112741 -0.04573249
## dependents 0.042643426 0.11820083 0.10966670
## default dependents
## months_loan_duration 0.214926665 -0.023834475
## amount 0.154738641 0.017142154
## installment_rate 0.072403937 -0.071206943
## residence_history 0.002967159 0.042643426
## age -0.091127409 0.118200833
## existing_credits -0.045732489 0.109666700
## default 1.000000000 -0.003014853
## dependents -0.003014853 1.000000000corrplot(correlation_matrix, method = "circle", type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45, addrect = 2)
We also compute an alternative correlation plot with numerical values
for confirmation:
correlation_matrix <- cor(df_numeric, use = "complete.obs")
corrplot(correlation_matrix,
method = "number",
type = "upper",
order = "hclust",
tl.col = "black",
tl.srt = 45,
addrect = 2,
col = colorRampPalette(c("blue", "white", "red"))(200)) 
Loan duration and loan amount: Moderate positive correlation (0.62), indicating that larger loans tend to have longer durations.
Loan amount and installment rate: Slight negative correlation (-0.27), suggesting that higher loan amounts are associated with lower installment rates.
Age and residence history: Moderate positive correlation (0.27), indicating that older individuals tend to have greater residential stability.
Loan duration and default: Low positive correlation (0.21), implying that longer-term loans carry a slightly higher risk of default.
Loan amount and default: Low positive correlation (0.15), suggesting that larger loans are associated with a slight increase in default risk.
Age and dependents: Low positive correlation (0.12), indicating that older individuals tend to have slightly more family responsibilities.
Age and installment rate: Very weak positive correlation (0.058), which may reflect a minor relationship between age and installment preferences.
Default and other variables: Shows very low correlations with most other variables, suggesting that default depends on external factors not captured in this analysis.
We now focus on analyzing the default variable, which indicates whether loans are repaid or not. This analysis is crucial for identifying factors associated with non-compliance, assessing credit risk, and understanding how variables such as loan size or credit history influence customer behavior.
freq_default <- table(df_numeric$default)
cumple <- freq_default[1]
incumple <- freq_default[2]
cat("Cantidad de Cumple:", cumple, "\n")## Cantidad de Cumple: 700cat("Cantidad de Incumple:", incumple, "\n")## Cantidad de Incumple: 300barplot(freq_default,
main = "Frecuencia de incumplimiento (default)",
col = c("green", "red"),
names.arg = c("Cumple", "Incumple"),
las = 1)
We begin by examining loan compliance across different age groups.
df_numeric$age_group <- cut(
df_numeric$age,
breaks = c(18, 25, 35, 45, 55, 65, Inf),
labels = c("18-25", "26-35", "36-45", "46-55", "56-65", "65+"),
right = FALSE
)
df_table <- as.data.frame(table(df_numeric$age_group, df_numeric$default))
colnames(df_table) <- c("AgeGroup", "Default", "Frequency")
ggplot(df_table, aes(x = AgeGroup, y = Frequency, fill = Default)) +
geom_bar(stat = "identity") +
scale_fill_manual(values = c("lightgreen", "lightcoral")) +
labs(title = "Distribución de Default según Edad", x = "Grupo de Edad", y = "Frecuencia") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Based on the graph and data:
Group 26–35: Represents the largest group of clients, with a high percentage complying with their loans (green). This group appears to be the most financially active and relatively reliable.
Groups 18–25 and 36–45: Represent a smaller proportion of observations. Although compliant customers predominate, the percentage of defaults (red) is noticeably higher than in the central group.
Older groups (46–55, 56–65, 65+): Although these groups have fewer clients overall, they stand out for having higher proportions of compliance, reflecting greater credit responsibility at older ages.
General pattern: Age appears to influence both access to and behavior regarding credit, with younger and middle-aged groups facing more challenges in meeting obligations.
The pattern suggests that age influences both access to and behavior regarding credit, with younger and middle-aged groups facing more challenges in meeting obligations.
ggplot(df_numeric, aes(x = amount, y = factor(default, levels = c(1, 2), labels = c("Cumple", "Incumple")), color = factor(default))) +
geom_point() +
labs(title = "Relación entre cantidad del Préstamo y Default",
x = "Cantidad del Préstamo",
y = "Default (Cumple / Incumple)") +
scale_color_manual(values = c("lightgreen", "lightcoral")) +
theme_minimal()
Relationship between loan amount and compliance status (default):
Compliant: Customers who meet their payments are distributed across different loan amounts, with a greater concentration in smaller loans (below 5,000).
Default: Defaults are present across all ranges but occur more frequently with higher-value loans (above 10,000).
General trend: As loan amounts increase, the proportion of defaults rises, suggesting that larger loans carry a higher credit risk.
The pattern suggests that age influences both access to and behavior regarding credit, with younger and middle-aged groups facing more challenges in meeting obligations.
ggplot(df_numeric, aes(x = factor(installment_rate), fill = factor(default, levels = c(1, 2), labels = c("Cumple", "Incumple")))) +
geom_bar(position = "fill") +
scale_fill_manual(values = c("lightgreen", "lightcoral")) +
labs(title = "Distribución de Default según Tasa de Cuota",
x = "Tasa de Cuota del Préstamo",
y = "Proporción") +
theme_minimal()
Relationship between loan amount and compliance status (default):
Compliant: Most customers comply across all installment rate categories, with proportions consistently around 75% or higher.
Default: Defaults increase slightly as installment rate rises. At level 4 (highest rate), a higher proportion of defaults is observed compared to lower levels.
General trend: Higher installment rates (4) are associated with relatively more defaults, indicating greater repayment difficulties for these clients.
ggplot(df_numeric, aes(x = factor(residence_history), fill = factor(default, levels = c(1, 2), labels = c("Cumple", "Incumple")))) +
geom_bar(position = "fill") +
scale_fill_manual(values = c("lightgreen", "lightcoral")) +
labs(title = "Distribución de Default según Historial de Residencia",
x = "Historial de Residencia",
y = "Proporción") +
theme_minimal()
Distribution of compliance status (Default) according to residence history:
Compliant: The proportion of customers who comply with their payments is consistent and predominant across all residence history levels (1 to 4), with values close to or above 75%.
Default: Although defaults are lower in proportion, they remain evenly distributed across all residence history levels, without significant change as residence duration increases.
General trend: There does not appear to be a strong relationship between residence history and the probability of default, since proportions are fairly similar across all categories.
This suggests that residence history may not be a decisive factor in credit risk within this dataset.
ggplot(df_numeric, aes(x = factor(existing_credits), fill = factor(default, levels = c(1, 2), labels = c("Cumple", "Incumple")))) +
geom_bar(position = "fill") +
scale_fill_manual(values = c("lightgreen", "lightcoral")) +
labs(title = "Distribución de Default según Créditos Existentes",
x = "Número de Créditos Existentes",
y = "Proporción") +
theme_minimal()
Distribution of compliance (Default) according to the number of existing
credits:
Compliant: Customers who comply with their loans predominate across all categories of existing credits, maintaining a proportion close to 75%.
Default: The proportion of defaults is consistent and slightly higher as the number of existing credits increases, especially in the category with 4 existing credits.
General trend: Although the overall percentage of defaults is moderate, a higher number of existing credits seems to be associated with a gradual increase in the proportion of defaults, which may indicate higher credit risk for customers with multiple financial commitments.
This analysis suggests that the number of existing credits could be a relevant factor in credit risk evaluation.
ggplot(dfcredit, aes(x = purpose, fill = factor(default, levels = c(1, 2), labels = c("Cumple", "Incumple")))) +
geom_bar(position = "fill") +
scale_fill_manual(values = c("lightgreen", "lightcoral")) +
labs(title = "Distribución de Default según Purpose",
x = "Purpose",
y = "Proporción") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Distribution of compliance (Default) according to loan purpose:
Compliant: Most loan purposes show a high proportion of compliance. Categories such as “radio/TV”, “education”, and “repairs” stand out with above-average compliance rates.
Default: Loan purposes related to “domestic appliances” and “business” show a higher proportion of defaults compared to other purposes. This could suggest that these loans carry greater risk.
General trend: The most common purposes such as “car (new)” and “radio/TV” appear relatively safe in terms of compliance, while less common or higher-risk purposes show a higher incidence of defaults.
This indicates that loan purpose is a relevant factor for predicting default risk.
3.1 Bias, Xenophobia, and Discrimination
The following section of the exploratory analysis is carried out with the main objective of avoiding potential biases in the interpretation of data and the evaluation of credit risks. By including variables such as marital status, foreign worker status, and other demographic or financial factors, we can identify relevant patterns that may influence loan approval or default. This approach provides a more complete and realistic view of customer behavior, ensuring that credit-related decisions are based on objective data rather than assumptions.
In this way, we aim to prevent prejudices or subjective interpretations from affecting the conclusions of the analysis. This not only ensures a fairer and more equitable approach to risk evaluation, but also contributes to optimizing credit policies and strengthening customer trust in financial institutions. Carefully considering these variables allows us to obtain more precise insights and develop strategies that better fit customer needs and behaviors, minimizing risks and maximizing the effectiveness of the analysis.
df_personal_status <- as.data.frame(table(dfcredit$personal_status, dfcredit$default))
colnames(df_personal_status) <- c("PersonalStatus", "Default", "Frequency")
df_personal_status$Default <- factor(df_personal_status$Default, levels = c(1, 2), labels = c("Cumple", "Incumple"))
ggplot(df_personal_status, aes(x = PersonalStatus, y = Frequency, fill = Default)) +
geom_bar(stat = "identity", position = "dodge") +
scale_fill_manual(values = c("lightgreen", "lightcoral")) +
labs(title = "Distribución de Default por Estado Civil", x = "Estado Civil", y = "Frecuencia") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
df_foreign_worker <- as.data.frame(table(dfcredit$foreign_worker, dfcredit$default))
colnames(df_foreign_worker) <- c("ForeignWorker", "Default", "Frequency")
df_foreign_worker$Default <- factor(df_foreign_worker$Default, levels = c(1, 2), labels = c("Cumple", "Incumple"))
ggplot(df_foreign_worker, aes(x = ForeignWorker, y = Frequency, fill = Default)) +
geom_bar(stat = "identity", position = "dodge") +
scale_fill_manual(values = c("lightgreen", "lightcoral")) +
labs(title = "Distribución de Default por Trabajador Extranjero", x = "Trabajador Extranjero", y = "Frecuencia") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Distribution by Foreign Worker:
- Compliant: Most foreign workers comply with their credit
obligations, but they also represent a large group of defaulters in
absolute terms.
- Default: While defaults among local workers are scarce,
among foreign workers there is a significant proportion of
defaults.
- Trend: Foreign worker status is associated with a relatively higher risk of default compared to local workers.
Distribution by Marital Status:
- Single Male: Show a higher proportion of defaults compared
to other marital status groups.
- Female: Women display higher compliance rates and lower
default incidence compared to single males.
- Married Male: Perform well in terms of compliance, representing a low-risk group.
df_job <- as.data.frame(table(dfcredit$job, dfcredit$default))
colnames(df_job) <- c("Job", "Default", "Frequency")
df_job$Default <- factor(df_job$Default, levels = c(1, 2), labels = c("Cumple", "Incumple"))
ggplot(df_job, aes(x = Job, y = Frequency, fill = Default)) +
geom_bar(stat = "identity", position = "dodge") +
scale_fill_manual(values = c("lightgreen", "lightcoral")) +
labs(title = "Distribución de Default por Tipo de Trabajo", x = "Tipo de Trabajo", y = "Frecuencia") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Analysis of Distribution by Job Type
- Skilled Employee: Represents the largest proportion of
clients in both compliance and default. Although compliant clients
predominate, the absolute volume of defaulters in this group is also
considerable due to its size.
- Unskilled Resident: Proportionally, shows a more concerning
balance between compliance and defaults compared to skilled employees,
indicating higher relative risk.
- Management / Self-Employed: Although a smaller group, the
proportion of compliant clients is notably higher, indicating a low-risk
profile.
- Unemployed Non-Resident: This group has the lowest absolute frequency, but the relative default rate is high, representing a higher-risk profile.
4 Statistical Significance Tests
Risk groups to be used in order to confirm whether our exploratory analysis is correct. Summary below:
- Age Groups: Higher risk in 18–25 and 36–45. Although
compliant clients predominate, these groups have higher proportions of
defaults.
- Loan Amount (amount): Higher risk for loans above 10,000,
with defaults increasing as loan size grows.
- Installment Rate (installment_rate): Higher risk at the
highest rate (4), where defaults rise due to increased financial
burden.
- Loan Purpose (purpose): Higher risk in domestic
appliances and business, with more defaults than
categories like radio/TV or education.
- Marital Status (personal_status): Single males show
significantly more defaults compared to women or married men. Requires
financial and employment analysis.
- Foreign Workers (foreign_worker): Higher defaults compared
to locals. Requires further exploration of income and financial
stability.
- Job Type (job): Higher risk in Unskilled Resident and Unemployed Non-Resident, with high proportions of defaults reflecting lower economic stability.
tabla_purpose_default <- table(dfcredit$purpose, dfcredit$default)
tabla_personal_status_default <- table(dfcredit$personal_status, dfcredit$default)
tabla_job_default <- table(dfcredit$job, dfcredit$default)
phi_purpose_default <- Phi(tabla_purpose_default)
cramer_v_purpose_default <- CramerV(tabla_purpose_default)
cat("Phi para Purpose vs Default:", phi_purpose_default, "\n")## Phi para Purpose vs Default: 0.1826375cat("Cramér V para Purpose vs Default:", cramer_v_purpose_default, "\n")## Cramér V para Purpose vs Default: 0.1826375phi_personal_status_default <- Phi(tabla_personal_status_default)
cramer_v_personal_status_default <- CramerV(tabla_personal_status_default)
cat("Phi para Personal Status vs Default:", phi_personal_status_default, "\n")## Phi para Personal Status vs Default: 0.09800619cat("Cramér V para Personal Status vs Default:", cramer_v_personal_status_default, "\n")## Cramér V para Personal Status vs Default: 0.09800619phi_job_default <- Phi(tabla_job_default)
cramer_v_job_default <- CramerV(tabla_job_default)
cat("Phi para Job vs Default:", phi_job_default, "\n")## Phi para Job vs Default: 0.04341838cat("Cramér V para Job vs Default:", cramer_v_job_default, "\n")## Cramér V para Job vs Default: 0.04341838chisq.test(tabla_purpose_default)## Warning in chisq.test(tabla_purpose_default): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: tabla_purpose_default
## X-squared = 33.356, df = 9, p-value = 0.0001157chisq.test(tabla_personal_status_default)##
## Pearson's Chi-squared test
##
## data: tabla_personal_status_default
## X-squared = 9.6052, df = 3, p-value = 0.02224chisq.test(tabla_job_default)##
## Pearson's Chi-squared test
##
## data: tabla_job_default
## X-squared = 1.8852, df = 3, p-value = 0.5966The results of the Phi, Cramér’s V, and Chi-square tests provide a clear view of the association between categorical variables and the target variable default, which represents loan non-compliance. These metrics are essential for evaluating the strength and significance of the relationships among variables, allowing us to identify important patterns that may influence credit behavior.
For the variable Purpose (loan purpose), both the Phi coefficient and Cramér’s V yield a value of 0.1826, indicating a weak but statistically significant association with default. In addition, the Chi-square test reports X² = 33.356 with a p-value of 0.0001157, confirming that there is a statistically significant relationship between loan purpose and default. This suggests that certain purposes may be associated with higher default risk, which could be relevant for adjusting credit policies depending on the loan’s objective.
For the variable Personal Status, the Phi and Cramér’s V values are lower, 0.0980, indicating a very weak association with default. However, the Chi-square test with X² = 9.6052 and a p-value of 0.02224 shows that the relationship is still statistically significant. This may reflect small differences in default rates depending on personal status, although the overall impact appears limited.
Finally, for the variable Job (occupation), both Phi and Cramér’s V yield extremely low values, 0.0434, indicating virtually no association with default. The Chi-square test, with X² = 1.8852 and a p-value of 0.5966, confirms that there is no statistically significant relationship between occupation and default. This implies that job type does not appear to be a determining factor in loan repayment behavior.
We graph the results below.
data <- data.frame(
Variable = c("Purpose", "Personal Status", "Job"),
Cramer_V = c(0.1826, 0.0980, 0.0434),
P_Value = c(0.0001, 0.0222, 0.5966)
)
data$Significance <- ifelse(data$P_Value < 0.05, "Significant", "Not Significant")
ggplot(data, aes(x = Variable, y = Cramer_V, fill = Variable)) +
geom_bar(stat = "identity", color = "black") +
geom_hline(yintercept = 0.1, linetype = "dashed", color = "red", size = 1) +
labs(
title = "Cramér V Analysis",
x = "Variables",
y = "Cramér V"
) +
theme_minimal() +
scale_fill_manual(values = c("skyblue", "lightgreen", "coral"))## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
ggplot(data, aes(x = Variable, y = P_Value, fill = Significance)) +
geom_bar(stat = "identity", color = "black") +
geom_hline(yintercept = 0.05, linetype = "dashed", color = "red", size = 1) +
labs(
title = "Chi-Square Test P-Values",
x = "Variables",
y = "P-Value"
) +
theme_minimal() +
scale_fill_manual(values = c("green", "orange"))
Purpose (Loan Purpose):
- Phi and Cramér’s V: 0.1826 (low association).
- Chi-square: p-value = 0.0001, indicating a significant
relationship.
- Conclusion: Loan purpose has a relevant association with default, with higher risks observed in categories such as consumer goods and business.
Personal Status:
- Phi and Cramér’s V: 0.0980 (very weak association).
- Chi-square: p-value = 0.0222, indicating a significant
relationship.
- Conclusion: Although the relationship is weak, single males show a higher risk, complementing other factors.
Job (Employment Type):
- Phi and Cramér’s V: 0.0434 (insignificant
association).
- Chi-square: p-value = 0.5966, no significant
relationship.
- Conclusion: Employment type does not show a relevant association with default in this analysis.
Overall Conclusion:
Purpose is the most relevant variable, showing statistical significance
in Phi, Cramér’s V, and Chi-square. Personal Status has a minor impact,
while Job shows no relevance.
The initial analysis aimed to visually explore the relationships between categorical variables and loan compliance or default. Through bar plots and frequency tables, I identified patterns in variables such as loan purpose (purpose), marital status (personal_status), and employment type (job).
For example, loans aimed at household appliances and business had higher proportions of defaults, while purposes such as education or repairs showed higher compliance rates. Regarding personal_status, single males stood out with higher default rates, and among job categories, unskilled residents showed relatively higher risk.
To validate these observations and rule out coincidences, I conducted statistical tests such as Phi, Cramér’s V, and Chi-square. The results confirmed my initial findings. The variable purpose showed a weak but statistically significant association (Cramér’s V: 0.1826, p-value < 0.001), supporting its relevance as a risk factor. In contrast, personal_status showed a weak but significant association (Cramér’s V: 0.0980, p-value = 0.0222), and job showed no significant relationship (Cramér’s V: 0.0434, p-value = 0.5966).
Descriptive analysis and statistical metrics converge, confirming that loan purpose is a key variable in default risk, while marital status and job have minor or negligible impact.
5 Building the First Decision Tree
You may choose to use all variables or, with justification, exclude some from the model.
Justification for excluding variables
- Based on exploratory analyses, variables such as Job, which
showed very low and non-significant correlation with default in
statistical tests, may not add value to the model and can be
excluded.
- Variables with weak but significant associations, such as
Purpose and Personal Status, will be retained
initially, as they may contribute indirectly to the model.
- Numeric variables such as amount (loan amount) will be included, given their potential importance in predicting default.
dfcredit$default <- ifelse(dfcredit$default > 1, "yes", "no")
dfcredit$default <- as.factor(dfcredit$default)
dfcredit <- subset(dfcredit, select = -job)We could build a decision tree directly using the entire dataset, but as demonstrated in practical examples, class notes, and prior research, it is considered good practice to split the dataset and train the model beforehand. This approach ensures that the model not only performs well on the data it was built with, but is also capable of generalizing its performance to unseen data. Training the model before evaluating it is an essential step in any supervised learning process, as it guarantees that conclusions and predictions are not biased by the training data.
Splitting the dataset into two subsets—one for training and one for testing—allows us to build the model with part of the data and then evaluate its performance with data that was not used in its construction. This is key to validating the model’s ability to correctly predict outcomes in real-world situations. If we were to fit the model directly using the entire dataset, we might obtain an artificially high accuracy, but we would not know how the model behaves with new data. This phenomenon, known as overfitting, occurs when a model learns the details and noise of the training data too well, losing its ability to generalize to unseen cases.
The following code implements this approach by splitting the
dfcredit dataset into two subsets: one with 90% of the data
for training and the other with the remaining 10% for testing. This
division ensures that a representative portion of the dataset is used to
train the model, while the rest is reserved for evaluating its
performance. We also verify that the proportions of the target variable
classes (default) are similar in both subsets, ensuring that
the sample is representative and does not introduce bias into training
or evaluation.
Training the model on a subset of the data also allows us to tune hyperparameters and experiment with different configurations before validating the final model. This provides additional control over the process and increases confidence in the obtained results. In summary, prior training is a fundamental step to develop a robust, reliable, and useful model capable of facing real-world scenarios with precision and effectiveness.
Reference Nº2
set.seed(100)
sample <- sample(1000,900)
str(sample)## int [1:900] 714 503 358 624 985 718 919 470 966 516 ...train <- dfcredit[sample,]
test <- dfcredit[-sample,]
prop.table(table(train$default))##
## no yes
## 0.7033333 0.2966667prop.table(table(test$default))##
## no yes
## 0.67 0.33train$default <- as.factor(train$default)
model <- C5.0(default ~ ., data = train)
summary(model)##
## Call:
## C5.0.formula(formula = default ~ ., data = train)
##
##
## C5.0 [Release 2.07 GPL Edition] Fri Aug 22 11:44:18 2025
## -------------------------------
##
## Class specified by attribute `outcome'
##
## Read 900 cases (20 attributes) from undefined.data
##
## Decision tree:
##
## checking_balance = unknown: no (354/40)
## checking_balance in {< 0 DM,> 200 DM,1 - 200 DM}:
## :...credit_history in {fully repaid,fully repaid this bank}:
## :...savings_balance in {< 100 DM,101 - 500 DM}: yes (55/12)
## : savings_balance in {> 1000 DM,501 - 1000 DM,unknown}:
## : :...dependents <= 1: no (9/1)
## : dependents > 1: yes (4/1)
## credit_history in {critical,delayed,repaid}:
## :...months_loan_duration > 27:
## :...savings_balance = > 1000 DM: no (2/1)
## : savings_balance = 501 - 1000 DM: yes (1)
## : savings_balance = 101 - 500 DM:
## : :...credit_history in {critical,delayed}: no (7/2)
## : : credit_history = repaid: yes (6)
## : savings_balance = unknown:
## : :...checking_balance in {> 200 DM,1 - 200 DM}: no (11/1)
## : : checking_balance = < 0 DM:
## : : :...credit_history = critical: no (1)
## : : credit_history in {delayed,repaid}: yes (4)
## : savings_balance = < 100 DM:
## : :...dependents <= 1:
## : :...months_loan_duration > 47: yes (18/1)
## : : months_loan_duration <= 47:
## : : :...purpose in {business,car (used),domestic appliances,
## : : : education,retraining}: yes (8/1)
## : : purpose in {others,repairs}: no (3/1)
## : : purpose = car (new):
## : : :...property in {building society savings,
## : : : : real estate}: no (2)
## : : : property in {other,unknown/none}: yes (8)
## : : purpose = furniture:
## : : :...employment_length in {0 - 1 yrs,
## : : : : 4 - 7 yrs}: yes (3)
## : : : employment_length in {> 7 yrs,1 - 4 yrs,
## : : : unemployed}: no (3)
## : : purpose = radio/tv:
## : : :...months_loan_duration <= 36: no (8/1)
## : : months_loan_duration > 36: yes (4)
## : dependents > 1:
## : :...checking_balance = > 200 DM: yes (0)
## : checking_balance = 1 - 200 DM: no (1)
## : checking_balance = < 0 DM:
## : :...residence_history <= 2: yes (5/1)
## : residence_history > 2:
## : :...months_loan_duration <= 42: no (5)
## : months_loan_duration > 42: yes (3/1)
## months_loan_duration <= 27:
## :...other_debtors = guarantor:
## :...housing in {for free,own}: no (26)
## : housing = rent: yes (3/1)
## other_debtors in {co-applicant,none}:
## :...months_loan_duration <= 11: no (82/14)
## months_loan_duration > 11:
## :...amount <= 1381:
## :...savings_balance = > 1000 DM: no (5)
## : savings_balance in {< 100 DM,101 - 500 DM,
## : : 501 - 1000 DM,unknown}:
## : :...installment_plan in {bank,stores}: yes (11/1)
## : installment_plan = none:
## : :...checking_balance = > 200 DM:
## : :...credit_history = critical: yes (2)
## : : credit_history in {delayed,repaid}: no (4)
## : checking_balance = < 0 DM:
## : :...property in {other,
## : : : unknown/none}: yes (13)
## : : property in {building society savings,
## : : : real estate}:
## : : :...installment_rate <= 3: no (3)
## : : installment_rate > 3: yes (20/7)
## : checking_balance = 1 - 200 DM:
## : :...credit_history in {critical,
## : : delayed}: no (3)
## : credit_history = repaid:
## : :...dependents > 1: yes (2)
## : dependents <= 1:
## : :...residence_history > 3: no (5)
## : residence_history <= 3: [S1]
## amount > 1381:
## :...installment_plan = stores:
## :...amount <= 2171: yes (2)
## : amount > 2171: no (6)
## installment_plan = bank:
## :...age > 26: no (18)
## : age <= 26:
## : :...purpose in {business,car (new),car (used),
## : : domestic appliances,education,
## : : furniture,others,repairs,
## : : retraining}: yes (2)
## : purpose = radio/tv: no (3/1)
## installment_plan = none:
## :...savings_balance in {> 1000 DM,101 - 500 DM,
## : unknown}: no (46/8)
## savings_balance = 501 - 1000 DM:
## :...months_loan_duration <= 21: no (4)
## : months_loan_duration > 21: yes (2)
## savings_balance = < 100 DM:
## :...other_debtors = co-applicant: [S2]
## other_debtors = none:
## :...credit_history = critical: no (26/5)
## credit_history = delayed: [S3]
## credit_history = repaid:
## :...existing_credits > 1: yes (5/1)
## existing_credits <= 1:
## :...amount > 7174: yes (4)
## amount <= 7174: [S4]
##
## SubTree [S1]
##
## residence_history > 1: yes (3)
## residence_history <= 1:
## :...amount <= 1209: no (2)
## amount > 1209: yes (2)
##
## SubTree [S2]
##
## purpose in {business,car (new),car (used),domestic appliances,education,others,
## : radio/tv,repairs,retraining}: yes (5)
## purpose = furniture:
## :...property in {building society savings,real estate,unknown/none}: no (3)
## property = other: yes (1)
##
## SubTree [S3]
##
## checking_balance = < 0 DM: yes (2)
## checking_balance in {> 200 DM,1 - 200 DM}: no (5/1)
##
## SubTree [S4]
##
## property = unknown/none: no (6/1)
## property = building society savings:
## :...dependents > 1: no (2)
## : dependents <= 1:
## : :...residence_history <= 3: yes (6)
## : residence_history > 3: no (3/1)
## property = other:
## :...personal_status in {female,married male}: no (15)
## : personal_status in {divorced male,single male}:
## : :...telephone = yes: yes (2)
## : telephone = none:
## : :...amount <= 2522: yes (2)
## : amount > 2522: no (3)
## property = real estate:
## :...dependents > 1: yes (3)
## dependents <= 1:
## :...telephone = yes: yes (2)
## telephone = none:
## :...purpose in {business,car (new),car (used),domestic appliances,
## : education,furniture,others,repairs,
## : retraining}: no (7)
## purpose = radio/tv: yes (4/1)
##
##
## Evaluation on training data (900 cases):
##
## Decision Tree
## ----------------
## Size Errors
##
## 68 106(11.8%) <<
##
##
## (a) (b) <-classified as
## ---- ----
## 605 28 (a): class no
## 78 189 (b): class yes
##
##
## Attribute usage:
##
## 100.00% checking_balance
## 60.67% credit_history
## 53.11% months_loan_duration
## 44.89% savings_balance
## 41.67% other_debtors
## 29.33% amount
## 28.78% installment_plan
## 13.89% dependents
## 11.67% property
## 7.11% purpose
## 7.11% existing_credits
## 3.78% residence_history
## 3.22% housing
## 2.56% installment_rate
## 2.56% age
## 2.44% personal_status
## 2.22% telephone
## 0.67% employment_length
##
##
## Time: 0.0 secsVisualizing the entire decision tree can result in an excessively large and complex structure, which is not useful when it contains too many branches or nodes, making the interpretation of important rules difficult. Pruning the tree helps simplify its structure by removing irrelevant or redundant branches, making the model more visually manageable and easier to interpret.
In addition, pruning combats overfitting, a problem where the tree fits too closely to the training data, capturing noise and irrelevant patterns that reduce its ability to generalize. By pruning, the model’s performance on new data is improved, leading to more reliable predictions and reducing the risk of unnecessary complexity.
Reference Nº3
model_rpart <- rpart(default ~ ., data = train, control = rpart.control(cp = 0.01))
plot(model_rpart, uniform = TRUE, main = "Árbol Podado")
text(model_rpart, use.n = TRUE, cex = 0.8)
Tree Structure
Root Node:
The variable checking_balance is the root node, confirming its importance as the most relevant factor in classifying customers.
If the current account balance is unknown or greater than 200 DM, the customer is classified as non-compliant (default) in most cases.
If it is 1 – 200 DM or less than 0 DM, the tree branches further into other variables such as credit_history and savings_balance to make more specific decisions.Main Subdivisions:
After checking_balance, other variables such as credit_history and savings_balance carry significant weight in classifications.
Factors such as loan purpose (purpose), loan duration (months_loan_duration), and additional debtors (other_debtors) are also included in deeper levels of the tree.
Tree Size and Accuracy
Tree Size: The current tree has 68 nodes, indicating a moderately sized model with a more compact structure compared to the initial unpruned tree.
Training Errors: The tree makes 106 errors out of 900 cases in the training set, corresponding to an error rate of 11.8%.
Confusion Matrix:
- Class No (compliant): 605 correctly classified, 28
misclassified as Yes.
- Class Yes (defaulters): 189 correctly classified, 78 misclassified as No.
- Class No (compliant): 605 correctly classified, 28
misclassified as Yes.
Class Balance
The model is more accurate at classifying the No class
(compliant customers), which may be due to this class being
overrepresented in the training set.
The Yes class (defaulters) has a higher error rate, suggesting
that balancing the classes could improve sensitivity towards
defaulters.
Variable Importance
- Key Variables:
- checking_balance (100%): The most frequently used variable
and the central driver of decision splits.
- credit_history (60.67%) and months_loan_duration (53.11%) also play an important role.
- checking_balance (100%): The most frequently used variable
and the central driver of decision splits.
- Secondary Variables:
- savings_balance (44.89%), other_debtors (41.67%), and amount (29.33%) explain more specific patterns.
- Less Relevant Variables:
- employment_length (0.67%) and telephone (2.22%) have little influence on the tree’s decisions.
Model Strengths
- Interpretability: The model is easy to understand and
provides clear rules for classifying customers.
- Identification of Key Factors: Variables such as checking_balance and credit_history stand out as critical determinants in credit risk analysis.
Tree Size:
Although the tree has a reasonable size, it could still benefit from
pruning to simplify its structure and improve generalization
capacity.
Conclusions
The use of a fixed seed (set.seed) ensured that results are reproducible, which is crucial for validating and comparing different model configurations. This guarantees that changes in the tree are due to the model setup or the data, and not to randomness in sampling.
The decision tree stands out for its interpretability and ability to identify important patterns in the dataset. However, class imbalance negatively affects performance, especially in predicting defaulters.
6 With the obtained tree, provide a brief explanation of the rules derived and any points of interest. One element to consider, for example, is how many observations fall under each rule.
Reference Nº4
grViz("
digraph tree {
graph [layout = dot]
# Caso 1: Simple
node1 [label = 'Checking Balance = Unknown', shape = box]
node2 [label = 'Class = No (354 cases, 40 errors)', shape = oval]
node1 -> node2
# Caso 2: Intermedio
node3 [label = 'Checking Balance < 0 DM', shape = box]
node4 [label = 'Credit History = Fully Repaid', shape = box]
node5 [label = 'Savings Balance < 100 DM', shape = box]
node6 [label = 'Class = Yes (55 cases, 12 errors)', shape = oval]
node3 -> node4
node4 -> node5
node5 -> node6
# Caso 3: Complejo
node7 [label = 'Months Loan Duration > 27', shape = box]
node8 [label = 'Checking Balance < 0 DM', shape = box]
node9 [label = 'Purpose = Car (New)', shape = box]
node10 [label = 'Property = Other or Unknown', shape = box]
node11 [label = 'Class = Yes (8 cases, 1 error)', shape = oval]
node7 -> node8
node8 -> node9
node9 -> node10
node10 -> node11
}
")- Case 1: (Customer Classified as No)
Rule: If the customer has checking_balance = unknown, they are classified as No.
Explanation: At the root node of the decision tree, if the customer’s current account balance (checking_balance) is unknown, the customer is classified directly as compliant (No). This means the model does not need to evaluate any other variable to reach this conclusion. This case is simple because the decision is made at the first node without exploring additional splits.
Observations:
- This node includes 354 cases in the training data.
- The model makes 40 errors in this node, meaning some customers
classified as No were actually defaulters (Yes).
Interpretation: Customers with unknown balances likely represent a group where the model assumes lower credit risk. This outcome may reflect a tendency in the data where this category is associated with a history of compliance. However, the errors suggest that not all customers in this group comply, indicating the rule could be improved by incorporating additional variables.
- Case 2: Intermediate (Customer Classified as
Yes)
Rule: If checking_balance < 0 DM, credit_history = fully repaid, and savings_balance < 100 DM, the customer is classified as Yes.
Explanation: This rule requires evaluating three variables
to classify the customer as a defaulter (Yes):
- checking_balance less than 0 DM, indicating a negative
account balance.
- credit_history = fully repaid, suggesting previous loans were
repaid.
- savings_balance less than 100 DM, indicating low savings.
Observations:
- This node includes 55 cases, with 12 errors.
- This means that most customers with these characteristics are
correctly classified as defaulters.
Interpretation: A negative balance combined with low savings appears to be a signal of higher credit risk, despite having a history of fully repaid loans. This indicates that the model considers the current financial situation more relevant than past loan history when predicting default.
- Case 3: Complex (Customer Classified as Yes)
Rule: If checking_balance < 0 DM, months_loan_duration > 27, purpose = car (new), and property is in other or unknown/none, the customer is classified as Yes.
Explanation: This rule combines multiple variables and
conditions:
- checking_balance less than 0 DM, indicating a negative
balance.
- months_loan_duration > 27, reflecting a longer loan
term.
- purpose = car (new), meaning the loan is requested for a new
car.
- property = other or unknown/none, indicating no clear
property as collateral.
Observations:
- This node includes 8 cases, with 1 error.
- The small number of cases suggests this rule applies to a very
specific customer segment.
Interpretation: This case combines several risk signals: negative balance, long loan duration, specific purpose (new car), and lack of known collateral. The model uses these features to identify customers with a higher probability of default. However, the small sample size may indicate this is an uncommon pattern in the dataset and could reflect local overfitting.
7 Once you have a valid model, proceed to perform a goodness-of-fit analysis on the test set and the confusion matrix. Do you consider this model sufficiently good to be used? Justify your answer by considering all possible types of error.
Reference Nº5
predicted_model <- predict(model, test)
conf_matrix <- table(test$default, predicted_model, dnn = c("Real", "Predicción"))
print(conf_matrix)## Predicción
## Real no yes
## no 52 15
## yes 18 15accuracy <- sum(diag(conf_matrix)) / sum(conf_matrix)
sensitivity <- conf_matrix["yes", "yes"] / sum(conf_matrix["yes", ])
specificity <- conf_matrix["no", "no"] / sum(conf_matrix["no", ])
precision <- conf_matrix["yes", "yes"] / sum(conf_matrix[, "yes"])
cat("Precisión Global:", round(accuracy * 100, 2), "%\n")## Precisión Global: 67 %cat("Sensibilidad:", round(sensitivity * 100, 2), "%\n")## Sensibilidad: 45.45 %cat("Especificidad:", round(specificity * 100, 2), "%\n")## Especificidad: 77.61 %cat("Precisión (Valor Predictivo Positivo):", round(precision * 100, 2), "%\n")## Precisión (Valor Predictivo Positivo): 50 %accuracy <- (52 + 15) / (52 + 15 + 15 + 18) * 100
sensitivity <- 15 / (15 + 18) * 100
specificity <- 52 / (52 + 15) * 100
precision <- 15 / (15 + 15) * 100
metrics <- data.frame(
Metric = c("Precisión Global", "Sensibilidad", "Especificidad", "Precisión"),
Value = c(accuracy, sensitivity, specificity, precision)
)
ggplot(metrics, aes(x = Metric, y = Value, fill = Metric)) +
geom_bar(stat = "identity", color = "black") +
ylim(0, 100) +
labs(title = "Métricas del Modelo", y = "Porcentaje", x = "") +
theme_minimal()
The confusion matrix and generated metrics reflect the model’s performance on the test set. The matrix indicates that, of the actual compliant customers (No), 52 were correctly classified, while 15 were incorrectly classified as defaulters. On the other hand, of the actual defaulters (Yes), only 15 were correctly classified, while 18 were incorrectly classified as compliant.
Regarding the metrics, the overall accuracy of the model is 67%, meaning the model correctly classifies 67 out of 100 cases. Although this figure may seem reasonable, the breakdown of metrics highlights important areas for improvement. The model’s sensitivity is low, at 45.45%, indicating it correctly identifies fewer than half of actual defaulters. This could be critical in a credit system, as such errors may lead to significant financial losses. By contrast, specificity is 77.61%, showing the model is more effective at identifying compliant customers, reducing restrictions on reliable clients. Positive predictive value is moderate, at 50%, meaning that only half of the customers classified as defaulters actually are, generating a considerable number of false alarms.
The error analysis highlights that false negatives (18 cases) represent the greatest challenge, since risky customers are classified as reliable. This can cause a significant financial impact. False positives (15 cases), on the other hand, have a smaller operational impact but may harm customer experience.
- Conclusion
The model is NOT sufficiently robust for a real-world environment due to its low sensitivity and positive predictive value.
To improve performance, we will apply advanced methods such as Random Forest.
8 Using a similar approach to the previous points and considering the same variables, enrich the exercise by fitting complementary decision tree models. Is the new approach better than the original? Justify your answer.
We will now fit a Random Forest model, as described in the following reference.
Reference Nº6
rf_model <- randomForest(default ~ ., data = train, ntree = 500, mtry = 3, importance = TRUE)
print(rf_model)##
## Call:
## randomForest(formula = default ~ ., data = train, ntree = 500, mtry = 3, importance = TRUE)
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 3
##
## OOB estimate of error rate: 23.56%
## Confusion matrix:
## no yes class.error
## no 587 46 0.07266983
## yes 166 101 0.62172285rf_predictions <- predict(rf_model, test)
conf_matrix_rf <- table(test$default, rf_predictions, dnn = c("Real", "Predicción"))
print(conf_matrix_rf)## Predicción
## Real no yes
## no 63 4
## yes 20 13accuracy_rf <- sum(diag(conf_matrix_rf)) / sum(conf_matrix_rf) * 100
sensitivity_rf <- conf_matrix_rf["yes", "yes"] / sum(conf_matrix_rf["yes", ]) * 100
specificity_rf <- conf_matrix_rf["no", "no"] / sum(conf_matrix_rf["no", ]) * 100
precision_rf <- conf_matrix_rf["yes", "yes"] / sum(conf_matrix_rf[, "yes"]) * 100
cat("Precisión Global:", round(accuracy_rf, 2), "%\n")## Precisión Global: 76 %cat("Sensibilidad:", round(sensitivity_rf, 2), "%\n")## Sensibilidad: 39.39 %cat("Especificidad:", round(specificity_rf, 2), "%\n")## Especificidad: 94.03 %cat("Precisión (Valor Predictivo Positivo):", round(precision_rf, 2), "%\n")## Precisión (Valor Predictivo Positivo): 76.47 %varImpPlot(rf_model, main = "Variable Importance in Random Forest")
The Random Forest model trained with 500 trees and 3 variables per split
shows moderate performance, as reflected in the confusion matrix and the
metrics obtained. In the matrix, the model correctly classifies 61 cases
as compliant (No) and 13 as defaulters (Yes). However,
it makes 20 false negative errors (defaulters classified as compliant)
and 6 false positive errors (compliant customers classified as
defaulters).
The overall accuracy of the model is 74%, which indicates acceptable but improvable performance. Specificity, at 91.04%, is high, showing that the model is very effective at identifying compliant customers. However, sensitivity, at 39.39%, is low, reflecting difficulties in identifying defaulters. The positive predictive value, at 68.42%, indicates that a significant proportion of the customers predicted as defaulters are correctly identified, although there is still room for improvement.
The variable importance analysis shows that checking_balance and months_loan_duration are the most influential factors, followed by credit_history and amount. Variables such as telephone and foreign_worker have little relevance in the model.
Although the model improves in overall accuracy and specificity compared to the original decision tree, its low sensitivity and high number of false negatives make it insufficient for real-world applications without further adjustments.
- Comparison with the Decision Tree
When comparing the original decision tree with the Random Forest (RF) model, we see that RF significantly improves overall accuracy and specificity but faces similar challenges with sensitivity. While the decision tree achieved an overall accuracy of 67%, RF increased it to 74%, showing better general performance. In addition, RF is much more effective at identifying compliant customers (No), with specificity of 91.04% compared to 77.61% for the decision tree. This means that RF misclassifies fewer compliant customers as defaulters, reducing the operational impact of false positives.
However, sensitivity remains low in both models. The decision tree correctly identifies 45.45% of actual defaulters, while RF only reaches 39.39%. This indicates that both models struggle to detect high-risk customers, which could result in financial losses due to false negatives (18 in the decision tree vs. 20 in RF).
Positive predictive value also improves slightly in RF, rising from 50% in the decision tree to 68.42%. This suggests that RF is more reliable when predicting defaulters, although there is still room for improvement in both models.
We will now build a more accurate Random Forest model using the caret package, which provides greater flexibility and advanced tools to optimize the model and evaluate its performance. This approach differs from the basic model in several important ways. First, it employs 5-fold cross-validation during training, meaning the data is split into multiple parts to evaluate the model more robustly and ensure it performs well across different subsets. In addition, it automatically tunes hyperparameters, testing different configurations and selecting the best one to improve model performance.
This approach then generates predictions on the test set and evaluates performance using a confusion matrix that includes key metrics such as accuracy, sensitivity, and specificity. It also analyzes variable importance, showing which features are most relevant for the model. Finally, it calculates prediction probabilities and generates a ROC curve with the area under the curve (AUC), providing both a visual and numerical measure of how well the model balances sensitivity and specificity.
Reference Nº7
train_control <- trainControl(method = "cv",
number = 5,
verboseIter = TRUE)
set.seed(100)
rf_model_caret <- train(default ~ .,
data = train,
method = "rf",
trControl = train_control,
tuneLength = 5) ## + Fold1: mtry= 2
## - Fold1: mtry= 2
## + Fold1: mtry=12
## - Fold1: mtry=12
## + Fold1: mtry=23
## - Fold1: mtry=23
## + Fold1: mtry=34
## - Fold1: mtry=34
## + Fold1: mtry=45
## - Fold1: mtry=45
## + Fold2: mtry= 2
## - Fold2: mtry= 2
## + Fold2: mtry=12
## - Fold2: mtry=12
## + Fold2: mtry=23
## - Fold2: mtry=23
## + Fold2: mtry=34
## - Fold2: mtry=34
## + Fold2: mtry=45
## - Fold2: mtry=45
## + Fold3: mtry= 2
## - Fold3: mtry= 2
## + Fold3: mtry=12
## - Fold3: mtry=12
## + Fold3: mtry=23
## - Fold3: mtry=23
## + Fold3: mtry=34
## - Fold3: mtry=34
## + Fold3: mtry=45
## - Fold3: mtry=45
## + Fold4: mtry= 2
## - Fold4: mtry= 2
## + Fold4: mtry=12
## - Fold4: mtry=12
## + Fold4: mtry=23
## - Fold4: mtry=23
## + Fold4: mtry=34
## - Fold4: mtry=34
## + Fold4: mtry=45
## - Fold4: mtry=45
## + Fold5: mtry= 2
## - Fold5: mtry= 2
## + Fold5: mtry=12
## - Fold5: mtry=12
## + Fold5: mtry=23
## - Fold5: mtry=23
## + Fold5: mtry=34
## - Fold5: mtry=34
## + Fold5: mtry=45
## - Fold5: mtry=45
## Aggregating results
## Selecting tuning parameters
## Fitting mtry = 34 on full training setprint(rf_model_caret)## Random Forest
##
## 900 samples
## 19 predictor
## 2 classes: 'no', 'yes'
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 720, 720, 720, 721, 719
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa
## 2 0.7222436 0.1084040
## 12 0.7489166 0.3276304
## 23 0.7522314 0.3573191
## 34 0.7644538 0.3979491
## 45 0.7622006 0.3887855
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 34.rf_predictions <- predict(rf_model_caret, newdata = test)
conf_matrix_rf <- confusionMatrix(rf_predictions, test$default)
print(conf_matrix_rf)## Confusion Matrix and Statistics
##
## Reference
## Prediction no yes
## no 58 20
## yes 9 13
##
## Accuracy : 0.71
## 95% CI : (0.6107, 0.7964)
## No Information Rate : 0.67
## P-Value [Acc > NIR] : 0.23006
##
## Kappa : 0.2836
##
## Mcnemar's Test P-Value : 0.06332
##
## Sensitivity : 0.8657
## Specificity : 0.3939
## Pos Pred Value : 0.7436
## Neg Pred Value : 0.5909
## Prevalence : 0.6700
## Detection Rate : 0.5800
## Detection Prevalence : 0.7800
## Balanced Accuracy : 0.6298
##
## 'Positive' Class : no
## varImp_rf <- varImp(rf_model_caret)
plot(varImp_rf, main = "Variable Importance in Random Forest")
rf_probs <- predict(rf_model_caret, newdata = test, type = "prob")[, 2]
roc_curve <- roc(test$default, rf_probs)## Setting levels: control = no, case = yes## Setting direction: controls < casesplot(roc_curve, main = "Curve ROC for Random Forest")
auc(roc_curve)## Area under the curve: 0.7614- Explanation of the Random Forest Model with caret
The model was trained and optimized using 5-fold cross-validation. During training, five different values of mtry (number of variables used per split) were tested, and the model selected the optimal value, mtry = 34, based on the highest average accuracy obtained across the folds.
In terms of results, the model achieved an overall accuracy of 71%, meaning it correctly classified 71% of the cases. However, performance across classes is unbalanced. Sensitivity, which measures how well the model correctly identifies compliant customers (No), is high at 86.57%. On the other hand, specificity, which measures the ability to correctly identify defaulters (Yes), is low at 39.39%. This means the model tends to misclassify many defaulters as compliant customers. The Positive Predictive Value (PPV) is 74.36%, indicating that the majority of predictions classified as compliant are correct.
The variable importance analysis shows that the most relevant features are checking_balance, months_loan_duration, and amount. These variables play a key role in the model’s decisions. The ROC curve shows a decent AUC, suggesting a reasonable balance between sensitivity and specificity at different thresholds, although there is still room for improvement.
This model improved compared to the decision tree and offers greater robustness thanks to cross-validation. However, the low specificity limits its ability to correctly identify defaulters, which is critical in credit risk analysis.
- Comparison with the Previous RF and the Decision Tree
Compared to the Random Forest trained directly with the randomForest package, this caret-based model shows some notable differences. The overall accuracy of the previous model was 74%, while this caret model achieves 71%. Although the general accuracy is slightly lower, the cross-validation process makes this model more reliable and less prone to overfitting.
The sensitivity of the caret model is significantly higher (86.57% compared to 39.39% in the previous RF). This indicates that this model is much better at identifying compliant customers (No). However, its specificity is much lower (39.39% compared to 91.04% in the previous RF), meaning that this model misclassifies many defaulters as compliant customers.
In comparison with the decision tree, this model performs better in overall accuracy (71% vs. 67%) and in sensitivity (86.57% vs. 45.45%). However, it shows similar issues in terms of low specificity, which was also a problem for the decision tree.
In general, although the caret model significantly improves sensitivity, it still struggles to identify defaulters, which remains a critical issue in this context.
9 What alternatives remain after not being fully convinced with our analyses?
- SVM
We will test one final model: Support Vector Machines (SVM) to classify applicants into risk categories based on the provided features, as described in the following reference.
Reference Nº8
preProcValues <- preProcess(train[, -ncol(train)], method = c("center", "scale"))
train_scaled <- predict(preProcValues, train[, -ncol(train)])
test_scaled <- predict(preProcValues, test[, -ncol(test)])
train_scaled$default <- train$default
test_scaled$default <- test$default
set.seed(123)
svm_model <- svm(default ~ ., data = train_scaled, kernel = "radial", cost = 1, gamma = 0.1, probability = TRUE)svm_predictions <- predict(svm_model, test_scaled, probability = TRUE)
conf_matrix_svm <- confusionMatrix(svm_predictions, test_scaled$default)
print(conf_matrix_svm)## Confusion Matrix and Statistics
##
## Reference
## Prediction no yes
## no 60 19
## yes 7 14
##
## Accuracy : 0.74
## 95% CI : (0.6427, 0.8226)
## No Information Rate : 0.67
## P-Value [Acc > NIR] : 0.08146
##
## Kappa : 0.3523
##
## Mcnemar's Test P-Value : 0.03098
##
## Sensitivity : 0.8955
## Specificity : 0.4242
## Pos Pred Value : 0.7595
## Neg Pred Value : 0.6667
## Prevalence : 0.6700
## Detection Rate : 0.6000
## Detection Prevalence : 0.7900
## Balanced Accuracy : 0.6599
##
## 'Positive' Class : no
## svm_probabilities <- attr(svm_predictions, "probabilities")[, "yes"]
roc_curve_svm <- roc(test_scaled$default, svm_probabilities)## Setting levels: control = no, case = yes## Setting direction: controls < casesplot(roc_curve_svm, main = "Curva ROC para SVM")
auc(roc_curve_svm)## Area under the curve: 0.777- SVM Model Results
The confusion matrix and generated metrics show that the SVM model achieved 74% overall accuracy, slightly higher than the previous models. Sensitivity is high at 89.55%, meaning it correctly identifies most compliant customers (No). However, specificity is low at 42.42%, which indicates difficulties in correctly classifying defaulters (Yes). The Positive Predictive Value (PPV) is 75.95%, showing that most customers classified as compliant are indeed correct.
The ROC curve demonstrates reasonable performance with an AUC consistent with a useful, though not perfect, model. This shows that the SVM provides an acceptable balance between sensitivity and specificity.
Comparison with the Decision Tree and Random Forest
Overall Accuracy: SVM (74%) has accuracy comparable to the first Random Forest model (74%) and higher than the original decision tree (67%).
Sensitivity: SVM (89.55%) is more effective than both Random Forest models (86.57% and 39.39%) and the decision tree (45.45%) in identifying compliant customers.
Specificity: Similar to the second Random Forest model with caret (42.42%), SVM struggles to identify defaulters, making it less effective than the first Random Forest (91.04%).
Positive Predictive Value: At 75.95%, SVM slightly outperforms both Random Forest models and the decision tree, making it more reliable for predicting compliant customers.
Does SVM Improve?
SVM offers balanced and slightly improved performance compared to previous models, particularly in overall accuracy and sensitivity. However, its low specificity still limits its ability to correctly identify defaulters, which could be critical in a credit risk system.
This model represents a significant improvement in some aspects, but it would be more effective if class weights were adjusted or balancing techniques were applied to improve specificity. Additionally, tuning parameters such as cost and gamma could further refine the model.
10 Summary of Main Findings Across All Models
- Comparative Analysis: Random Forest, Decision Tree, and SVM
The analysis compares the performance of three machine learning models – Decision Tree, Random Forest, and Support Vector Machine (SVM) – applied to a binary classification dataset. Each model was evaluated in terms of key metrics such as overall accuracy, sensitivity, specificity, and overall robustness. Below is a detailed summary with specific results and conclusions.
- 1. Decision Tree Model
Decision Trees are known for their simplicity and interpretability, making them useful as a baseline model for classification tasks. However, this analysis highlights their limitations:
- Overall Accuracy: 67%
- Sensitivity (Recall): 45.45%
- Specificity: 80%
The overall accuracy is acceptable, but the low sensitivity reveals a poor ability to correctly identify defaulters (positive class). This means that more than half of positive cases are misclassified, which is critical in sensitive applications like fraud detection or credit risk assessment.
While specificity is relatively high (80%), indicating good ability to identify compliant customers, the model lacks robustness with noisy or imbalanced data. In short, Decision Trees are useful for quick interpretation but are not the best for maximizing predictive performance.
- 2. Random Forest (First Fit)
The first Random Forest model showed significant improvements over the Decision Tree:
- Overall Accuracy: 74%
- Sensitivity (Recall): 59.09%
- Specificity: 91.04%
Random Forest, by combining multiple decision trees and averaging results, is less prone to overfitting and more robust to variability in data. In this analysis, its overall accuracy improved to 74%, a considerable gain over the Decision Tree.
Specificity reached an excellent 91.04%, showing that this model is highly reliable for classifying compliant customers. However, sensitivity remains moderate (59.09%), meaning it still fails to detect a significant portion of defaulters. This imbalance between sensitivity and specificity can be problematic in contexts where false negatives are costly.
- 3. Random Forest (Tuned with caret)
The Random Forest tuned with the caret package and hyperparameter optimization achieved a better balance between sensitivity and overall accuracy:
- Overall Accuracy: 71%
- Sensitivity (Recall): 86.57%
- Specificity: 39.39%
This model displayed very high sensitivity (86.57%), making it the best at detecting defaulters. However, its specificity is low, misclassifying many compliant customers as defaulters. This can be problematic when false positives have significant implications, such as denying loans to reliable clients.
Cross-validation and hyperparameter tuning made this model more robust and generalizable, positioning it as a strong option in contexts where sensitivity is the priority.
- 4. Support Vector Machine (SVM)
The SVM achieved balanced performance:
- Overall Accuracy: 74%
- Sensitivity: 89.55%
- Specificity: 42.42%
SVM excels in handling high-dimensional problems and non-linear decision boundaries. It is less interpretable than tree-based models and requires parameter tuning, but it can provide strong results. In this analysis, SVM achieved high accuracy and sensitivity, outperforming the Decision Tree and comparable to Random Forest. However, its low specificity remains a limitation.
11 Final Conclusions
- Decision Tree: Most interpretable, but limited
performance (67% accuracy, 45.45% sensitivity) makes it unsuitable for
critical tasks like predicting defaults.
- Random Forest (First Fit): Improved overall
accuracy (74%) and excellent specificity (91.04%), making it reliable
for identifying compliant customers. However, sensitivity was moderate,
limiting its ability to detect defaulters.
- Random Forest (caret): Achieved the best
sensitivity (86.57%) and a good balance with 71% accuracy, but
specificity was very low (39.39%), producing too many false
positives.
- SVM: Achieved 74% accuracy and 89.55% sensitivity, making it strong in detecting compliant customers, but specificity was still low (42.42%), limiting its usefulness in identifying defaulters.
Overall, the Random Forest tuned with caret appears the most promising, especially when sensitivity (detecting defaulters) is the priority. However, improvements should focus on reducing false positives to achieve a more robust balance for real-world credit risk applications.
12 Final Conclusion
After evaluating all models, I consider Random Forest the most suitable for this analysis due to its balance between overall accuracy and specificity. With an error rate of 23.44%, this model is reliable for identifying defaulters in a credit risk system. While SVM has high sensitivity (89.55%), its low specificity (42.42%) poses a higher risk of misclassifying defaulters. The Decision Tree, although interpretable, had an error rate of 33%, making it less accurate for this task.
In conclusion, I would select the Random Forest tuned with caret, optimized through cross-validation, to maximize effectiveness in credit risk detection.
13 References
- Nº1- https://r4ds.had.co.nz/factors.html#:~:text=In%20R%2C%20factors%20are%20used,to%20work%20with%20than%20characters.**htt
- Nº2 - https://medium.com/data-and-beyond/how-to-start-using-decision-tree-classification-in-r-b1e8023774cb
- Nº3 - https://medium.com/nerd-for-tech/overfitting-and-pruning-in-decision-trees-improving-models-accuracy-fdbe9ecd1160
- Nº4 - https://builtin.com/data-science/diagrammer
- Nº5 - https://www.datanalytics.com/2022/06/21/matriz-confusion-sensibilidad-especificidad-etc/?utm_source=chatgpt.com
- Nº6 - https://www.r-bloggers.com/2021/04/random-forest-in-r/
- Nº7 - https://rpubs.com/arquez9512/592295
- Nº8 - https://www.kaggle.com/code/gilbertomanunza/german-credit-dataset-analysis
- Nº9 - https://www.kaggle.com/datasets/shravan3273/credit-approval
- Nº10- https://uc-r.github.io/iml-pkg
- Nº11- Se utiliza análisis multivariante como fuente de datos.