Project 607
Olya Fomicheva
12/9/2017
For my project I selected the data set that I found on Lending Club’s website (https://www.lendingclub.com). The data is provided for potential investors. The data set contains information about loans that were issued from 2007 to the third quarter of 2017.
Lending Club is the world’s largest peer-to-peer lending platform that enables borrowers to obtain a loan, and investors to purchase notes backed by payments made on loans.
The goals of the project are
To find the equation that best predicts the probability of weather the load will be paid off or not.
To understand what might might cause the probability to change.
Find the classifier that can predict whether the loan will be paid off or not with higher accuracy
An investor earns money when loan is fully paid of and loses money when loan is charged off. If an investor obtains the results generated by the model that classify loans he would be able to make better investment decisions.
While I was reviewing Landing Club’s website I found out that investors can see the information such as loan rate, loan term, interest rate, borrower’s FICO score, loan amount and loan purpose. Moreover, they have an ability to filter by borrower’s employment length and monthly income.
In order to collect the data I downloaded (data source: https://www.lendingclub.com/info/download-data.action ) and merged 11 files that contain data from 2007 to the third quarter of 2017. To reduce the loading time I implemented the following steps.
#1. read in a few records of the input file to identify the classes of the input file and assign that column class to the input file while reading the entire data set
data_2007_2011 <- read.csv(file="https://cdn-stage.fedweb.org/fed-2/13/LoanStats3a.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2012_2013 <- read.csv(file="https://cdn-stage.fedweb.org/fed-2/13/LoanStats3b.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2014 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats3c.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2015 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats3d.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2016_q1 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2016Q1.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2016_q2 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2016Q2.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2016_q3 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2016Q3.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2016_q4 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2016Q4.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2017_q1 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2017Q1.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2017_q2 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2017Q2.csv",
stringsAsFactors=T, header=T, nrows=5)
data_2017_q3 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2017Q3.csv",
stringsAsFactors=T, header=T, nrows=5)
#2. replace all missing values with NAs
data_2007_2011 <- data_2007_2011[is.na(data_2007_2011)]
data_2012_2013 <- data_2012_2013[is.na(data_2012_2013)]
data_2014 <- data_2014[is.na(data_2014)]
data_2015 <- data_2015[is.na(data_2015)]
data_2016_q1 <- data_2016_q1[is.na(data_2016_q1)]
data_2016_q2 <- data_2016_q1[is.na(data_2016_q2)]
data_2016_q3 <- data_2016_q1[is.na(data_2016_q3)]
data_2016_q4 <- data_2016_q1[is.na(data_2016_q4)]
data_2017_q1 <- data_2017_q1[is.na(data_2017_q1)]
data_2017_q2 <- data_2017_q2[is.na(data_2017_q2)]
data_2017_q3 <- data_2017_q3[is.na(data_2017_q3)]
#3. determine classes
data_2007_2011.colclass <- sapply(data_2007_2011,class)
data_2012_2013.colclass <- sapply(data_2012_2013,class)
data_2014.colclass <- sapply(data_2014,class)
data_2015.colclass <- sapply(data_2015,class)
data_2016_q1.colclass <- sapply(data_2016_q1,class)
data_2016_q2.colclass <- sapply(data_2016_q2,class)
data_2016_q3.colclass <- sapply(data_2016_q3,class)
data_2016_q4.colclass <- sapply(data_2016_q4,class)
data_2017_q1.colclass <- sapply(data_2017_q1,class)
data_2017_q2.colclass <- sapply(data_2017_q2,class)
data_2017_q3.colclass <- sapply(data_2017_q3,class)
#4. assign that column class to the input file while reading the entire data set and define comment.char parameter.
data_2007_2011 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats3a.csv",
stringsAsFactors=T,
header=T,colClasses=data_2007_2011.colclass, comment.char="")
data_2012_2013 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats3b.csv",
stringsAsFactors=T,
header=T,colClasses=data_2007_2011.colclass, comment.char="")
data_2014 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats3c.csv",
stringsAsFactors=T, colClasses=data_2014.colclass, comment.char="")
data_2015 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats3d.csv",
stringsAsFactors=T, header=T, colClasses=data_2015.colclass, comment.char="")
data_2016_q1 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2016Q1.csv",
stringsAsFactors=T, header=T,colClasses=data_2016_q1.colclass, comment.char="")
data_2016_q2 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2016Q2.csv",
stringsAsFactors=T, header=T,colClasses=data_2016_q2.colclass, comment.char="")
data_2016_q3 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2016Q3.csv",
stringsAsFactors=T, header=T,colClasses=data_2016_q3.colclass, comment.char="")
data_2016_q4 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2016Q4.csv",
stringsAsFactors=T, header=T,colClasses=data_2016_q4.colclass, comment.char="")
data_2017_q1 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2017Q1.csv",
stringsAsFactors=T, header=T,colClasses=data_2017_q1.colclass, comment.char="")
data_2017_q2 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2017Q2.csv",
stringsAsFactors=T, header=T,colClasses=data_2017_q2.colclass, comment.char="")
data_2017_q3 <- read.csv("https://cdn-stage.fedweb.org/fed-2/13/LoanStats_2017Q3.csv",
stringsAsFactors=T, header=T,colClasses=data_2017_q3.colclass, comment.char="")#5. merge csv files
full_data <- rbind(data_2007_2011[1:51],data_2012_2013[1:51],data_2014[1:51],data_2015[1:51],data_2016_q1[1:51],data_2016_q2[1:51],data_2016_q3[1:51],data_2016_q4[1:51],data_2017_q1[1:51],data_2017_q2[1:51],data_2017_q3[1:51])
head(full_data)## id member_id loan_amnt funded_amnt funded_amnt_inv term int_rate
## 1 NA 5000 5000 4975 36 months 10.65%
## 2 NA 2500 2500 2500 60 months 15.27%
## 3 NA 2400 2400 2400 36 months 15.96%
## 4 NA 10000 10000 10000 36 months 13.49%
## 5 NA 3000 3000 3000 60 months 12.69%
## 6 NA 5000 5000 5000 36 months 7.90%
## installment grade sub_grade emp_title emp_length
## 1 162.87 B B2 10+ years
## 2 59.83 C C4 Ryder < 1 year
## 3 84.33 C C5 10+ years
## 4 339.31 C C1 AIR RESOURCES BOARD 10+ years
## 5 67.79 B B5 University Medical Group 1 year
## 6 156.46 A A4 Veolia Transportaton 3 years
## home_ownership annual_inc verification_status issue_d loan_status
## 1 RENT 24000 Verified 11-Dec Fully Paid
## 2 RENT 30000 Source Verified 11-Dec Charged Off
## 3 RENT 12252 Not Verified 11-Dec Fully Paid
## 4 RENT 49200 Source Verified 11-Dec Fully Paid
## 5 RENT 80000 Source Verified 11-Dec Fully Paid
## 6 RENT 36000 Source Verified 11-Dec Fully Paid
## pymnt_plan url
## 1 n NA
## 2 n NA
## 3 n NA
## 4 n NA
## 5 n NA
## 6 n NA
## desc
## 1 Borrower added on 12/22/11 > I need to upgrade my business technologies.<br>
## 2 Borrower added on 12/22/11 > I plan to use this money to finance the motorcycle i am looking at. I plan to have it paid off as soon as possible/when i sell my old bike. I only need this money because the deal im looking at is to good to pass up.<br><br> Borrower added on 12/22/11 > I plan to use this money to finance the motorcycle i am looking at. I plan to have it paid off as soon as possible/when i sell my old bike.I only need this money because the deal im looking at is to good to pass up. I have finished college with an associates degree in business and its takingmeplaces<br>
## 3
## 4 Borrower added on 12/21/11 > to pay for property tax (borrow from friend, need to pay back) & central A/C need to be replace. I'm very sorry to let my loan expired last time.<br>
## 5 Borrower added on 12/21/11 > I plan on combining three large interest bills together and freeing up some extra each month to pay toward other bills. I've always been a good payor but have found myself needing to make adjustments to my budget due to a medical scare. My job is very stable, I love it.<br>
## 6
## purpose title zip_code addr_state
## 1 credit_card Computer 860xx AZ
## 2 car bike 309xx GA
## 3 small_business real estate business 606xx IL
## 4 other personel 917xx CA
## 5 other Personal 972xx OR
## 6 wedding My wedding loan I promise to pay back 852xx AZ
## dti delinq_2yrs earliest_cr_line inq_last_6mths mths_since_last_delinq
## 1 27.65 0 Jan-85 1 NA
## 2 1.00 0 Apr-99 5 NA
## 3 8.72 0 1-Nov 2 NA
## 4 20.00 0 Feb-96 1 35
## 5 17.94 0 Jan-96 0 38
## 6 11.20 0 4-Nov 3 NA
## mths_since_last_record open_acc pub_rec revol_bal revol_util total_acc
## 1 NA 3 0 13648 83.70% 9
## 2 NA 3 0 1687 9.40% 4
## 3 NA 2 0 2956 98.50% 10
## 4 NA 10 0 5598 21% 37
## 5 NA 15 0 27783 53.90% 38
## 6 NA 9 0 7963 28.30% 12
## initial_list_status out_prncp out_prncp_inv total_pymnt total_pymnt_inv
## 1 f 0 0 5863.155 5833.84
## 2 f 0 0 1014.530 1014.53
## 3 f 0 0 3005.667 3005.67
## 4 f 0 0 12231.890 12231.89
## 5 f 0 0 4066.908 4066.91
## 6 f 0 0 5632.210 5632.21
## total_rec_prncp total_rec_int total_rec_late_fee recoveries
## 1 5000.00 863.16 0.00 0.0
## 2 456.46 435.17 0.00 122.9
## 3 2400.00 605.67 0.00 0.0
## 4 10000.00 2214.92 16.97 0.0
## 5 3000.00 1066.91 0.00 0.0
## 6 5000.00 632.21 0.00 0.0
## collection_recovery_fee last_pymnt_d last_pymnt_amnt next_pymnt_d
## 1 0.00 15-Jan 171.62
## 2 1.11 13-Apr 119.66
## 3 0.00 14-Jun 649.91
## 4 0.00 15-Jan 357.48
## 5 0.00 17-Jan 67.30
## 6 0.00 15-Jan 161.03
## last_credit_pull_d collections_12_mths_ex_med
## 1 17-Sep 0
## 2 16-Oct 0
## 3 17-Jun 0
## 4 16-Apr 0
## 5 17-Jan 0
## 6 17-Feb 0
## mths_since_last_major_derog
## 1 NA
## 2 NA
## 3 NA
## 4 NA
## 5 NA
## 6 NAAfter that I determined all types of loan statuses.
levels(factor(full_data$loan_status))## [1] ""
## [2] "Charged Off"
## [3] "Does not meet the credit policy. Status:Charged Off"
## [4] "Does not meet the credit policy. Status:Fully Paid"
## [5] "Fully Paid"
## [6] "Current"
## [7] "Default"
## [8] "In Grace Period"
## [9] "Late (16-30 days)"
## [10] "Late (31-120 days)"I filtered the data so that the data set contain loans with “Fully Paid” or “Charged Off” statuses. I ignored loans with statuses “Current”, “Late (31-120 days)”, “Late (16-30 days)” and “Default” since theoretically borrowers still can pay them off.
full_data <- full_data %>% mutate(loan_status=str_replace(loan_status, "Does not meet the credit policy. Status:", "")) %>% filter(loan_status %in% c("Fully Paid","Charged Off"))Also, I removed all attributes that investors can’t see on the website and kept only the ones that they can see. Moreover, I converted term and interest rate attribute to numerical format.
## loan_status loan_amnt term int_rate installment grade emp_length
## 1 Fully Paid 5000 36 10.65 162.87 B 10+ years
## 2 Charged Off 2500 60 15.27 59.83 C < 1 year
## 3 Fully Paid 2400 36 15.96 84.33 C 10+ years
## 4 Fully Paid 10000 36 13.49 339.31 C 10+ years
## 5 Fully Paid 3000 60 12.69 67.79 B 1 year
## 6 Fully Paid 5000 36 7.90 156.46 A 3 years
## home_ownership annual_inc verification_status dti delinq_2yrs
## 1 RENT 24000 Verified 27.65 0
## 2 RENT 30000 Source Verified 1.00 0
## 3 RENT 12252 Not Verified 8.72 0
## 4 RENT 49200 Source Verified 20.00 0
## 5 RENT 80000 Source Verified 17.94 0
## 6 RENT 36000 Source Verified 11.20 0
## inq_last_6mths mths_since_last_delinq mths_since_last_record open_acc
## 1 1 NA NA 3
## 2 5 NA NA 3
## 3 2 NA NA 2
## 4 1 35 NA 10
## 5 0 38 NA 15
## 6 3 NA NA 9
## pub_rec revol_bal revol_util total_acc collections_12_mths_ex_med
## 1 0 13648 83 9 0
## 2 0 1687 9 4 0
## 3 0 2956 98 10 0
## 4 0 5598 21 37 0
## 5 0 27783 53 38 0
## 6 0 7963 28 12 0
## mths_since_last_major_derog
## 1 NA
## 2 NA
## 3 NA
## 4 NA
## 5 NA
## 6 NASince the response variable “loan status” is a binary categorical variable (that has two possible outcomes - “Paid Off” or “Charged Off”) and explanatory variables are numerical and categorical variables I used logistic regression for data set analysis.
In order to find the best fitting model that will provide the best prediction about the response variable one should use non-redundant explanatory variables. In order to decide which explanatory variables to include in multiple logistic regression I checked whether dependent variables are correlated between each other or not.
#removing categorical variables
full_data_no_categorical<- full_data %>% select(-loan_status,-grade,-emp_length,-home_ownership,-verification_status)
cor(full_data_no_categorical,use="complete.obs")## loan_amnt term int_rate
## loan_amnt 1.000000000 0.422905078 0.252943051
## term 0.422905078 1.000000000 0.449439920
## int_rate 0.252943051 0.449439920 1.000000000
## installment 0.960984857 0.201161598 0.251209631
## annual_inc 0.396604274 0.077325539 -0.024229579
## dti -0.004296079 0.055376313 0.154213650
## delinq_2yrs 0.004823642 -0.013761784 0.044475316
## inq_last_6mths -0.019746327 -0.002598566 0.242287085
## mths_since_last_delinq -0.030847229 0.006928472 -0.050570450
## mths_since_last_record -0.020720434 0.025732174 0.022453452
## open_acc 0.145728246 0.086797964 0.068295286
## pub_rec 0.031823800 -0.024404755 0.006143159
## revol_bal 0.218459342 0.051399233 -0.006254746
## revol_util 0.109403712 0.034683183 0.095508757
## total_acc 0.106496607 0.069087858 0.001666116
## collections_12_mths_ex_med -0.003320038 -0.009964323 0.003916385
## mths_since_last_major_derog -0.019175444 0.004729816 -0.029554970
## installment annual_inc dti
## loan_amnt 0.960984857 0.396604274 -0.0042960793
## term 0.201161598 0.077325539 0.0553763132
## int_rate 0.251209631 -0.024229579 0.1542136500
## installment 1.000000000 0.392374700 -0.0018279538
## annual_inc 0.392374700 1.000000000 -0.2858904922
## dti -0.001827954 -0.285890492 1.0000000000
## delinq_2yrs 0.011625624 0.042238702 -0.0020443121
## inq_last_6mths 0.009682516 0.040434813 0.0004220809
## mths_since_last_delinq -0.038752539 -0.076417767 0.0204770180
## mths_since_last_record -0.026630255 -0.086111918 0.0615709422
## open_acc 0.139589986 0.092781884 0.2540949157
## pub_rec 0.042574297 0.082048619 -0.0488774759
## revol_bal 0.214007210 0.255702205 0.0733672979
## revol_util 0.117137922 0.050101528 0.1431764418
## total_acc 0.094812658 0.105119526 0.1645578233
## collections_12_mths_ex_med 0.000183462 0.005928169 0.0064742469
## mths_since_last_major_derog -0.023985298 -0.042258911 0.0328661843
## delinq_2yrs inq_last_6mths
## loan_amnt 0.0048236422 -0.0197463266
## term -0.0137617839 -0.0025985660
## int_rate 0.0444753161 0.2422870854
## installment 0.0116256241 0.0096825159
## annual_inc 0.0422387017 0.0404348126
## dti -0.0020443121 0.0004220809
## delinq_2yrs 1.0000000000 0.0282431493
## inq_last_6mths 0.0282431493 1.0000000000
## mths_since_last_delinq -0.4979427822 0.0032003344
## mths_since_last_record -0.0124547371 -0.0347099768
## open_acc 0.0550553163 0.1503937659
## pub_rec 0.0006722893 0.0040616085
## revol_bal 0.0064078761 -0.0122525865
## revol_util 0.0001444110 -0.0794601846
## total_acc 0.0423192281 0.1703407140
## collections_12_mths_ex_med 0.0847557528 0.0004772454
## mths_since_last_major_derog -0.3953539971 0.0124708097
## mths_since_last_delinq mths_since_last_record
## loan_amnt -0.030847229 -0.020720434
## term 0.006928472 0.025732174
## int_rate -0.050570450 0.022453452
## installment -0.038752539 -0.026630255
## annual_inc -0.076417767 -0.086111918
## dti 0.020477018 0.061570942
## delinq_2yrs -0.497942782 -0.012454737
## inq_last_6mths 0.003200334 -0.034709977
## mths_since_last_delinq 1.000000000 -0.006842418
## mths_since_last_record -0.006842418 1.000000000
## open_acc -0.040857028 0.031370633
## pub_rec -0.004742984 -0.269376093
## revol_bal -0.019583893 -0.024295713
## revol_util -0.015932256 0.041013824
## total_acc -0.003720052 -0.144489072
## collections_12_mths_ex_med -0.097995842 -0.005553399
## mths_since_last_major_derog 0.689480972 -0.007275000
## open_acc pub_rec revol_bal
## loan_amnt 0.14572825 0.0318237998 0.218459342
## term 0.08679796 -0.0244047554 0.051399233
## int_rate 0.06829529 0.0061431595 -0.006254746
## installment 0.13958999 0.0425742965 0.214007210
## annual_inc 0.09278188 0.0820486188 0.255702205
## dti 0.25409492 -0.0488774759 0.073367298
## delinq_2yrs 0.05505532 0.0006722893 0.006407876
## inq_last_6mths 0.15039377 0.0040616085 -0.012252587
## mths_since_last_delinq -0.04085703 -0.0047429835 -0.019583893
## mths_since_last_record 0.03137063 -0.2693760931 -0.024295713
## open_acc 1.00000000 -0.0184278479 0.162964627
## pub_rec -0.01842785 1.0000000000 0.011407285
## revol_bal 0.16296463 0.0114072853 1.000000000
## revol_util -0.07903746 -0.0002151927 0.230578235
## total_acc 0.59745422 -0.0586662051 0.079748021
## collections_12_mths_ex_med 0.01444761 0.0169394696 -0.007964900
## mths_since_last_major_derog -0.01320742 0.0099003795 0.002334282
## revol_util total_acc
## loan_amnt 0.1094037119 0.106496607
## term 0.0346831827 0.069087858
## int_rate 0.0955087571 0.001666116
## installment 0.1171379217 0.094812658
## annual_inc 0.0501015282 0.105119526
## dti 0.1431764418 0.164557823
## delinq_2yrs 0.0001444110 0.042319228
## inq_last_6mths -0.0794601846 0.170340714
## mths_since_last_delinq -0.0159322556 -0.003720052
## mths_since_last_record 0.0410138239 -0.144489072
## open_acc -0.0790374605 0.597454218
## pub_rec -0.0002151927 -0.058666205
## revol_bal 0.2305782349 0.079748021
## revol_util 1.0000000000 -0.086334311
## total_acc -0.0863343109 1.000000000
## collections_12_mths_ex_med -0.0258469002 -0.023336431
## mths_since_last_major_derog 0.0221548906 -0.006425679
## collections_12_mths_ex_med
## loan_amnt -0.0033200383
## term -0.0099643227
## int_rate 0.0039163850
## installment 0.0001834620
## annual_inc 0.0059281689
## dti 0.0064742469
## delinq_2yrs 0.0847557528
## inq_last_6mths 0.0004772454
## mths_since_last_delinq -0.0979958421
## mths_since_last_record -0.0055533989
## open_acc 0.0144476057
## pub_rec 0.0169394696
## revol_bal -0.0079648997
## revol_util -0.0258469002
## total_acc -0.0233364306
## collections_12_mths_ex_med 1.0000000000
## mths_since_last_major_derog -0.1270235332
## mths_since_last_major_derog
## loan_amnt -0.019175444
## term 0.004729816
## int_rate -0.029554970
## installment -0.023985298
## annual_inc -0.042258911
## dti 0.032866184
## delinq_2yrs -0.395353997
## inq_last_6mths 0.012470810
## mths_since_last_delinq 0.689480972
## mths_since_last_record -0.007275000
## open_acc -0.013207424
## pub_rec 0.009900380
## revol_bal 0.002334282
## revol_util 0.022154891
## total_acc -0.006425679
## collections_12_mths_ex_med -0.127023533
## mths_since_last_major_derog 1.000000000#chart.Correlation(full_data_no_categorical, method="spearman",histogram=TRUE)According to the correlation matrix loan amount and installment there are four pairs of variables that are highly correlated. Those pairs are:
- loan amount and installment
- the number of open accounts and the number of total accounts
- the number of months since the borrower’s last delinquency and the number of 30+ days past-due incidences of delinquency in the borrower’s credit file for the past 2 years
- the number of months since the borrower’s last delinquency and the number of since most recent 90-day or worse rating
Both highly correlated variables should not be in a final regression model.
In order to find the best regression model I ran the step function that analyses all combination of variables and selects the best regression model based on lowest AIC (Akaike’s criterion) value. Lower values of AIC indicate the preferred model, that is, the one with the fewest parameters that still provides an adequate fit to the data.
full_data.omit = na.omit(full_data)
model.null = glm(loan_status ~ 1,
data = full_data.omit,
family = binomial(link="logit")
)
model.full = glm(loan_status ~ .,
data = full_data.omit,
family = binomial(link="logit")
)
step(model.null,
scope = list(upper=model.full),
direction = "both",
test = "Chisq",
data = full_data)## Start: AIC=38611.8
## loan_status ~ 1
##
## Df Deviance AIC LRT Pr(>Chi)
## + grade 6 36736 36750 1873.51 < 2.2e-16 ***
## + int_rate 1 37092 37096 1517.43 < 2.2e-16 ***
## + term 1 37555 37559 1054.57 < 2.2e-16 ***
## + dti 1 37891 37895 719.12 < 2.2e-16 ***
## + loan_amnt 1 37991 37995 618.82 < 2.2e-16 ***
## + installment 1 38155 38159 455.20 < 2.2e-16 ***
## + open_acc 1 38411 38415 199.08 < 2.2e-16 ***
## + verification_status 2 38411 38417 199.28 < 2.2e-16 ***
## + home_ownership 3 38411 38419 199.21 < 2.2e-16 ***
## + revol_util 1 38528 38532 81.78 < 2.2e-16 ***
## + inq_last_6mths 1 38535 38539 74.47 < 2.2e-16 ***
## + emp_length 11 38518 38542 92.03 6.667e-15 ***
## + delinq_2yrs 1 38569 38573 41.13 1.423e-10 ***
## + mths_since_last_delinq 1 38576 38580 33.71 6.407e-09 ***
## + annual_inc 1 38579 38583 30.62 3.134e-08 ***
## + collections_12_mths_ex_med 1 38587 38591 22.85 1.748e-06 ***
## + revol_bal 1 38594 38598 15.47 8.404e-05 ***
## + mths_since_last_major_derog 1 38604 38608 5.47 0.01938 *
## + pub_rec 1 38605 38609 5.12 0.02370 *
## + mths_since_last_record 1 38605 38609 4.54 0.03307 *
## <none> 38610 38612
## + total_acc 1 38609 38613 0.77 0.37955
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=36750.29
## loan_status ~ grade
##
## Df Deviance AIC LRT Pr(>Chi)
## + dti 1 36323 36339 413.41 < 2.2e-16 ***
## + term 1 36533 36549 203.05 < 2.2e-16 ***
## + loan_amnt 1 36535 36551 201.53 < 2.2e-16 ***
## + home_ownership 3 36576 36596 160.23 < 2.2e-16 ***
## + installment 1 36612 36628 124.14 < 2.2e-16 ***
## + open_acc 1 36617 36633 119.23 < 2.2e-16 ***
## + emp_length 11 36632 36668 104.18 < 2.2e-16 ***
## + verification_status 2 36691 36709 45.74 1.168e-10 ***
## + revol_util 1 36704 36720 32.30 1.319e-08 ***
## + int_rate 1 36706 36722 30.59 3.193e-08 ***
## + annual_inc 1 36710 36726 26.55 2.563e-07 ***
## + collections_12_mths_ex_med 1 36716 36732 20.57 5.752e-06 ***
## + delinq_2yrs 1 36716 36732 20.31 6.598e-06 ***
## + revol_bal 1 36719 36735 17.63 2.679e-05 ***
## + mths_since_last_delinq 1 36720 36736 15.84 6.887e-05 ***
## + mths_since_last_record 1 36732 36748 4.31 0.03782 *
## + pub_rec 1 36733 36749 3.24 0.07175 .
## + inq_last_6mths 1 36733 36749 3.22 0.07266 .
## + mths_since_last_major_derog 1 36734 36750 2.25 0.13362
## <none> 36736 36750
## + total_acc 1 36736 36752 0.06 0.80158
## - grade 6 38610 38612 1873.51 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=36338.87
## loan_status ~ grade + dti
##
## Df Deviance AIC LRT Pr(>Chi)
## + loan_amnt 1 36085 36103 238.24 < 2.2e-16 ***
## + term 1 36103 36121 219.45 < 2.2e-16 ***
## + installment 1 36173 36191 149.44 < 2.2e-16 ***
## + home_ownership 3 36178 36200 144.96 < 2.2e-16 ***
## + emp_length 11 36237 36275 85.53 1.244e-13 ***
## + verification_status 2 36277 36297 45.86 1.102e-10 ***
## + open_acc 1 36284 36302 39.28 3.673e-10 ***
## + int_rate 1 36293 36311 29.83 4.707e-08 ***
## + delinq_2yrs 1 36300 36318 23.33 1.366e-06 ***
## + mths_since_last_delinq 1 36301 36319 21.66 3.262e-06 ***
## + collections_12_mths_ex_med 1 36303 36321 19.93 8.022e-06 ***
## + revol_util 1 36313 36331 10.04 0.001533 **
## + total_acc 1 36313 36331 9.71 0.001834 **
## + pub_rec 1 36314 36332 8.41 0.003732 **
## + revol_bal 1 36315 36333 7.52 0.006102 **
## + mths_since_last_major_derog 1 36318 36336 5.31 0.021258 *
## <none> 36323 36339
## + annual_inc 1 36322 36340 1.02 0.312494
## + mths_since_last_record 1 36322 36340 0.62 0.429703
## + inq_last_6mths 1 36322 36340 0.55 0.459223
## - dti 1 36736 36750 413.41 < 2.2e-16 ***
## - grade 6 37891 37895 1567.81 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=36102.63
## loan_status ~ grade + dti + loan_amnt
##
## Df Deviance AIC LRT Pr(>Chi)
## + home_ownership 3 35876 35900 209.07 < 2.2e-16 ***
## + term 1 35985 36005 99.58 < 2.2e-16 ***
## + emp_length 11 35970 36010 114.82 < 2.2e-16 ***
## + installment 1 36017 36037 67.85 < 2.2e-16 ***
## + annual_inc 1 36042 36062 42.43 7.319e-11 ***
## + int_rate 1 36050 36070 34.53 4.204e-09 ***
## + verification_status 2 36056 36078 28.25 7.347e-07 ***
## + total_acc 1 36059 36079 25.61 4.178e-07 ***
## + delinq_2yrs 1 36060 36080 25.06 5.571e-07 ***
## + collections_12_mths_ex_med 1 36063 36083 21.19 4.150e-06 ***
## + mths_since_last_delinq 1 36065 36085 19.73 8.898e-06 ***
## + open_acc 1 36068 36088 16.60 4.619e-05 ***
## + pub_rec 1 36078 36098 6.43 0.01119 *
## + mths_since_last_major_derog 1 36080 36100 4.76 0.02920 *
## + revol_util 1 36082 36102 2.58 0.10856
## <none> 36085 36103
## + mths_since_last_record 1 36083 36103 1.26 0.26086
## + revol_bal 1 36084 36104 0.56 0.45461
## + inq_last_6mths 1 36084 36104 0.50 0.47748
## - loan_amnt 1 36323 36339 238.24 < 2.2e-16 ***
## - dti 1 36535 36551 450.12 < 2.2e-16 ***
## - grade 6 37243 37249 1158.75 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35899.56
## loan_status ~ grade + dti + loan_amnt + home_ownership
##
## Df Deviance AIC LRT Pr(>Chi)
## + term 1 35760 35786 115.67 < 2.2e-16 ***
## + installment 1 35795 35821 80.31 < 2.2e-16 ***
## + emp_length 11 35778 35824 97.28 6.162e-16 ***
## + int_rate 1 35839 35865 36.45 1.564e-09 ***
## + delinq_2yrs 1 35846 35872 29.99 4.342e-08 ***
## + annual_inc 1 35846 35872 29.75 4.916e-08 ***
## + mths_since_last_delinq 1 35850 35876 25.42 4.605e-07 ***
## + open_acc 1 35853 35879 22.86 1.741e-06 ***
## + collections_12_mths_ex_med 1 35856 35882 19.21 1.172e-05 ***
## + total_acc 1 35859 35885 16.60 4.623e-05 ***
## + verification_status 2 35858 35886 17.20 0.0001842 ***
## + revol_util 1 35868 35894 7.09 0.0077667 **
## + pub_rec 1 35870 35896 5.75 0.0164890 *
## + mths_since_last_major_derog 1 35870 35896 5.13 0.0235422 *
## <none> 35876 35900
## + mths_since_last_record 1 35874 35900 1.53 0.2156855
## + inq_last_6mths 1 35874 35900 1.51 0.2189319
## + revol_bal 1 35876 35902 0.02 0.8815250
## - home_ownership 3 36085 36103 209.07 < 2.2e-16 ***
## - loan_amnt 1 36178 36200 302.34 < 2.2e-16 ***
## - dti 1 36312 36334 435.95 < 2.2e-16 ***
## - grade 6 36965 36977 1089.41 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35785.89
## loan_status ~ grade + dti + loan_amnt + home_ownership + term
##
## Df Deviance AIC LRT Pr(>Chi)
## + emp_length 11 35655 35703 104.45 < 2.2e-16 ***
## + int_rate 1 35720 35748 40.23 2.260e-10 ***
## + delinq_2yrs 1 35725 35753 35.21 2.953e-09 ***
## + mths_since_last_delinq 1 35729 35757 30.54 3.277e-08 ***
## + open_acc 1 35738 35766 21.81 3.004e-06 ***
## + annual_inc 1 35738 35766 21.62 3.323e-06 ***
## + collections_12_mths_ex_med 1 35739 35767 20.61 5.622e-06 ***
## + total_acc 1 35740 35768 19.95 7.967e-06 ***
## + verification_status 2 35741 35771 18.75 8.494e-05 ***
## + revol_util 1 35751 35779 9.11 0.002537 **
## + pub_rec 1 35751 35779 8.66 0.003257 **
## + mths_since_last_major_derog 1 35754 35782 6.37 0.011587 *
## + inq_last_6mths 1 35754 35782 6.16 0.013033 *
## <none> 35760 35786
## + installment 1 35758 35786 1.74 0.187287
## + mths_since_last_record 1 35759 35787 0.64 0.425373
## + revol_bal 1 35760 35788 0.19 0.663781
## - term 1 35876 35900 115.67 < 2.2e-16 ***
## - loan_amnt 1 35918 35942 158.49 < 2.2e-16 ***
## - home_ownership 3 35985 36005 225.17 < 2.2e-16 ***
## - dti 1 36198 36222 438.08 < 2.2e-16 ***
## - grade 6 36437 36451 677.60 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35703.44
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length
##
## Df Deviance AIC LRT Pr(>Chi)
## + int_rate 1 35615 35665 40.55 1.914e-10 ***
## + delinq_2yrs 1 35619 35669 36.30 1.693e-09 ***
## + mths_since_last_delinq 1 35624 35674 31.77 1.738e-08 ***
## + open_acc 1 35629 35679 26.21 3.062e-07 ***
## + collections_12_mths_ex_med 1 35635 35685 20.21 6.941e-06 ***
## + total_acc 1 35637 35687 17.99 2.218e-05 ***
## + annual_inc 1 35642 35692 13.51 0.0002377 ***
## + verification_status 2 35641 35693 14.75 0.0006265 ***
## + revol_util 1 35644 35694 11.93 0.0005535 ***
## + pub_rec 1 35647 35697 8.68 0.0032252 **
## + inq_last_6mths 1 35648 35698 7.24 0.0071142 **
## + mths_since_last_major_derog 1 35649 35699 6.13 0.0132866 *
## + installment 1 35653 35703 2.17 0.1408510
## <none> 35655 35703
## + mths_since_last_record 1 35655 35705 0.74 0.3892936
## + revol_bal 1 35655 35705 0.40 0.5268580
## - emp_length 11 35760 35786 104.45 < 2.2e-16 ***
## - term 1 35778 35824 122.84 < 2.2e-16 ***
## - loan_amnt 1 35832 35878 177.01 < 2.2e-16 ***
## - home_ownership 3 35863 35905 207.19 < 2.2e-16 ***
## - dti 1 36072 36118 416.37 < 2.2e-16 ***
## - grade 6 36330 36366 674.89 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35664.89
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate
##
## Df Deviance AIC LRT Pr(>Chi)
## + delinq_2yrs 1 35579 35631 36.24 1.747e-09 ***
## + mths_since_last_delinq 1 35581 35633 33.40 7.486e-09 ***
## + open_acc 1 35590 35642 25.27 4.973e-07 ***
## + total_acc 1 35595 35647 20.04 7.586e-06 ***
## + collections_12_mths_ex_med 1 35596 35648 19.22 1.164e-05 ***
## + annual_inc 1 35600 35652 15.12 0.0001008 ***
## + verification_status 2 35598 35652 16.59 0.0002491 ***
## + revol_util 1 35601 35653 13.66 0.0002190 ***
## + installment 1 35602 35654 12.82 0.0003428 ***
## + inq_last_6mths 1 35606 35658 8.50 0.0035595 **
## + pub_rec 1 35607 35659 8.10 0.0044290 **
## + mths_since_last_major_derog 1 35608 35660 7.19 0.0073372 **
## <none> 35615 35665
## + mths_since_last_record 1 35613 35665 1.51 0.2198582
## + revol_bal 1 35615 35667 0.36 0.5494714
## - int_rate 1 35655 35703 40.55 1.914e-10 ***
## - emp_length 11 35720 35748 104.77 < 2.2e-16 ***
## - term 1 35742 35790 126.80 < 2.2e-16 ***
## - loan_amnt 1 35795 35843 179.99 < 2.2e-16 ***
## - home_ownership 3 35825 35869 209.68 < 2.2e-16 ***
## - grade 6 35882 35920 267.29 < 2.2e-16 ***
## - dti 1 36031 36079 415.74 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35630.65
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs
##
## Df Deviance AIC LRT Pr(>Chi)
## + total_acc 1 35556 35610 23.00 1.619e-06 ***
## + open_acc 1 35556 35610 22.16 2.508e-06 ***
## + annual_inc 1 35561 35615 17.57 2.764e-05 ***
## + verification_status 2 35561 35617 17.66 0.0001463 ***
## + collections_12_mths_ex_med 1 35563 35617 15.21 9.634e-05 ***
## + revol_util 1 35564 35618 14.24 0.0001608 ***
## + installment 1 35565 35619 13.87 0.0001956 ***
## + mths_since_last_delinq 1 35568 35622 10.68 0.0010834 **
## + pub_rec 1 35571 35625 8.13 0.0043559 **
## + inq_last_6mths 1 35571 35625 8.03 0.0046057 **
## <none> 35579 35631
## + mths_since_last_record 1 35577 35631 1.70 0.1923600
## + revol_bal 1 35578 35632 0.34 0.5615886
## + mths_since_last_major_derog 1 35579 35633 0.13 0.7210945
## - delinq_2yrs 1 35615 35665 36.24 1.747e-09 ***
## - int_rate 1 35619 35669 40.49 1.975e-10 ***
## - emp_length 11 35685 35715 105.92 < 2.2e-16 ***
## - term 1 35711 35761 132.52 < 2.2e-16 ***
## - loan_amnt 1 35759 35809 180.22 < 2.2e-16 ***
## - home_ownership 3 35794 35840 215.72 < 2.2e-16 ***
## - grade 6 35841 35881 261.98 < 2.2e-16 ***
## - dti 1 35998 36048 419.09 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35609.65
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc
##
## Df Deviance AIC LRT Pr(>Chi)
## + open_acc 1 35470 35526 86.03 < 2.2e-16 ***
## + verification_status 2 35538 35596 17.97 0.0001251 ***
## + inq_last_6mths 1 35540 35596 15.27 9.337e-05 ***
## + installment 1 35541 35597 14.71 0.0001253 ***
## + collections_12_mths_ex_med 1 35541 35597 14.25 0.0001604 ***
## + annual_inc 1 35543 35599 13.12 0.0002928 ***
## + revol_util 1 35545 35601 10.24 0.0013740 **
## + mths_since_last_delinq 1 35546 35602 9.90 0.0016514 **
## + pub_rec 1 35549 35605 6.76 0.0093373 **
## <none> 35556 35610
## + revol_bal 1 35555 35611 0.57 0.4511160
## + mths_since_last_record 1 35555 35611 0.38 0.5398402
## + mths_since_last_major_derog 1 35556 35612 0.09 0.7668467
## - total_acc 1 35579 35631 23.00 1.619e-06 ***
## - delinq_2yrs 1 35595 35647 39.20 3.827e-10 ***
## - int_rate 1 35598 35650 42.71 6.343e-11 ***
## - emp_length 11 35659 35691 103.68 < 2.2e-16 ***
## - term 1 35692 35744 136.72 < 2.2e-16 ***
## - loan_amnt 1 35746 35798 190.65 < 2.2e-16 ***
## - home_ownership 3 35762 35810 206.09 < 2.2e-16 ***
## - grade 6 35819 35861 263.20 < 2.2e-16 ***
## - dti 1 35997 36049 440.89 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35525.62
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc
##
## Df Deviance AIC LRT Pr(>Chi)
## + annual_inc 1 35452 35510 17.68 2.612e-05 ***
## + verification_status 2 35452 35512 17.84 0.0001337 ***
## + revol_util 1 35454 35512 15.59 7.885e-05 ***
## + installment 1 35456 35514 13.17 0.0002840 ***
## + collections_12_mths_ex_med 1 35457 35515 12.23 0.0004697 ***
## + inq_last_6mths 1 35459 35517 10.92 0.0009531 ***
## + mths_since_last_delinq 1 35461 35519 8.23 0.0041228 **
## + pub_rec 1 35464 35522 5.74 0.0166118 *
## <none> 35470 35526
## + mths_since_last_record 1 35469 35527 0.40 0.5273230
## + revol_bal 1 35470 35528 0.11 0.7401254
## + mths_since_last_major_derog 1 35470 35528 0.09 0.7693954
## - delinq_2yrs 1 35505 35559 35.77 2.217e-09 ***
## - int_rate 1 35514 35568 43.90 3.460e-11 ***
## - open_acc 1 35556 35610 86.03 < 2.2e-16 ***
## - total_acc 1 35556 35610 86.87 < 2.2e-16 ***
## - emp_length 11 35581 35615 111.11 < 2.2e-16 ***
## - term 1 35609 35663 139.87 < 2.2e-16 ***
## - loan_amnt 1 35640 35694 170.04 < 2.2e-16 ***
## - home_ownership 3 35679 35729 209.56 < 2.2e-16 ***
## - grade 6 35732 35776 262.04 < 2.2e-16 ***
## - dti 1 35827 35881 357.52 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35509.94
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc
##
## Df Deviance AIC LRT Pr(>Chi)
## + revol_util 1 35433 35493 18.588 1.623e-05 ***
## + verification_status 2 35433 35495 18.553 9.359e-05 ***
## + installment 1 35439 35499 12.701 0.0003654 ***
## + inq_last_6mths 1 35439 35499 12.552 0.0003958 ***
## + collections_12_mths_ex_med 1 35440 35500 12.436 0.0004212 ***
## + mths_since_last_delinq 1 35442 35502 9.649 0.0018949 **
## + pub_rec 1 35445 35505 7.311 0.0068524 **
## <none> 35452 35510
## + mths_since_last_record 1 35451 35511 0.771 0.3798338
## + revol_bal 1 35452 35512 0.368 0.5439891
## + mths_since_last_major_derog 1 35452 35512 0.131 0.7169657
## - annual_inc 1 35470 35526 17.682 2.612e-05 ***
## - delinq_2yrs 1 35490 35546 37.789 7.883e-10 ***
## - int_rate 1 35497 35553 45.528 1.505e-11 ***
## - total_acc 1 35533 35589 81.387 < 2.2e-16 ***
## - emp_length 11 35553 35589 101.556 < 2.2e-16 ***
## - open_acc 1 35543 35599 90.594 < 2.2e-16 ***
## - term 1 35583 35639 130.879 < 2.2e-16 ***
## - loan_amnt 1 35637 35693 185.415 < 2.2e-16 ***
## - home_ownership 3 35652 35704 200.255 < 2.2e-16 ***
## - grade 6 35715 35761 263.176 < 2.2e-16 ***
## - dti 1 35722 35778 269.725 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35493.35
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util
##
## Df Deviance AIC LRT Pr(>Chi)
## + verification_status 2 35415 35479 18.678 8.794e-05 ***
## + inq_last_6mths 1 35418 35480 15.288 9.229e-05 ***
## + collections_12_mths_ex_med 1 35420 35482 13.495 0.0002392 ***
## + installment 1 35421 35483 12.085 0.0005083 ***
## + mths_since_last_delinq 1 35424 35486 9.578 0.0019694 **
## + pub_rec 1 35426 35488 7.547 0.0060107 **
## <none> 35433 35493
## + mths_since_last_record 1 35432 35494 1.047 0.3062975
## + mths_since_last_major_derog 1 35433 35495 0.242 0.6224561
## + revol_bal 1 35433 35495 0.133 0.7149611
## - revol_util 1 35452 35510 18.588 1.623e-05 ***
## - annual_inc 1 35454 35512 20.684 5.418e-06 ***
## - delinq_2yrs 1 35472 35530 38.213 6.343e-10 ***
## - int_rate 1 35481 35539 47.636 5.131e-12 ***
## - total_acc 1 35510 35568 76.320 < 2.2e-16 ***
## - emp_length 11 35538 35576 104.886 < 2.2e-16 ***
## - open_acc 1 35530 35588 97.048 < 2.2e-16 ***
## - term 1 35567 35625 133.351 < 2.2e-16 ***
## - loan_amnt 1 35610 35668 176.639 < 2.2e-16 ***
## - home_ownership 3 35642 35696 208.305 < 2.2e-16 ***
## - dti 1 35668 35726 234.738 < 2.2e-16 ***
## - grade 6 35696 35744 262.880 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35478.68
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status
##
## Df Deviance AIC LRT Pr(>Chi)
## + inq_last_6mths 1 35400 35466 14.945 0.0001107 ***
## + collections_12_mths_ex_med 1 35402 35468 13.146 0.0002881 ***
## + installment 1 35403 35469 11.899 0.0005618 ***
## + mths_since_last_delinq 1 35405 35471 9.597 0.0019490 **
## + pub_rec 1 35408 35474 6.977 0.0082583 **
## <none> 35415 35479
## + mths_since_last_record 1 35414 35480 0.585 0.4443052
## + mths_since_last_major_derog 1 35414 35480 0.181 0.6707073
## + revol_bal 1 35415 35481 0.115 0.7347541
## - verification_status 2 35433 35493 18.678 8.794e-05 ***
## - revol_util 1 35433 35495 18.712 1.520e-05 ***
## - annual_inc 1 35436 35498 21.459 3.614e-06 ***
## - delinq_2yrs 1 35454 35516 39.381 3.487e-10 ***
## - int_rate 1 35465 35527 50.077 1.478e-12 ***
## - total_acc 1 35491 35553 76.520 < 2.2e-16 ***
## - emp_length 11 35513 35555 97.873 4.706e-16 ***
## - open_acc 1 35512 35574 97.035 < 2.2e-16 ***
## - term 1 35549 35611 134.484 < 2.2e-16 ***
## - loan_amnt 1 35579 35641 163.909 < 2.2e-16 ***
## - home_ownership 3 35612 35670 196.882 < 2.2e-16 ***
## - dti 1 35649 35711 234.259 < 2.2e-16 ***
## - grade 6 35678 35730 263.677 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35465.73
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status + inq_last_6mths
##
## Df Deviance AIC LRT Pr(>Chi)
## + collections_12_mths_ex_med 1 35387 35455 13.199 0.0002800 ***
## + installment 1 35388 35456 11.435 0.0007208 ***
## + mths_since_last_delinq 1 35389 35457 10.371 0.0012802 **
## + pub_rec 1 35393 35461 6.977 0.0082545 **
## <none> 35400 35466
## + mths_since_last_record 1 35399 35467 0.560 0.4543541
## + mths_since_last_major_derog 1 35399 35467 0.301 0.5832474
## + revol_bal 1 35400 35468 0.113 0.7362599
## - inq_last_6mths 1 35415 35479 14.945 0.0001107 ***
## - verification_status 2 35418 35480 18.334 0.0001044 ***
## - revol_util 1 35421 35485 21.399 3.729e-06 ***
## - annual_inc 1 35423 35487 23.687 1.133e-06 ***
## - delinq_2yrs 1 35439 35503 39.512 3.260e-10 ***
## - int_rate 1 35452 35516 52.315 4.727e-13 ***
## - emp_length 11 35499 35543 99.289 2.470e-16 ***
## - total_acc 1 35483 35547 83.662 < 2.2e-16 ***
## - open_acc 1 35492 35556 92.606 < 2.2e-16 ***
## - term 1 35543 35607 143.380 < 2.2e-16 ***
## - loan_amnt 1 35572 35636 172.021 < 2.2e-16 ***
## - home_ownership 3 35600 35660 200.002 < 2.2e-16 ***
## - dti 1 35640 35704 240.650 < 2.2e-16 ***
## - grade 6 35652 35706 252.455 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35454.53
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status + inq_last_6mths +
## collections_12_mths_ex_med
##
## Df Deviance AIC LRT Pr(>Chi)
## + installment 1 35375 35445 11.310 0.0007711 ***
## + mths_since_last_delinq 1 35378 35448 8.885 0.0028751 **
## + pub_rec 1 35380 35450 6.783 0.0092052 **
## <none> 35387 35455
## + mths_since_last_record 1 35386 35456 0.511 0.4745557
## + revol_bal 1 35386 35456 0.103 0.7479974
## + mths_since_last_major_derog 1 35387 35457 0.023 0.8803784
## - collections_12_mths_ex_med 1 35400 35466 13.199 0.0002800 ***
## - inq_last_6mths 1 35402 35468 14.998 0.0001076 ***
## - verification_status 2 35405 35469 17.996 0.0001236 ***
## - revol_util 1 35409 35475 22.509 2.091e-06 ***
## - annual_inc 1 35411 35477 24.014 9.566e-07 ***
## - delinq_2yrs 1 35422 35488 35.564 2.468e-09 ***
## - int_rate 1 35438 35504 51.314 7.870e-13 ***
## - emp_length 11 35486 35532 99.013 2.800e-16 ***
## - total_acc 1 35467 35533 80.828 < 2.2e-16 ***
## - open_acc 1 35477 35543 90.715 < 2.2e-16 ***
## - term 1 35531 35597 144.192 < 2.2e-16 ***
## - loan_amnt 1 35559 35625 172.286 < 2.2e-16 ***
## - home_ownership 3 35585 35647 198.856 < 2.2e-16 ***
## - dti 1 35626 35692 239.435 < 2.2e-16 ***
## - grade 6 35637 35693 250.729 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35445.22
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status + inq_last_6mths +
## collections_12_mths_ex_med + installment
##
## Df Deviance AIC LRT Pr(>Chi)
## + mths_since_last_delinq 1 35366 35438 9.000 0.0026992 **
## + pub_rec 1 35369 35441 6.604 0.0101768 *
## - loan_amnt 1 35377 35445 1.738 0.1873772
## <none> 35375 35445
## + mths_since_last_record 1 35375 35447 0.509 0.4757351
## + revol_bal 1 35375 35447 0.070 0.7907009
## + mths_since_last_major_derog 1 35375 35447 0.026 0.8715877
## - installment 1 35387 35455 11.310 0.0007711 ***
## - collections_12_mths_ex_med 1 35388 35456 13.074 0.0002994 ***
## - inq_last_6mths 1 35390 35458 14.533 0.0001377 ***
## - verification_status 2 35393 35459 17.811 0.0001356 ***
## - revol_util 1 35397 35465 21.800 3.026e-06 ***
## - annual_inc 1 35399 35467 23.379 1.330e-06 ***
## - delinq_2yrs 1 35412 35480 36.540 1.495e-09 ***
## - int_rate 1 35437 35505 61.562 4.291e-15 ***
## - term 1 35445 35513 69.348 < 2.2e-16 ***
## - emp_length 11 35475 35523 100.066 < 2.2e-16 ***
## - total_acc 1 35456 35524 81.199 < 2.2e-16 ***
## - open_acc 1 35464 35532 89.124 < 2.2e-16 ***
## - home_ownership 3 35574 35638 198.608 < 2.2e-16 ***
## - dti 1 35615 35683 239.476 < 2.2e-16 ***
## - grade 6 35632 35690 257.064 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35438.22
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status + inq_last_6mths +
## collections_12_mths_ex_med + installment + mths_since_last_delinq
##
## Df Deviance AIC LRT Pr(>Chi)
## + pub_rec 1 35360 35434 6.709 0.0095944 **
## + mths_since_last_major_derog 1 35362 35436 4.371 0.0365566 *
## - loan_amnt 1 35368 35438 1.781 0.1820678
## <none> 35366 35438
## + mths_since_last_record 1 35366 35440 0.601 0.4383232
## + revol_bal 1 35366 35440 0.059 0.8086500
## - mths_since_last_delinq 1 35375 35445 9.000 0.0026992 **
## - installment 1 35378 35448 11.425 0.0007246 ***
## - collections_12_mths_ex_med 1 35378 35448 11.585 0.0006650 ***
## - delinq_2yrs 1 35381 35451 14.849 0.0001165 ***
## - inq_last_6mths 1 35381 35451 15.247 9.433e-05 ***
## - verification_status 2 35384 35452 17.811 0.0001357 ***
## - revol_util 1 35388 35458 21.732 3.135e-06 ***
## - annual_inc 1 35391 35461 24.967 5.831e-07 ***
## - int_rate 1 35429 35499 62.921 2.151e-15 ***
## - term 1 35436 35506 70.156 < 2.2e-16 ***
## - total_acc 1 35445 35515 79.250 < 2.2e-16 ***
## - emp_length 11 35466 35516 100.169 < 2.2e-16 ***
## - open_acc 1 35454 35524 87.568 < 2.2e-16 ***
## - home_ownership 3 35567 35633 200.971 < 2.2e-16 ***
## - dti 1 35607 35677 240.428 < 2.2e-16 ***
## - grade 6 35624 35684 258.143 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35433.51
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status + inq_last_6mths +
## collections_12_mths_ex_med + installment + mths_since_last_delinq +
## pub_rec
##
## Df Deviance AIC LRT Pr(>Chi)
## + mths_since_last_major_derog 1 35355 35431 4.163 0.0413185 *
## - loan_amnt 1 35361 35433 1.715 0.1903017
## <none> 35360 35434
## + revol_bal 1 35359 35435 0.046 0.8301274
## + mths_since_last_record 1 35360 35436 0.003 0.9563428
## - pub_rec 1 35366 35438 6.709 0.0095944 **
## - mths_since_last_delinq 1 35369 35441 9.105 0.0025486 **
## - installment 1 35371 35443 11.245 0.0007985 ***
## - collections_12_mths_ex_med 1 35371 35443 11.396 0.0007362 ***
## - delinq_2yrs 1 35374 35446 14.815 0.0001186 ***
## - inq_last_6mths 1 35375 35447 15.256 9.387e-05 ***
## - verification_status 2 35377 35447 17.271 0.0001777 ***
## - revol_util 1 35381 35453 21.968 2.773e-06 ***
## - annual_inc 1 35386 35458 26.767 2.296e-07 ***
## - int_rate 1 35422 35494 62.159 3.168e-15 ***
## - term 1 35430 35502 70.525 < 2.2e-16 ***
## - total_acc 1 35436 35508 76.195 < 2.2e-16 ***
## - emp_length 11 35459 35511 99.882 < 2.2e-16 ***
## - open_acc 1 35446 35518 86.769 < 2.2e-16 ***
## - home_ownership 3 35560 35628 200.483 < 2.2e-16 ***
## - dti 1 35601 35673 241.783 < 2.2e-16 ***
## - grade 6 35616 35678 256.169 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35431.35
## loan_status ~ grade + dti + loan_amnt + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status + inq_last_6mths +
## collections_12_mths_ex_med + installment + mths_since_last_delinq +
## pub_rec + mths_since_last_major_derog
##
## Df Deviance AIC LRT Pr(>Chi)
## - loan_amnt 1 35357 35431 1.707 0.1913507
## <none> 35355 35431
## + revol_bal 1 35355 35433 0.048 0.8262588
## + mths_since_last_record 1 35355 35433 0.001 0.9703426
## - mths_since_last_major_derog 1 35360 35434 4.163 0.0413185 *
## - pub_rec 1 35362 35436 6.501 0.0107836 *
## - installment 1 35367 35441 11.253 0.0007950 ***
## - collections_12_mths_ex_med 1 35368 35442 12.529 0.0004006 ***
## - mths_since_last_delinq 1 35369 35443 13.223 0.0002765 ***
## - inq_last_6mths 1 35370 35444 14.980 0.0001087 ***
## - verification_status 2 35373 35445 17.628 0.0001487 ***
## - delinq_2yrs 1 35371 35445 16.117 5.955e-05 ***
## - revol_util 1 35377 35451 21.194 4.151e-06 ***
## - annual_inc 1 35382 35456 27.139 1.894e-07 ***
## - int_rate 1 35417 35491 61.293 4.919e-15 ***
## - term 1 35426 35500 70.618 < 2.2e-16 ***
## - total_acc 1 35431 35505 75.528 < 2.2e-16 ***
## - emp_length 11 35456 35510 100.299 < 2.2e-16 ***
## - open_acc 1 35441 35515 85.768 < 2.2e-16 ***
## - home_ownership 3 35557 35627 201.702 < 2.2e-16 ***
## - dti 1 35596 35670 240.364 < 2.2e-16 ***
## - grade 6 35609 35673 253.873 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=35431.06
## loan_status ~ grade + dti + home_ownership + term + emp_length +
## int_rate + delinq_2yrs + total_acc + open_acc + annual_inc +
## revol_util + verification_status + inq_last_6mths + collections_12_mths_ex_med +
## installment + mths_since_last_delinq + pub_rec + mths_since_last_major_derog
##
## Df Deviance AIC LRT Pr(>Chi)
## <none> 35357 35431
## + loan_amnt 1 35355 35431 1.707 0.1913507
## + revol_bal 1 35357 35433 0.067 0.7962285
## + mths_since_last_record 1 35357 35433 0.001 0.9733566
## - mths_since_last_major_derog 1 35361 35433 4.171 0.0411216 *
## - pub_rec 1 35364 35436 6.564 0.0104046 *
## - collections_12_mths_ex_med 1 35370 35442 12.585 0.0003888 ***
## - mths_since_last_delinq 1 35370 35442 13.192 0.0002811 ***
## - inq_last_6mths 1 35372 35444 15.327 9.044e-05 ***
## - verification_status 2 35375 35445 17.542 0.0001552 ***
## - delinq_2yrs 1 35373 35445 15.956 6.482e-05 ***
## - revol_util 1 35378 35450 21.352 3.821e-06 ***
## - annual_inc 1 35386 35458 28.465 9.540e-08 ***
## - int_rate 1 35418 35490 60.728 6.554e-15 ***
## - total_acc 1 35432 35504 75.417 < 2.2e-16 ***
## - emp_length 11 35457 35509 100.030 < 2.2e-16 ***
## - open_acc 1 35443 35515 86.168 < 2.2e-16 ***
## - installment 1 35539 35611 182.291 < 2.2e-16 ***
## - home_ownership 3 35559 35627 202.234 < 2.2e-16 ***
## - dti 1 35597 35669 240.002 < 2.2e-16 ***
## - grade 6 35609 35671 252.185 < 2.2e-16 ***
## - term 1 35650 35722 293.043 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call: glm(formula = loan_status ~ grade + dti + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status + inq_last_6mths +
## collections_12_mths_ex_med + installment + mths_since_last_delinq +
## pub_rec + mths_since_last_major_derog, family = binomial(link = "logit"),
## data = full_data.omit)
##
## Coefficients:
## (Intercept) gradeB
## 3.434e+00 -5.621e-01
## gradeC gradeD
## -1.138e+00 -1.644e+00
## gradeE gradeF
## -2.144e+00 -2.411e+00
## gradeG dti
## -2.689e+00 -2.710e-02
## home_ownershipOWN home_ownershipRENT
## -2.842e-01 -4.066e-01
## home_ownershipANY term
## -1.058e+00 -2.481e-02
## emp_length1 year emp_length10+ years
## 6.867e-02 3.027e-01
## emp_length2 years emp_length3 years
## 1.534e-01 1.718e-01
## emp_length4 years emp_length5 years
## 1.559e-01 1.778e-01
## emp_length6 years emp_length7 years
## 2.102e-01 2.829e-01
## emp_length8 years emp_length9 years
## 1.571e-01 1.667e-01
## emp_lengthn/a int_rate
## -1.651e-01 7.601e-02
## delinq_2yrs total_acc
## -4.956e-02 1.239e-02
## open_acc annual_inc
## -3.128e-02 1.922e-06
## revol_util verification_statusSource Verified
## -2.941e-03 -1.512e-01
## verification_statusVerified inq_last_6mths
## -1.317e-01 -4.745e-02
## collections_12_mths_ex_med installment
## -2.149e-01 -8.799e-04
## mths_since_last_delinq pub_rec
## 3.070e-03 -3.824e-02
## mths_since_last_major_derog
## -1.607e-03
##
## Degrees of Freedom: 36221 Total (i.e. Null); 36185 Residual
## Null Deviance: 38610
## Residual Deviance: 35360 AIC: 35430The step function ignored redundant variables (the variables that are highly correlated). The best models shown below:
final.model <- glm(formula = loan_status ~ grade + dti + home_ownership + term +
emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
annual_inc + revol_util + verification_status + inq_last_6mths +
collections_12_mths_ex_med + installment + mths_since_last_delinq +
pub_rec + mths_since_last_major_derog, family = binomial(link = "logit"),
data = full_data.omit)
summary(final.model)##
## Call:
## glm(formula = loan_status ~ grade + dti + home_ownership + term +
## emp_length + int_rate + delinq_2yrs + total_acc + open_acc +
## annual_inc + revol_util + verification_status + inq_last_6mths +
## collections_12_mths_ex_med + installment + mths_since_last_delinq +
## pub_rec + mths_since_last_major_derog, family = binomial(link = "logit"),
## data = full_data.omit)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5369 0.3621 0.5534 0.7258 2.4048
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.434e+00 1.442e-01 23.817 < 2e-16
## gradeB -5.621e-01 8.512e-02 -6.603 4.02e-11
## gradeC -1.138e+00 9.916e-02 -11.481 < 2e-16
## gradeD -1.644e+00 1.240e-01 -13.260 < 2e-16
## gradeE -2.144e+00 1.515e-01 -14.150 < 2e-16
## gradeF -2.411e+00 1.911e-01 -12.618 < 2e-16
## gradeG -2.689e+00 2.348e-01 -11.452 < 2e-16
## dti -2.710e-02 1.755e-03 -15.446 < 2e-16
## home_ownershipOWN -2.842e-01 4.494e-02 -6.324 2.55e-10
## home_ownershipRENT -4.066e-01 2.899e-02 -14.029 < 2e-16
## home_ownershipANY -1.058e+00 9.513e-01 -1.113 0.265872
## term -2.481e-02 1.436e-03 -17.272 < 2e-16
## emp_length1 year 6.867e-02 7.433e-02 0.924 0.355566
## emp_length10+ years 3.027e-01 5.543e-02 5.461 4.72e-08
## emp_length2 years 1.534e-01 6.833e-02 2.245 0.024757
## emp_length3 years 1.718e-01 6.924e-02 2.481 0.013086
## emp_length4 years 1.559e-01 7.310e-02 2.132 0.032993
## emp_length5 years 1.778e-01 7.349e-02 2.420 0.015540
## emp_length6 years 2.102e-01 7.920e-02 2.654 0.007956
## emp_length7 years 2.829e-01 8.161e-02 3.467 0.000527
## emp_length8 years 1.571e-01 7.973e-02 1.971 0.048715
## emp_length9 years 1.667e-01 8.529e-02 1.955 0.050639
## emp_lengthn/a -1.651e-01 6.911e-02 -2.389 0.016912
## int_rate 7.601e-02 9.796e-03 7.760 8.51e-15
## delinq_2yrs -4.956e-02 1.219e-02 -4.067 4.77e-05
## total_acc 1.239e-02 1.444e-03 8.586 < 2e-16
## open_acc -3.128e-02 3.359e-03 -9.312 < 2e-16
## annual_inc 1.922e-06 3.750e-07 5.125 2.98e-07
## revol_util -2.941e-03 6.367e-04 -4.619 3.85e-06
## verification_statusSource Verified -1.512e-01 3.702e-02 -4.085 4.41e-05
## verification_statusVerified -1.317e-01 3.934e-02 -3.348 0.000814
## inq_last_6mths -4.745e-02 1.208e-02 -3.929 8.51e-05
## collections_12_mths_ex_med -2.149e-01 5.958e-02 -3.607 0.000310
## installment -8.799e-04 6.495e-05 -13.547 < 2e-16
## mths_since_last_delinq 3.070e-03 8.439e-04 3.638 0.000275
## pub_rec -3.824e-02 1.475e-02 -2.592 0.009546
## mths_since_last_major_derog -1.607e-03 7.846e-04 -2.048 0.040558
##
## (Intercept) ***
## gradeB ***
## gradeC ***
## gradeD ***
## gradeE ***
## gradeF ***
## gradeG ***
## dti ***
## home_ownershipOWN ***
## home_ownershipRENT ***
## home_ownershipANY
## term ***
## emp_length1 year
## emp_length10+ years ***
## emp_length2 years *
## emp_length3 years *
## emp_length4 years *
## emp_length5 years *
## emp_length6 years **
## emp_length7 years ***
## emp_length8 years *
## emp_length9 years .
## emp_lengthn/a *
## int_rate ***
## delinq_2yrs ***
## total_acc ***
## open_acc ***
## annual_inc ***
## revol_util ***
## verification_statusSource Verified ***
## verification_statusVerified ***
## inq_last_6mths ***
## collections_12_mths_ex_med ***
## installment ***
## mths_since_last_delinq ***
## pub_rec **
## mths_since_last_major_derog *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 38610 on 36221 degrees of freedom
## Residual deviance: 35357 on 36185 degrees of freedom
## AIC: 35431
##
## Number of Fisher Scoring iterations: 4By looking at the summary statistics, I concluded that the variables “home_ownershipANY”, “emp_length1 year” and “emp_length9 years” are not statistically significant (they don’t affect the outcome) because theirs p-value is greater that 0.05 level of significance.
Based on the results of the glm function I built the following logit function:
#logit(p) = ln(p/(p-1)) =
#logit_p=
#(3.434e+00)-(5.621e-01)*gradeB-(1.138e+00)*gradeC-(1.644e+00)*gradeD-(2.144e+00)*gradeE -(2.144e+00)*gradeF-(2.689e+00)*gradeG-(2.710e-02)*dti -(2.842e-(1.512e-01)*verificationstatussourseverified+(1.317e-01)*verificationstatussverified-(4.745e-02)*inqlast6mths-(2.149e-01)*collections12mthsexmed-(8.799e-04)*installment +(3.070e-03)*mthssincelastdelinq-(3.284e-02)*pubrec+(1.607e-03)*mthssincelastmajorderog-01)*homeownershipOWN-(4.066e-01)*homeownershipRENT-(2.481e-02)*term+(3.027e-01)*emlengh10years +(1.534e-01)*emplengthyears+(1.718e-01)*emplength3years+(1.559e-01)*emplength4years+(1.778e-01)*emplength5years+(2.102-01)*emplength6years+(2.829-01)*emplength7years+(1.571e-01)*emplength8years-(1.651e-01)*emplengthn/a+years+(7.601e-02)*intrate-(4.956e-02)*deling2yrs+(1.239e-02)*totalacc-(3.128-02)*opeacc+(1.922e-06)*annualinc-(2.941e-03)*revolutil The natural logarithm of the odds ratio is equivalent to a linear function of the independent variables. The antilog of the logit function allows us to find the estimated regression equation.
The estimated regression equation is shown below:
#p_hat = e^logit_p/(1+e^logit_p)In order to illustrate how the equation works I will show how grade can affect the probability of whether the loan will be paid off or not.
Let’s change the loan grade and hold all remaining variables constant.
#create vectors to store grades and probabilities
grade <- c()
probability <- c()
#grade A
logit_p_A = (3.434e+00)-(5.621e-01)*0-(1.138e+00)*0-(1.644e+00)*0-(2.144e+00)*0 -(2.411e+00)*0-(2.689e+00)*0
probability[1] = exp(1)^logit_p_A/(1+exp(1)^logit_p_A)
grade[1] <- "grade A"
#grade B
logit_p_B = (3.434e+00)-(5.621e-01)*1-(1.138e+00)*0-(1.644e+00)*0-(2.144e+00)*0 -(2.411e+00)*0-(2.689e+00)*0
probability[2] = exp(1)^logit_p_B/(1+exp(1)^logit_p_B)
grade[2] <- "grade B"
#grade C
logit_p_C = (3.434e+00)-(5.621e-01)*0-(1.138e+00)*1-(1.644e+00)*0-(2.144e+00)*0 -(2.411e+00)*0-(2.689e+00)*0
probability[3] = exp(1)^logit_p_C/(1+exp(1)^logit_p_C)
grade[3] <- "grade C"
#grade D
logit_p_D = (3.434e+00)-(5.621e-01)*0-(1.138e+00)*0-(1.644e+00)*1-(2.144e+00)*0 -(2.411e+00)*0-(2.689e+00)*0
probability[4] = exp(1)^logit_p_D/(1+exp(1)^logit_p_D)
grade[4] <- "grade D"
#grade E
logit_p_E = (3.434e+00)-(5.621e-01)*0-(1.138e+00)*0-(1.644e+00)*0-(2.144e+00)*1 -(2.411e+00)*0-(2.689e+00)*0
probability[5] = exp(1)^logit_p_E/(1+exp(1)^logit_p_E)
grade[5] <- "grade E"
#grade F
logit_p_F = (3.434e+00)-(5.621e-01)*0-(1.138e+00)*0-(1.644e+00)*0-(2.144e+00)*0 -(2.411e+00)*1-(2.689e+00)*0
probability[6] = exp(1)^logit_p_F/(1+exp(1)^logit_p_F)
grade[6] <- "grade F"
#grade G
logit_p_G = (3.434e+00)-(5.621e-01)*0-(1.138e+00)*0-(1.644e+00)*0-(2.144e+00)*0 -(2.411e+00)*0-(2.689e+00)*1
probability[7] = exp(1)^logit_p_G/(1+exp(1)^logit_p_G)
grade[7] <- "grade G"
#table with results
prob_table <- data.frame(grade,probability)
head(prob_table)## grade probability
## 1 grade A 0.9687504
## 2 grade B 0.9464397
## 3 grade C 0.9085452
## 4 grade D 0.8569273
## 5 grade E 0.7841472
## 6 grade F 0.7355566#graph
g <- ggplot(prob_table, aes(grade,probability))
g + ggtitle("Change in probability based on change in grade") + geom_bar(stat="identity")
The bar chart above shows how change in grades reflects probability while holding all other variables constant.
#create vectors to store change in dti and probabilitiies
dti_value <- c()
probability <- c()
for (i in 1:100){
dti_value[i] <- i
logit_p_dti = (3.434e+00)-(2.710e-02)*i
probability[i] = exp(1)^logit_p_dti/(1+exp(1)^logit_p_dti)
}
dti_table <- data.frame(dti_value,probability)
head(dti_table)## dti_value probability
## 1 1 0.9679195
## 2 2 0.9670672
## 3 3 0.9661931
## 4 4 0.9652967
## 5 5 0.9643773
## 6 6 0.9634345#graph
g <- ggplot(data=dti_table, aes(x=dti_value,y=probability))
g + geom_line()+ ggtitle("Change in probability based on change in Debt to Income ratio")+labs(x="Debt to Income ratio,%")
The bar chart above shows how change in debt to income ratio reflects probability while holding all other variables constant.
By using logit function investor can verify how change in variable or combinations of variables can affect probability while holding all other variables constant.
The second part of my research focuses on finding a classifier that can predict whether the loan belongs to paid off or charged off class with higher accuracy. I considered J48, Naive Bayes, Ibk classifier and SMO classifier.
Before running classifiers I adjusted the data set, so that, it doesn’t contain redundant or statistically insignificant variables.
#full_data <- full_data %>% select(-loan_amnt,-revol_bal,-mths_since_last_record)J48 classifier. It uses ID3 algorithm that constructs the decision tree by employing a top-down, greedy search through the given sets to test each attribute at every tree node.
#create vectors to store accuracies values and errors values
classifier_name <-c()
Accuracy_mean <- c()
Accuracy_upper <- c()
Accuracy_lower <- c()
Kappa <- c()
MAE <- c()
RMSE <- c()
RAE <- c()
RRSE <- c()I used 66% of data for training and 34% for testing. In order to reduce the error I generated training set 50 times and ran each classifier 50 times.
classifier_name[1] <-c("J48")
#create empty vectors to store accuracies values and errors values for a certain classifier
pctCorrect_vector <- c()
Kappa_vector <- c()
MAE_vector <- c()
RMSE_vector <- c()
RAE_vector <- c()
RRSE_vector <- c()
for (i in 1:50){
#set the seed of R‘s random number generator
set.seed(i)
#create 66% training data set
training <- full_data[sample(nrow(full_data)),][1:round(0.66*nrow(full_data)),]
resultJ48 <- J48(loan_status ~., training)
evaluation <- evaluate_Weka_classifier(resultJ48)$details
pctCorrect_value <- evaluation["pctCorrect"]
Kappa_value <- evaluation["kappa"]
MAE_value <- evaluation["meanAbsoluteError"]
RMSE_value <- evaluation["rootMeanSquaredError"]
RAE_value <- evaluation["rootMeanSquaredError"]
RRSE_value <- evaluation["rootRelativeSquaredError"]
#add the value generated after each iteration to the vector
pctCorrect_vector <- c(pctCorrect_vector,pctCorrect_value)
Kappa_vector <- c(Kappa_vector, Kappa_value)
MAE_vector <- c(MAE_vector, MAE_value)
RMSE_vector <- c(RMSE_vector, RMSE_value)
RAE_vector <- c(RAE_vector, RAE_value)
RRSE_vector <- c(RRSE_vector, RRSE_value)
}
#calculate mean and standard deviation of accuracies and all errors
Accuracy_mean[1] <- mean(pctCorrect_vector)
pctCorrect_sd <- sd(pctCorrect_vector)
Accuracy_upper[1] <-Accuracy_mean[1] + pctCorrect_sd
Accuracy_lower <-Accuracy_mean[1] - pctCorrect_sd
Kappa[1] <- mean(Kappa_vector)
MAE[1] <- mean(MAE_vector)
RMSE[1] <- mean(RMSE_vector)
RAE[1] <- mean(RAE_vector)
RRSE[1] <- mean(RRSE_vector)Naive Bayes. This classifier is a simple probabilistic classifier that works based on applying Bayes’ theorem with strong independence assumptions. Naive Bayes classifiers can handle an arbitrary number of independent variables whether continuous or categorical
classifier_name[2] <-c("Naive Bayes")
#create empty vectors to store accuracies values and errors values
pctCorrect_vector <- c()
Kappa_vector <- c()
MAE_vector <- c()
RMSE_vector <- c()
RAE_vector <- c()
RRSE_vector <- c()
for (i in 1:50){
set.seed(i)
#create 66% training data set
training <- full_data[sample(nrow(full_data)),][1:round(0.66*nrow(full_data)),]
NB <- make_Weka_classifier("weka/classifiers/bayes/NaiveBayes")
result_NaiveBayes <- NB(loan_status ~., training)
evaluation <- evaluate_Weka_classifier(result_NaiveBayes)$details
pctCorrect_value <- evaluation["pctCorrect"]
Kappa_value <- evaluation["kappa"]
MAE_value <- evaluation["meanAbsoluteError"]
RMSE_value <- evaluation["rootMeanSquaredError"]
RAE_value <- evaluation["rootMeanSquaredError"]
RRSE_value <- evaluation["rootRelativeSquaredError"]
#add the value generated after each iteration to the vector
pctCorrect_vector <- c(pctCorrect_vector,pctCorrect_value)
Kappa_vector <- c(Kappa_vector, Kappa_value)
MAE_vector <- c(MAE_vector, MAE_value)
RMSE_vector <- c(RMSE_vector, RMSE_value)
RAE_vector <- c(RAE_vector, RAE_value)
RRSE_vector <- c(RRSE_vector, RRSE_value)
}
#calculate mean and standard deviation of accuracies and all errors
Accuracy_mean[2] <- mean(pctCorrect_vector)
pctCorrect_sd[2] <- sd(pctCorrect_vector)
Accuracy_upper[2] <-Accuracy_mean[2] + pctCorrect_sd[2]
Accuracy_lower[2] <-Accuracy_mean[2] - pctCorrect_sd[2]
Kappa[2] <- mean(Kappa_vector)
MAE[2] <- mean(MAE_vector)
RMSE[2] <- mean(RMSE_vector)
RAE[2] <- mean(RAE_vector)
RRSE[2] <- mean(RRSE_vector)IBk classifier. It implements the k-nearest neighbor algorithm that stores all available cases and classifies new cases based on a similarity measure such as Euclidean distance, Manhattan Distance or Makowski distance.
classifier_name[3] <-c("Knn")
#ignore the loop for this classifier since it loads very slow
#for (i in 1:50){
#set.seed(i)
#create 66% training data set
training <- full_data[sample(nrow(full_data)),][1:round(0.66*nrow(full_data)),]
knn <- IBk(loan_status ~., training)
evaluation <- evaluate_Weka_classifier(knn)$details
pctCorrect_value <- evaluation["pctCorrect"]
Kappa_value <- evaluation["Kappa"]
MAE_value <- evaluation["meanAbsoluteError"]
RMSE_value <- evaluation["rootMeanSquaredError"]
RAE_value <- evaluation["rootMeanSquaredError"]
RRSE_value <- evaluation["rootRelativeSquaredError"]
#}
#calculate mean and standard deviation of accuracies and all errors
Accuracy_mean[3] <- mean(pctCorrect_value)
#pctCorrect_sd[3] <- sd(pctCorrect_value)
Accuracy_upper[3] <- ""
Accuracy_lower[3] <- ""
Kappa[3] <- mean(Kappa_value)
MAE[3] <- mean(MAE_value)
RMSE[3] <- mean(RMSE_value)
RAE[3] <- mean(RAE_value)
RRSE[3] <- mean(RRSE_value)Support Vector Machine (SMO classifier) performs classification by constructing an N-dimensional hyper plane that optimally separates the data into two categories. SVM models are closely related to neural networks. SVM model that is uses a sigmoid kernel function s equivalent to a two-layer perceptron neural network.
classifier_name[4] <-c("SVM")
#ignore the loop for this classifier since it loads very slow
#for (i in 1:50){
#set.seed(i)
#create 66% training data set
training <- full_data[sample(nrow(full_data)),][1:round(0.66*nrow(full_data)),]
SVM <- SMO(loan_status ~., training)
evaluation <- evaluate_Weka_classifier(SVM)$details
pctCorrect_value <- evaluation["pctCorrect"]
Kappa_value <- evaluation["kappa"]
MAE_value <- evaluation["meanAbsoluteError"]
RMSE_value <- evaluation["rootMeanSquaredError"]
RAE_value <- evaluation["rootMeanSquaredError"]
RRSE_value <- evaluation["rootRelativeSquaredError"]
#}
#calculate mean and standard deviation of accuracies and all errors
Accuracy_mean[4] <- mean(pctCorrect_value)
#pctCorrect_sd[4] <- sd(pctCorrect_value)
Accuracy_upper[4] <- ""
Accuracy_lower[4] <- ""
Kappa[4] <- mean(Kappa_value)
MAE[4] <- mean(MAE_value)
RMSE[4] <- mean(RMSE_value)
RAE[4] <- mean(RAE_value)
RRSE[4] <- mean(RRSE_value) data_table <- data.frame(classifier_name, Accuracy_mean, Accuracy_upper, Accuracy_lower, Kappa, MAE, RMSE, RAE, RRSE)
data_table## classifier_name Accuracy_mean Accuracy_upper Accuracy_lower
## 1 J48 77.20244 77.474168268397 76.9307023318712
## 2 Naive Bayes 65.88770 67.1079614504185 64.6674348453141
## 3 Knn 71.33875
## 4 SVM 77.66718
## Kappa MAE RMSE RAE RRSE
## 1 0.04889376 0.3159595 0.4167403 0.4167403 99.74316
## 2 0.14666984 0.3886717 0.4922871 0.4922871 117.82535
## 3 NA 0.2866303 0.5353396 0.5353396 128.48147
## 4 0.00000000 0.2233282 0.4725761 0.4725761 113.47004I considered the following errors in my analysis:
Mean Absolute Error (MAE) shows the deviation between predicted and actual outcome.
Root Mean Squared Error (RMSD) measures the error between predicted and actual results.
Relative Absolute Error (RAE) measures by normalizing with respect to the performance obtained by predicting the classes’ prior probabilities as estimated from the training data with a simple Laplace estimator.
#rename accuracy_mean column and divide by 100
#converting wide data format to long data
data <- data_table %>% rename(Accuracy = Accuracy_mean) %>% mutate(Accuracy = Accuracy/100) %>% select(-Accuracy_upper,-Accuracy_lower,-Kappa,-RRSE)
data <- data %>% gather(accuracy_error,value,colnames(data)[2]:colnames(data)[5]) ggplot(data, aes(factor(accuracy_error), value, fill = classifier_name)) + geom_bar(stat="identity", position = "dodge") + scale_fill_brewer(palette = "Set1")
According to the bar chart above, Support Vector Mashine classifier and J48 classifier have higher accuracies while J48 classifier has pretty low MAE, RMSD and RAE. I can conclude that J48 classifier is the optimal classifier because it has the heist accuracy and pretty low error values.
Let’s check.
#34% data for testing
testing <- full_data[sample(nrow(full_data)),][(round(0.66*nrow(full_data))+1):nrow(full_data),]
J48_pred <- predict(resultJ48, newdata = testing)
table(testing$loan_status, J48_pred)## J48_pred
## Charged Off Fully Paid
## Charged Off 9826 43511
## Fully Paid 15715 194053The confusion matrix shows that the accuracy of prediction is pretty high.
The goals of the project have been achieved. I figured out the equation that estimates the probability of weather the load will be paid off or not, demonstrated how different variables can affect the probability and found the optimal classifier that can predict whether the loan will be paid off or not with higher accuracy.
Each part of the project was a challenge for me since I’m new to statistics and R. The biggest problem was that some of the function were running very slow because the initial merged data set contains 773838 observation.