Financing College: Anatomy of Parent PLUS Loans
Rhowena Vespa RPh, MBA
2022-05-12
library(distill)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(readr)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──## ✔ ggplot2 3.3.6 ✔ purrr 0.3.4
## ✔ tibble 3.1.7 ✔ stringr 1.4.0
## ✔ tidyr 1.2.0 ✔ forcats 0.5.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()library(knitr)
library(ggplot2)
library("readxl")BACKGROUND
One of the federal loan programs available to help finance college education is the parent PLUS program. This college financing program has increased popularity through the years. It is a loan program for parents of undergraduates to borrow money from the federal government to bridge the gap between the cost of attendance and available financial resources such as student loans, grants, and scholarships. According to the data from over 800 school institutions, there are currently over 273,000 parent borrowers comprising the $ 84.3B outstanding loan balance in this program. There are minimal requirements to qualify for parent PLUS loans, namely being a parent of a dependent student and not have adverse credit history (with exemptions allowed). There is no debt-to-income ratio requirement to secure any loan amount. These minimal requirements have made the loans and college education more accessible to parents, notwithstanding their ability to repay the debt. Parent debt is an inter-generational social science problem. Both parents and children are saddled with loans that threaten their current and future financial security.
RESEARCH AND METHODS
This multifaceted study uses quantitative methods to examine the characteristics of parent PLUS loans including demographic profiles, loan amounts, type of borrowers, and analyze trends on repayment and default rates from over 800 post-secondary schools in the US.
METHODS:
-Data is sourced from March 2022 US Department of Education
College Scorecard
-Missing Not At Random (MNAR) data (e.g. NULL, Privacy
Suppressed) was handled using listwise deletion. Imputation
of MNAR is not preferred as it will give misleading results
-Exploratory data analysis, data visualization and
descriptive statistics.
-Correlation Matrix to evaluate strongly correlated variables
-Simple and multiple regression analyses
-Post hoc test using EMM (Estimated Marginal Means)
-Diagnostic Plots evaluation of regression model Data
loans<- read_excel("LOANS.xlsx",)
Eloans <-na.omit(loans)Eloans<-rename(Eloans, State=STABBR)Eloans<-rename(Eloans,SAT=SAT_AVG)Eloans<- rename(Eloans,COST=COSTT4_A)Eloans <-rename(Eloans,Students=LPPPLUS_CNT)Eloans<- rename(Eloans,Repay5yr=DBRR5_PP_UG_RT) Eloans<- rename(Eloans,Repay10yr=DBRR10_PP_UG_RT)Eloans<- rename(Eloans,Repay20yr=DBRR20_PP_UG_RT)Eloans<- rename(Eloans,ParentLoan=PLUS_DEBT_INST_MD)Eloans<- rename(Eloans,StudentLoan=DEBT_MDN )Eloans<-rename(Eloans, Default3yr=BBRR3_PP_UG_DFLT)Eloans<- rename(Eloans,NoDegree=OMENRUP_ALL_POOLED_SUPP)Eloans<-rename(Eloans, PellBorrowerLoan=PLUS_DEBT_INST_PELL_MD)Eloans<- rename(Eloans,NoPellBorrowerLoan=PLUS_DEBT_INST_NOPELL_MD)Eloans<-rename(Eloans,Parents=BBRR1_PP_UG_N)dim(Eloans)## [1] 865 35Sum of Total outstanding Parent PLUS Loan balance
TPL<-sum(Eloans$LPPPLUS_AMT)
print(paste("Total outstanding Parent PLUS Loan balance is",TPL))## [1] "Total outstanding Parent PLUS Loan balance is 84303788470"Sum of Number of students associated with outstanding Parent PLUS Loan balances
TSL<-sum(Eloans$Students)
print(paste("Total Number of students associated with outstanding Parent PLUS Loan balances is", TSL))## [1] "Total Number of students associated with outstanding Parent PLUS Loan balances is 2730197"LOAN DISTRIBUTION ACROSS THE US
Fig 1. Who is borrowing how much?
Method: Descriptive Statistics
ggplot(Eloans, aes(x = State , y= Parents, fill = COST)) +
geom_bar(position="dodge",stat = "identity") +
labs(x = "State",
y = "Parents with Loans",
title = "Number of Parents who took Loans vs Cost to attend
(One Academic Year Data)") +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1,size=8),
axis.text.y = element_text(size=12),
axis.title.y = element_text(size=12),
axis.title.x = element_text(size=12),
plot.title = element_text(size=12,hjust=0.5))
Observation
-One Year Data Distribution
-Pennsylvania had highest number of parent PLUS borrowers followed by
Arizona,Texas and Michigan, ave cost of attendance <$40,000
-New York has highest ave cost of attendance > $40,000
-California has a mix of high and mid-level ave cost of attendance.
-Mean parent PLUS loans =$15,551
-Ave cost of attendance =$27,548LOAN AMOUNTS AND SCHOOL SELECTIVITY
Fig 2. Where are the loans disbursed?
Method: Regression Analysis
library(hexbin)
ggplot(Eloans, aes(SAT, ParentLoan)) +
geom_hex(bins = 20, color = "white")+
scale_fill_gradient(low = "#00AFBB", high = "#FC4E07")+
theme_minimal() +
geom_smooth(method = "lm") +
ggtitle( "Loans Distribution Across Selective Universities (p-value<0.05)" )+
theme(axis.text=element_text(size=14),
axis.title=element_text(size=14,face="bold"))## `geom_smooth()` using formula 'y ~ x'
SAT_lm<-lm(ParentLoan~SAT,Eloans)
summary(SAT_lm)##
## Call:
## lm(formula = ParentLoan ~ SAT, data = Eloans)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21865 -6885 -1560 4992 66762
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -42600.486 3577.839 -11.91 <2e-16 ***
## SAT 58.120 3.101 18.74 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10420 on 863 degrees of freedom
## Multiple R-squared: 0.2893, Adjusted R-squared: 0.2885
## F-statistic: 351.3 on 1 and 863 DF, p-value: < 2.2e-16Observations
-Figure 2 shows positive correlation between parent PLUS loan amounts and average SAT scores at the institutions.
-Higher loan amounts are disbursed at more selective schools with higher SAT score averages
-Universities with mid-range SAT scores disbursed more loans < $25,000BORROWER BEHAVIOR
Fig 3. Does Income Influence Borrower Behavior?
Method: Regression Analysis
The maximum 4-year undergraduate student loan is $27,000 at an interest rate of 3.73% while parent loans have no limit and a higher interest rate of 6.28%. This study used regression analysis to compare borrowing behaviors between 2 groups namely Pell and Non-Pell Grant recipients. Pell grants are need based awards that does not have to be repaid and are available only to undergraduates who display exceptional financial need. Most Pell grants are awarded to 90.6% of parent of households with income < $20,000 and 86.7% of parents with income 20K-40K. The mean debt of parent of Pell grant recipients is $18,412 vs non-Pell grant recipients with $30,821.
PPL2<-lm(ParentLoan~PellBorrowerLoan, Eloans)
summary(PPL2)##
## Call:
## lm(formula = ParentLoan ~ PellBorrowerLoan, data = Eloans)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20307 -2563 -1041 1338 32771
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.962e+03 3.358e+02 8.819 <2e-16 ***
## PellBorrowerLoan 1.150e+00 1.605e-02 71.623 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4689 on 863 degrees of freedom
## Multiple R-squared: 0.856, Adjusted R-squared: 0.8558
## F-statistic: 5130 on 1 and 863 DF, p-value: < 2.2e-16PPL1<-lm(ParentLoan~NoPellBorrowerLoan, Eloans)
summary(PPL1)##
## Call:
## lm(formula = ParentLoan ~ NoPellBorrowerLoan, data = Eloans)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14541.6 -1441.7 303.1 1717.2 21088.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.704e+02 2.656e+02 -2.9 0.00382 **
## NoPellBorrowerLoan 8.079e-01 7.779e-03 103.9 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3363 on 863 degrees of freedom
## Multiple R-squared: 0.9259, Adjusted R-squared: 0.9258
## F-statistic: 1.079e+04 on 1 and 863 DF, p-value: < 2.2e-16L1<-ggplot(Eloans, aes(x = StudentLoan,y = PellBorrowerLoan)) +
geom_point(color=2) +
geom_smooth(method = "lm") +
labs(x="Student Loan Amounts", y="Parent Loan Amounts", title = "Pell Grant Recipients
(𝑅²: 0.856,p-value: < 0.05)")L2<-ggplot(Eloans, aes(x = StudentLoan,y = NoPellBorrowerLoan)) +
geom_point(color=2) +
geom_smooth(method = "lm") +
labs(x="Student Loan Amounts", y="Parent Loan Amounts", title = "Non-Pell Grant Recipents
(𝑅²:0.9259,p-value: < 0.05)")library(see)
plots(L1, L2, n_rows = 1)## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
Default_Cor <- select(Eloans,c("Default3yr","ParentLoan","COST", "Repay5yr", "Repay10yr" , "Repay20yr",
"PellBorrowerLoan","NoPellBorrowerLoan","NoDegree"))Observations
-Student maximum loan amounts for both groups are $27,000
-Low- and moderate-income parents borrowed less amount compared
to moderate-and high-income households.
-However, considering the median household income, the
debt-to-income ratio of low- and moderate-income parents of
Pell grant recipients is much higher than parents of Non-Pell
grant recipients. Parents with higher debt-to-income ratio are
more likely to have difficulty repaying loans.
-Median 3-year default rate of parents loans with Pell grants
is higher at 14% compared to 10% for parents Non-Pell grant
recipients.EXAMINING DEFAULT RATES
Fig 4. What influences default rates?
Method: Correlation Matrix
The College Scorecard has a rich and very wide data on aid, repayment, income, completion, etc on an institutional level. This study is limited to exploring some variables that may be correlated to default rates on parent loans. The correlation matrix to understand default rates factors the following variables: Loan Amounts, Cost of Attendance, 5-,10-,and 20-year Repayment Rates, Pell Grant and Non-Pell Grant Loan Amounts and Degree Completion.
library(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2ggcorr(Default_Cor, nbreaks = 4,low = "steelblue", mid = "white", high = "red", label = TRUE, label_size = 5, hjust = 0.85, layout.exp = 3)
Observation
The two variableswith highest correlation coefficients (positively
correlation) to default rates are:
1.***Repay5yr, (cor 0.6)*** - Undergraduate Parent PLUS Loan
dollar-based 5-year repayment rate
2.***No Degree, (cor 0.5)***- Percentage of all students that did
not receive an award and whose enrollment status is unknown after
leaving this institution within 8 years of entryPREDICTING DEFAULT RATES
Fig 5. Can default rates be predicted?
Method: Regression Analysis, Model Evaluation, Estimated Marginal Means (EMM) Post Hoc Test lm(formula = Default3yr ~ Repay5yr + NoDegree, data = Eloans)
Predicted values of a 3-year default rate using EMM (estimated marginal means) fitted with multiple linear regression model.
Default1 <-lm(Default3yr~Repay5yr+NoDegree, data = Eloans)summary(Default1)##
## Call:
## lm(formula = Default3yr ~ Repay5yr + NoDegree, data = Eloans)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.102440 -0.021622 -0.005443 0.016983 0.131494
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.041400 0.005007 -8.268 5.12e-16 ***
## Repay5yr 0.139053 0.006954 19.995 < 2e-16 ***
## NoDegree 0.111405 0.010970 10.155 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03111 on 862 degrees of freedom
## Multiple R-squared: 0.4659, Adjusted R-squared: 0.4646
## F-statistic: 375.9 on 2 and 862 DF, p-value: < 2.2e-16library(ggeffects)
lm(Default3yr~Repay5yr+NoDegree, data = Eloans) %>%
ggemmeans(terms = c("Repay5yr", "NoDegree")) %>%
plot () +
ggtitle( "EMMEANS:Predicted Values of 3-year Default Rate" )+
theme(axis.text=element_text(size=14),
axis.title=element_text(size=14,face="bold"))## Loading required namespace: emmeans
Observation
The mean percentage of undergraduate student Parent PLUS Loan borrowers in default after 3 years is 14.7%, with a max of 59% (Data from 2,766 institutions)
HIGHER DEFAULT RATE FOR:
-Parents who entered a repayment plan within 5 years of loan disbursement AND
-Parents whose students did not complete a degreeMODEL EVALUATION -Diagnostic Plots
Default_lm<- lm(Default3yr~Repay5yr+NoDegree, data=Eloans)
summary(Default_lm)##
## Call:
## lm(formula = Default3yr ~ Repay5yr + NoDegree, data = Eloans)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.102440 -0.021622 -0.005443 0.016983 0.131494
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.041400 0.005007 -8.268 5.12e-16 ***
## Repay5yr 0.139053 0.006954 19.995 < 2e-16 ***
## NoDegree 0.111405 0.010970 10.155 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03111 on 862 degrees of freedom
## Multiple R-squared: 0.4659, Adjusted R-squared: 0.4646
## F-statistic: 375.9 on 2 and 862 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(Default_lm)
Assumptions: Multicollinearity and Heteroskedascity
performance::check_collinearity(Default_lm)## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF Increased SE Tolerance
## Repay5yr 1.15 1.07 0.87
## NoDegree 1.15 1.07 0.87Low Correlation, No Multicollinearity, regression model is good.
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## liftAssumption: Heteroskesdacity, use Breusch-Pagan test
lmtest::bptest(lm(Default3yr~NoDegree+Repay5yr, data=Eloans))##
## studentized Breusch-Pagan test
##
## data: lm(Default3yr ~ NoDegree + Repay5yr, data = Eloans)
## BP = 20.909, df = 2, p-value = 2.882e-05Result: At p-value <0.05, homoscedasticity rejected in favor of heteroskedasticity
Transformation:
Transformed dependent variable using Box Cox Transformation and applied Breusch-Pagan test
Default_BCMod <- caret::BoxCoxTrans(Eloans$Default3yr)
print(Default_BCMod)## Box-Cox Transformation
##
## 865 data points used to estimate Lambda
##
## Input data summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.02000 0.05000 0.08000 0.08081 0.10000 0.30000
##
## Largest/Smallest: 15
## Sample Skewness: 1.18
##
## Estimated Lambda: 0.1
## With fudge factor, Lambda = 0 will be used for transformationsNEloans <- cbind(Eloans, dist_new=predict(Default_BCMod, Eloans$Default3yr)) # append the transformed variable
head(NEloans) # view the top 6 rows## INSTNM State UGDS SAT COST PCTPELL PCTFLOAN
## 1 Alabama A & M University AL 5271 939 23053 0.7019 0.7361
## 2 University of Alabama at Birmingham AL 13328 1234 24495 0.3512 0.4798
## 3 University of Alabama in Huntsville AL 7785 1319 23917 0.2536 0.3976
## 4 Alabama State University AL 375 946 21866 0.7627 0.8232
## 5 The University of Alabama AL 319 1261 29872 0.1772 0.3802
## 6 Auburn University at Montgomery AL 447 1082 19849 0.4644 0.5391
## LPSTAFFORD_CNT LPSTAFFORD_AMT Students LPPPLUS_AMT Parents BBRR1_PP_NOPELL_N
## 1 32214 952539931 5398 124751228 1062 150
## 2 59241 1805698825 3903 95560297 806 322
## 3 20387 423083320 1444 32335435 289 112
## 4 34809 968253338 4638 98316982 1135 147
## 5 77636 1837713282 12086 676026693 2568 1377
## 6 23837 511627872 1369 18241142 300 73
## BBRR1_PP_PELL_N CDR3 DBRR1_PP_UG_RT Repay5yr Repay10yr Default3yr
## 1 912 0.176 1.155044 1.2040422 0.9109411 0.20
## 2 484 0.063 1.068891 0.9748241 0.6820359 0.08
## 3 177 0.065 1.040121 0.8645943 0.4597370 0.09
## 4 988 0.180 1.140748 1.2583712 0.8876563 0.20
## 5 1191 0.054 1.065396 0.9187667 0.6487990 0.07
## 6 227 0.109 1.097795 1.1208157 0.5972791 0.14
## ParentLoan StudentLoan PPLUS_PCT_HIGH_POOLED_SUPP Repay20yr BBRR3_PP_PELL_N
## 1 16552 15250 30 0.3771945 683
## 2 18586 15085 10 0.4306524 353
## 3 15354 14000 10 0.2390932 155
## 4 18289 17500 25 0.3885780 711
## 5 44851 17671 15 0.3586384 1062
## 6 8000 12000 10 0.4559485 139
## BBRR3_PP_PELL_DFLT BBRR3_PP_NOPELL_DFLT BBRR3_PP_NOPELL_N PellBorrowerLoan
## 1 0.29 0.10 116 15944
## 2 0.14 0.05 249 15304
## 3 0.20 0.20 84 13300
## 4 0.39 0.20 87 16882
## 5 0.10 0.03 1082 38868
## 6 0.20 0.20 64 7507
## NoPellBorrowerLoan PELL_RPY_3YR_RT_SUPP NOPELL_RPY_3YR_RT_SUPP OMENRUP_ALL
## 1 19004 0.2390405 0.3492958 0.3016
## 2 22178 0.4716981 0.5892070 0.1832
## 3 16956 0.4832808 0.6783920 0.1716
## 4 25046 0.2079327 0.3333333 0.2262
## 5 48411 0.5159860 0.7126540 0.0820
## 6 10000 0.3853631 0.5775034 0.2807
## NoDegree OMENRUP_PELL_ALL OMENRUP8_FTFT dist_new
## 1 0.2789 0.3271 0.3243 -1.609438
## 2 0.2017 0.1915 0.1549 -2.525729
## 3 0.1730 0.2063 0.1450 -2.407946
## 4 0.2481 0.2543 0.2229 -1.609438
## 5 0.0813 0.1448 0.0623 -2.659260
## 6 0.2993 0.2945 0.2898 -1.966113lmMod_def <- lm(dist_new ~ NoDegree, data=NEloans)
bptest(lmMod_def)##
## studentized Breusch-Pagan test
##
## data: lmMod_def
## BP = 0.047752, df = 1, p-value = 0.827Result: New p-value = 0.827 after transformation: homoscedasticity not rejected
Evaluate New Diagnostic Plots using Box Cox Transformed Variable
Default_lm2<- lm(dist_new~Repay5yr+NoDegree, data=NEloans)
summary(Default_lm2)##
## Call:
## lm(formula = dist_new ~ Repay5yr + NoDegree, data = NEloans)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.20735 -0.25334 -0.01247 0.29037 1.17292
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.06186 0.06509 -62.402 <2e-16 ***
## Repay5yr 1.58272 0.09041 17.507 <2e-16 ***
## NoDegree 1.40450 0.14261 9.849 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4045 on 862 degrees of freedom
## Multiple R-squared: 0.4149, Adjusted R-squared: 0.4135
## F-statistic: 305.6 on 2 and 862 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(Default_lm2)
CONCLUSION
With rising costs of education, parent PLUS loans have become increasing popular for families. The availability of parent PLUS loans have made post-secondary education accessible to more low- and moderate-income families. The mean cost of attendance per year is $38,144 and the mean parent PLUS loan is $24,131, with a max of $91,987 at an interest rate of 6.28%. According to the US Census Bureau, the median household income in the US is $67,521 The lack of limit of loan amounts and absence of debt-to-income ratio requirement have allowed parents to borrow more than their ability to repay. Comparison of parents of Pell grant recipients and non-Pell grant recipient borrower behavior is alarming. Most Pell grant recipient parents have income <$40,000 and median loan amount of $16,000, with a max of $95,089. Parents who entered repayment with 5 years of loan disbursement with students who did not complete the degree are most likely to default on the loan. This is likely due to personal circumstances such as family obligations or sought employment.
At a default rate of 14.7%, further analysis on this federal loan program is needed to better understand and prevent families from being entrapped in debt and exacerbate wealth disparities across races.
LIMITATIONS OF THE STUDY
-The College Scorecard has data on 6,694 institutions all over the US but
this study is limited to only 865 schools due to missing data (e.g NULL and Privacy Suppressed).
-The most recent data also discontinued collecting information relating to
income, an important variable that could increase statistical power of this
model.
-The researcher used listwise deletion to handle the missing data. Due to
the large size of the missing not at random (MNAR) data, multiple
imputation is not preferred as it may provide misleading results.
-Regression model used to analyze default rates was limited to a couple of
the variables with high correlation coefficients. The College Scorecard
data is a very rich source of information. Unfortunately, the most recent
data have discontinued releasing information on earnings and income.
Further examination and analysis of underlying factors (e.g. race,
first-generation students, gender, family characteristics) could probably
increase the explanatory power of the model.FUTURE WORK: Loan Default Prediction using Decision Tree Classifier
Model currently has low accuracy, possible due to variance of continuous variables.Further work is needed.
Eloans_train_test <- function(Eloans, size = 0.8, train = TRUE) {
n_row = nrow(Eloans)
total_row = size * n_row
train_sample <- 1:total_row
if (train == TRUE) {
return (Eloans[train_sample, ])
} else {
return (Eloans[-train_sample, ])
}
}Eloans_train <-Eloans_train_test(Eloans, 0.8, train = TRUE)
Eloans_test <- Eloans_train_test(Eloans, 0.8, train = FALSE)
dim(Eloans_train)## [1] 692 35dim(Eloans_test)## [1] 173 35prop.table(table(Eloans_train$Default3yr))##
## 0.02 0.03 0.04 0.05 0.06 0.07
## 0.031791908 0.044797688 0.075144509 0.235549133 0.062138728 0.010115607
## 0.08 0.09 0.1 0.11 0.12 0.14
## 0.036127168 0.174855491 0.187861272 0.001445087 0.011560694 0.069364162
## 0.16 0.17 0.18 0.19 0.2 0.22
## 0.007225434 0.002890173 0.002890173 0.031791908 0.005780347 0.004335260
## 0.24 0.3
## 0.002890173 0.001445087prop.table(table(Eloans_test$Default3yr))##
## 0.02 0.03 0.04 0.05 0.06 0.07
## 0.046242775 0.075144509 0.075144509 0.260115607 0.069364162 0.023121387
## 0.08 0.09 0.1 0.12 0.14 0.16
## 0.011560694 0.104046243 0.173410405 0.023121387 0.057803468 0.017341040
## 0.18 0.19 0.2 0.22 0.24
## 0.005780347 0.040462428 0.005780347 0.005780347 0.005780347library(rpart)
library(rpart.plot)
Eloansfit <- rpart(Default3yr~NoDegree+Repay5yr, data = Eloans_train, method = 'anova')
rpart.plot(Eloansfit, extra = 101)
predict(Eloansfit, Eloans_train, type = 'vector')## 1 2 3 4 5 6 7
## 0.19294118 0.13200000 0.09466667 0.19294118 0.10161290 0.19294118 0.07046512
## 8 9 10 11 12 13 14
## 0.07745342 0.07745342 0.14884615 0.19294118 0.09466667 0.07745342 0.07745342
## 15 16 17 18 19 20 21
## 0.19294118 0.05383886 0.09466667 0.07046512 0.13200000 0.19294118 0.09466667
## 22 23 24 25 26 27 28
## 0.07046512 0.05383886 0.13200000 0.07745342 0.13200000 0.09466667 0.07745342
## 29 30 31 32 33 34 35
## 0.13200000 0.05383886 0.05383886 0.05383886 0.07046512 0.09466667 0.07745342
## 36 37 38 39 40 41 42
## 0.05383886 0.09466667 0.05383886 0.05383886 0.09466667 0.05383886 0.05383886
## 43 44 45 46 47 48 49
## 0.09466667 0.05383886 0.05383886 0.05383886 0.05383886 0.05383886 0.05383886
## 50 51 52 53 54 55 56
## 0.05383886 0.05383886 0.07745342 0.05383886 0.07046512 0.07745342 0.07745342
## 57 58 59 60 61 62 63
## 0.05383886 0.09466667 0.13200000 0.05383886 0.05383886 0.07046512 0.09466667
## 64 65 66 67 68 69 70
## 0.09466667 0.07046512 0.05383886 0.05383886 0.05383886 0.07745342 0.05383886
## 71 72 73 74 75 76 77
## 0.05383886 0.05383886 0.07046512 0.05383886 0.05383886 0.07046512 0.05383886
## 78 79 80 81 82 83 84
## 0.07046512 0.05383886 0.07046512 0.07745342 0.09466667 0.07745342 0.05383886
## 85 86 87 88 89 90 91
## 0.05383886 0.07745342 0.05383886 0.07745342 0.07745342 0.07745342 0.07745342
## 92 93 94 95 96 97 98
## 0.05383886 0.09466667 0.07745342 0.14884615 0.07745342 0.05383886 0.07046512
## 99 100 101 102 103 104 105
## 0.10161290 0.10161290 0.07046512 0.09466667 0.19294118 0.07745342 0.14884615
## 106 107 108 109 110 111 112
## 0.07046512 0.05383886 0.05383886 0.14884615 0.10161290 0.19294118 0.09466667
## 113 114 115 116 117 118 119
## 0.07745342 0.07745342 0.07046512 0.14884615 0.09466667 0.07745342 0.09466667
## 120 121 122 123 124 125 126
## 0.10161290 0.09466667 0.07046512 0.07046512 0.13200000 0.07046512 0.05383886
## 127 128 129 130 131 132 133
## 0.14884615 0.09466667 0.09466667 0.09466667 0.07046512 0.13200000 0.07745342
## 134 135 136 137 138 139 140
## 0.07745342 0.14884615 0.14884615 0.05383886 0.13200000 0.13200000 0.05383886
## 141 142 143 144 145 146 147
## 0.14884615 0.05383886 0.07046512 0.09466667 0.13200000 0.05383886 0.07046512
## 148 149 150 151 152 153 154
## 0.09466667 0.14884615 0.05383886 0.09466667 0.10161290 0.14884615 0.09466667
## 155 156 157 158 159 160 161
## 0.14884615 0.09466667 0.10161290 0.09466667 0.09466667 0.09466667 0.07046512
## 162 163 164 165 166 167 168
## 0.09466667 0.07745342 0.07745342 0.09466667 0.07745342 0.07745342 0.09466667
## 169 170 171 172 173 174 175
## 0.07046512 0.05383886 0.07745342 0.05383886 0.09466667 0.05383886 0.07745342
## 176 177 178 179 180 181 182
## 0.05383886 0.05383886 0.05383886 0.07046512 0.07046512 0.07745342 0.07745342
## 183 184 185 186 187 188 189
## 0.07745342 0.05383886 0.09466667 0.07046512 0.05383886 0.05383886 0.07745342
## 190 191 192 193 194 195 196
## 0.09466667 0.10161290 0.07046512 0.07745342 0.10161290 0.07745342 0.05383886
## 197 198 199 200 201 202 203
## 0.07046512 0.05383886 0.07745342 0.05383886 0.05383886 0.05383886 0.07046512
## 204 205 206 207 208 209 210
## 0.07046512 0.09466667 0.09466667 0.09466667 0.09466667 0.13200000 0.07745342
## 211 212 213 214 215 216 217
## 0.09466667 0.05383886 0.09466667 0.07745342 0.07745342 0.05383886 0.05383886
## 218 219 220 221 222 223 224
## 0.05383886 0.05383886 0.07745342 0.07046512 0.07745342 0.05383886 0.07745342
## 225 226 227 228 229 230 231
## 0.07046512 0.07745342 0.05383886 0.09466667 0.09466667 0.07745342 0.05383886
## 232 233 234 235 236 237 238
## 0.05383886 0.05383886 0.05383886 0.09466667 0.07745342 0.05383886 0.05383886
## 239 240 241 242 243 244 245
## 0.05383886 0.07745342 0.07745342 0.07745342 0.05383886 0.07745342 0.07745342
## 246 247 248 249 250 251 252
## 0.07745342 0.07745342 0.05383886 0.07745342 0.07745342 0.07745342 0.07046512
## 253 254 255 256 257 258 259
## 0.09466667 0.09466667 0.09466667 0.19294118 0.07046512 0.09466667 0.07745342
## 260 261 262 263 264 265 266
## 0.09466667 0.07745342 0.09466667 0.09466667 0.19294118 0.07046512 0.09466667
## 267 268 269 270 271 272 273
## 0.13200000 0.09466667 0.13200000 0.09466667 0.19294118 0.09466667 0.07745342
## 274 275 276 277 278 279 280
## 0.14884615 0.07745342 0.07745342 0.07046512 0.07745342 0.07745342 0.14884615
## 281 282 283 284 285 286 287
## 0.07046512 0.07745342 0.05383886 0.07745342 0.05383886 0.07046512 0.19294118
## 288 289 290 291 292 293 294
## 0.14884615 0.07046512 0.05383886 0.05383886 0.07046512 0.10161290 0.05383886
## 295 296 297 298 299 300 301
## 0.05383886 0.05383886 0.05383886 0.07745342 0.09466667 0.14884615 0.07046512
## 302 303 304 305 306 307 308
## 0.07046512 0.07745342 0.07745342 0.05383886 0.05383886 0.07046512 0.07046512
## 309 310 311 312 313 314 315
## 0.07745342 0.05383886 0.07046512 0.07745342 0.05383886 0.07046512 0.09466667
## 316 317 318 319 320 321 322
## 0.07046512 0.05383886 0.07745342 0.07046512 0.05383886 0.07046512 0.05383886
## 323 324 325 326 327 328 329
## 0.07745342 0.05383886 0.05383886 0.13200000 0.05383886 0.05383886 0.05383886
## 330 331 332 333 334 335 336
## 0.07745342 0.07046512 0.09466667 0.09466667 0.07745342 0.07745342 0.07745342
## 337 338 339 340 341 342 343
## 0.05383886 0.07745342 0.09466667 0.07745342 0.05383886 0.05383886 0.05383886
## 344 345 346 347 348 349 350
## 0.07745342 0.09466667 0.07745342 0.09466667 0.09466667 0.09466667 0.07745342
## 351 352 353 354 355 356 357
## 0.09466667 0.07745342 0.09466667 0.07745342 0.05383886 0.05383886 0.05383886
## 358 359 360 361 362 363 364
## 0.07745342 0.05383886 0.05383886 0.07745342 0.07745342 0.07745342 0.07046512
## 365 366 367 368 369 370 371
## 0.07745342 0.05383886 0.07745342 0.05383886 0.19294118 0.09466667 0.10161290
## 372 373 374 375 376 377 378
## 0.13200000 0.14884615 0.09466667 0.05383886 0.07745342 0.07745342 0.07046512
## 379 380 381 382 383 384 385
## 0.07745342 0.09466667 0.07745342 0.07745342 0.09466667 0.05383886 0.07745342
## 386 387 388 389 390 391 392
## 0.05383886 0.09466667 0.05383886 0.07745342 0.07046512 0.05383886 0.07745342
## 393 394 395 396 397 398 399
## 0.07745342 0.07745342 0.05383886 0.05383886 0.07745342 0.07745342 0.07745342
## 400 401 402 403 404 405 406
## 0.07745342 0.05383886 0.07745342 0.05383886 0.05383886 0.07745342 0.07745342
## 407 408 409 410 411 412 413
## 0.05383886 0.05383886 0.09466667 0.05383886 0.05383886 0.07745342 0.05383886
## 414 415 416 417 418 419 420
## 0.10161290 0.13200000 0.10161290 0.05383886 0.10161290 0.07046512 0.07046512
## 421 422 423 424 425 426 427
## 0.07046512 0.05383886 0.10161290 0.09466667 0.07046512 0.07046512 0.14884615
## 428 429 430 431 432 433 434
## 0.10161290 0.05383886 0.07046512 0.05383886 0.09466667 0.09466667 0.10161290
## 435 436 437 438 439 440 441
## 0.05383886 0.05383886 0.05383886 0.05383886 0.05383886 0.05383886 0.09466667
## 442 443 444 445 446 447 448
## 0.07046512 0.07046512 0.07745342 0.05383886 0.10161290 0.05383886 0.07046512
## 449 450 451 452 453 454 455
## 0.13200000 0.05383886 0.09466667 0.07745342 0.09466667 0.14884615 0.07046512
## 456 457 458 459 460 461 462
## 0.05383886 0.10161290 0.10161290 0.05383886 0.07046512 0.10161290 0.19294118
## 463 464 465 466 467 468 469
## 0.09466667 0.09466667 0.07745342 0.07745342 0.05383886 0.05383886 0.07046512
## 470 471 472 473 474 475 476
## 0.09466667 0.05383886 0.09466667 0.05383886 0.07745342 0.05383886 0.10161290
## 477 478 479 480 481 482 483
## 0.07745342 0.07745342 0.07745342 0.07745342 0.09466667 0.09466667 0.05383886
## 484 485 486 487 488 489 490
## 0.05383886 0.05383886 0.05383886 0.05383886 0.07745342 0.05383886 0.09466667
## 491 492 493 494 495 496 497
## 0.05383886 0.05383886 0.05383886 0.05383886 0.05383886 0.05383886 0.05383886
## 498 499 500 501 502 503 504
## 0.09466667 0.05383886 0.05383886 0.07046512 0.10161290 0.07745342 0.05383886
## 505 506 507 508 509 510 511
## 0.10161290 0.09466667 0.07046512 0.07745342 0.14884615 0.05383886 0.05383886
## 512 513 514 515 516 517 518
## 0.05383886 0.10161290 0.10161290 0.09466667 0.07046512 0.19294118 0.09466667
## 519 520 521 522 523 524 525
## 0.13200000 0.07745342 0.07046512 0.09466667 0.14884615 0.05383886 0.07745342
## 526 527 528 529 530 531 532
## 0.07745342 0.14884615 0.05383886 0.14884615 0.05383886 0.07046512 0.10161290
## 533 534 535 536 537 538 539
## 0.10161290 0.13200000 0.07745342 0.07046512 0.14884615 0.05383886 0.07745342
## 540 541 542 543 544 545 546
## 0.07745342 0.09466667 0.05383886 0.05383886 0.09466667 0.09466667 0.07046512
## 547 548 549 550 551 552 553
## 0.05383886 0.05383886 0.05383886 0.09466667 0.09466667 0.05383886 0.09466667
## 554 555 556 557 558 559 560
## 0.09466667 0.09466667 0.09466667 0.05383886 0.09466667 0.07745342 0.07745342
## 561 562 563 564 565 566 567
## 0.05383886 0.05383886 0.07046512 0.07745342 0.07745342 0.07745342 0.09466667
## 568 569 570 571 572 573 574
## 0.09466667 0.05383886 0.05383886 0.09466667 0.07046512 0.05383886 0.09466667
## 575 576 577 578 579 580 581
## 0.09466667 0.10161290 0.07046512 0.07745342 0.07745342 0.07745342 0.05383886
## 582 583 584 585 586 587 588
## 0.09466667 0.09466667 0.09466667 0.07745342 0.07745342 0.07745342 0.09466667
## 589 590 591 592 593 594 595
## 0.05383886 0.05383886 0.13200000 0.07745342 0.07745342 0.09466667 0.05383886
## 596 597 598 599 600 601 602
## 0.05383886 0.05383886 0.07745342 0.07745342 0.05383886 0.05383886 0.09466667
## 603 604 605 606 607 608 609
## 0.05383886 0.07745342 0.07745342 0.07745342 0.05383886 0.07745342 0.07046512
## 610 611 612 613 614 615 616
## 0.07046512 0.05383886 0.05383886 0.09466667 0.09466667 0.09466667 0.05383886
## 617 618 619 620 621 622 623
## 0.09466667 0.09466667 0.09466667 0.09466667 0.05383886 0.09466667 0.07745342
## 624 625 626 627 628 629 630
## 0.07745342 0.05383886 0.07745342 0.05383886 0.09466667 0.09466667 0.09466667
## 631 632 633 634 635 636 637
## 0.09466667 0.09466667 0.09466667 0.09466667 0.07745342 0.05383886 0.14884615
## 638 639 640 641 642 643 644
## 0.09466667 0.05383886 0.09466667 0.07046512 0.05383886 0.07745342 0.07046512
## 645 646 647 648 649 650 651
## 0.14884615 0.09466667 0.07046512 0.05383886 0.05383886 0.07745342 0.07745342
## 652 653 654 655 656 657 658
## 0.07745342 0.05383886 0.07745342 0.09466667 0.09466667 0.07745342 0.07745342
## 659 660 661 662 663 664 665
## 0.05383886 0.05383886 0.07745342 0.05383886 0.13200000 0.07046512 0.05383886
## 666 667 668 669 670 671 672
## 0.05383886 0.07046512 0.05383886 0.07745342 0.09466667 0.07046512 0.05383886
## 673 674 675 676 677 678 679
## 0.05383886 0.09466667 0.05383886 0.07745342 0.05383886 0.05383886 0.07745342
## 680 681 682 683 684 685 686
## 0.10161290 0.19294118 0.05383886 0.07046512 0.19294118 0.05383886 0.13200000
## 687 688 689 690 691 692
## 0.07046512 0.13200000 0.13200000 0.09466667 0.07046512 0.10161290predict_unseen <-predict(Eloansfit, Eloans_test, type = 'vector')Eloans_mat <- table(Eloans_test$Default3yr, predict_unseen)
Eloans_mat## predict_unseen
## 0.0538388625592417 0.0704651162790697 0.0774534161490683
## 0.02 5 0 3
## 0.03 10 0 3
## 0.04 3 4 4
## 0.05 15 8 17
## 0.06 1 2 5
## 0.07 0 0 1
## 0.08 0 0 0
## 0.09 1 5 3
## 0.1 4 4 11
## 0.12 0 1 0
## 0.14 0 0 0
## 0.16 0 1 0
## 0.18 0 0 0
## 0.19 0 1 3
## 0.2 0 0 0
## 0.22 0 0 0
## 0.24 0 0 0
## predict_unseen
## 0.0946666666666665 0.101612903225806 0.132 0.148846153846154
## 0.02 0 0 0 0
## 0.03 0 0 0 0
## 0.04 2 0 0 0
## 0.05 4 1 0 0
## 0.06 3 0 1 0
## 0.07 3 0 0 0
## 0.08 2 0 0 0
## 0.09 6 3 0 0
## 0.1 9 1 0 1
## 0.12 2 0 0 0
## 0.14 6 1 1 1
## 0.16 0 0 0 1
## 0.18 0 0 0 1
## 0.19 1 1 0 0
## 0.2 0 0 0 0
## 0.22 0 0 0 1
## 0.24 0 0 0 0
## predict_unseen
## 0.192941176470588
## 0.02 0
## 0.03 0
## 0.04 0
## 0.05 0
## 0.06 0
## 0.07 0
## 0.08 0
## 0.09 0
## 0.1 0
## 0.12 1
## 0.14 1
## 0.16 1
## 0.18 0
## 0.19 1
## 0.2 1
## 0.22 0
## 0.24 1accuracy_Test <- sum(diag(Eloans_mat)) / sum(Eloans_mat)
print(paste('Accuracy for test', accuracy_Test))## [1] "Accuracy for test 0.0751445086705202"FUTURE WORK: Loan Default Prediction using Random Forest
Random Forest using mtry=3 and 500 trees has been initiated Need to continue work on running and testing the model, confusionMatrix and importance plots
Eloans <-select(Eloans,-c(INSTNM))library(randomForest)## randomForest 4.7-1## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:ggplot2':
##
## margin## The following object is masked from 'package:dplyr':
##
## combinelibrary(caret)
library(e1071)Eloans.rf <- randomForest(Default3yr~ ., data = Eloans, mtry = 3,
importance = TRUE, na.action = na.omit)
print(Eloans.rf)##
## Call:
## randomForest(formula = Default3yr ~ ., data = Eloans, mtry = 3, importance = TRUE, na.action = na.omit)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 3
##
## Mean of squared residuals: 0.000375702
## % Var explained: 79.2Etrain_test <- function(Eloans, size = 0.8, train = TRUE) {
n_row = nrow(Eloans)
total_row = size * n_row
train_sample <- 1:total_row
if (train == TRUE) {
return (Eloans[train_sample, ])
} else {
return (Eloans[-train_sample, ])
}
}Etrain <-Etrain_test(Eloans, 0.8, train = TRUE)
Etest <- Etrain_test(Eloans, 0.8, train = FALSE)
dim(Etrain)## [1] 692 34dim(Etest)## [1] 173 34set.seed(120) # Setting seed
classifier_RF <- randomForest(x = Etrain[-5],
y = Etrain$STABBR,
ntree = 500)## Warning: Unknown or uninitialised column: `STABBR`.classifier_RF##
## Call:
## randomForest(x = Etrain[-5], y = Etrain$STABBR, ntree = 500)
## Type of random forest: unsupervised
## Number of trees: 500
## No. of variables tried at each split: 5REFERENCES
Data Home: College Scorecard. Data Home | College Scorecard. (n.d.). Retrieved May 11, 2022, from https://collegescorecard.ed.gov/data/
2015–16 National Postsecondary Student Aid Study (npsas:16) student … (n.d.). Retrieved May 12, 2022, from https://nces.ed.gov/pubs2018/2018466.pdf
Federal Student Aid. (n.d.). Retrieved May 11, 2022, from https://studentaid.gov/plus-app/parent/landing
Wickham, H., & Grolemund, G. (2016). R for data science: Visualize, model, transform, tidy, and import data. OReilly Media.
R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
[SMSS] Agresti, Alan. Statistical Methods for the Social Sciences. 5th Edition. Pearson, 2018. Wickham, H., & Grolemund, G. (2016). R for data science: Visualize, model, transform, tidy, and import data. OReilly Media