Data 621: Homework 4 - Data Exploration & Data Preparation
George Cruz Deschamps, Karim Hammoud, Maliat Islam, Matthew Lucich, Gabriella Maritnez, Ken Popkin
DATA 621 – Business Analytics and Data Mining Homework #4 Assignment Requirements
Overview In this homework assignment, you will explore, analyze and model a data set containing approximately 8000 records representing a customer at an auto insurance company. Each record has two response variables. The first response variable, TARGET_FLAG, is a 1 or a 0. A “1” means that the person was in a car crash. A zero means that the person was not in a car crash. The second response variable is TARGET_AMT. This value is zero if the person did not crash their car. But if they did crash their car, this number will be a value greater than zero.
Your objective is to build multiple linear regression and binary logistic regression models on the training data to predict the probability that a person will crash their car and also the amount of money it will cost if the person does crash their car. You can only use the variables given to you (or variables that you derive from the variables provided).
library(tidyverse)
library(ggplot2)
library(mice)
library(car)
library(Hmisc)
library(corrplot)
library(pscl)
library(boot)
library(MASS)
library(caret)Load data
# Load insurance csv
df_ins_raw <- read.csv("insurance_training_data.csv")
# Removing index as instructed
df_ins_raw <- subset(df_ins_raw, select = -c(INDEX))
# Preview data
glimpse(df_ins_raw)## Rows: 8,161
## Columns: 25
## $ TARGET_FLAG <int> 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1…
## $ TARGET_AMT <dbl> 0.000, 0.000, 0.000, 0.000, 0.000, 2946.000, 0.000, 4021.0…
## $ KIDSDRIV <int> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ AGE <int> 60, 43, 35, 51, 50, 34, 54, 37, 34, 50, 53, 43, 55, 53, 45…
## $ HOMEKIDS <int> 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 2, 1…
## $ YOJ <int> 11, 11, 10, 14, NA, 12, NA, NA, 10, 7, 14, 5, 11, 11, 0, 1…
## $ INCOME <chr> "$67,349", "$91,449", "$16,039", "", "$114,986", "$125,301…
## $ PARENT1 <chr> "No", "No", "No", "No", "No", "Yes", "No", "No", "No", "No…
## $ HOME_VAL <chr> "$0", "$257,252", "$124,191", "$306,251", "$243,925", "$0"…
## $ MSTATUS <chr> "z_No", "z_No", "Yes", "Yes", "Yes", "z_No", "Yes", "Yes",…
## $ SEX <chr> "M", "M", "z_F", "M", "z_F", "z_F", "z_F", "M", "z_F", "M"…
## $ EDUCATION <chr> "PhD", "z_High School", "z_High School", "<High School", "…
## $ JOB <chr> "Professional", "z_Blue Collar", "Clerical", "z_Blue Colla…
## $ TRAVTIME <int> 14, 22, 5, 32, 36, 46, 33, 44, 34, 48, 15, 36, 25, 64, 48,…
## $ CAR_USE <chr> "Private", "Commercial", "Private", "Private", "Private", …
## $ BLUEBOOK <chr> "$14,230", "$14,940", "$4,010", "$15,440", "$18,000", "$17…
## $ TIF <int> 11, 1, 4, 7, 1, 1, 1, 1, 1, 7, 1, 7, 7, 6, 1, 6, 6, 7, 4, …
## $ CAR_TYPE <chr> "Minivan", "Minivan", "z_SUV", "Minivan", "z_SUV", "Sports…
## $ RED_CAR <chr> "yes", "yes", "no", "yes", "no", "no", "no", "yes", "no", …
## $ OLDCLAIM <chr> "$4,461", "$0", "$38,690", "$0", "$19,217", "$0", "$0", "$…
## $ CLM_FREQ <int> 2, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2…
## $ REVOKED <chr> "No", "No", "No", "No", "Yes", "No", "No", "Yes", "No", "N…
## $ MVR_PTS <int> 3, 0, 3, 0, 3, 0, 0, 10, 0, 1, 0, 0, 3, 3, 3, 0, 0, 0, 0, …
## $ CAR_AGE <int> 18, 1, 10, 6, 17, 7, 1, 7, 1, 17, 11, 1, 9, 10, 5, 13, 16,…
## $ URBANICITY <chr> "Highly Urban/ Urban", "Highly Urban/ Urban", "Highly Urba…DATA CLEANING
Fix formatting
remove_z <- function(x){
str_replace(x, 'z_', '')
}
# Remove extraneous z_
df_ins_raw <- mutate_all(df_ins_raw, funs(remove_z))## Warning: `funs()` was deprecated in dplyr 0.8.0.
## Please use a list of either functions or lambdas:
##
## # Simple named list:
## list(mean = mean, median = median)
##
## # Auto named with `tibble::lst()`:
## tibble::lst(mean, median)
##
## # Using lambdas
## list(~ mean(., trim = .2), ~ median(., na.rm = TRUE))
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.remove_dollar <- function(x){
str_replace(x, '\\$', '')
}
# Remove dollar sign from variables
df_ins_raw <- mutate_all(df_ins_raw, funs(remove_dollar))
remove_comma <- function(x){
str_replace(x, ',', '')
}
# Remove commas from variables
df_ins_raw <- mutate_all(df_ins_raw, funs(remove_comma))
# Preview updated data
glimpse(df_ins_raw)## Rows: 8,161
## Columns: 25
## $ TARGET_FLAG <chr> "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "0"…
## $ TARGET_AMT <chr> "0", "0", "0", "0", "0", "2946", "0", "4021", "2501", "0",…
## $ KIDSDRIV <chr> "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0"…
## $ AGE <chr> "60", "43", "35", "51", "50", "34", "54", "37", "34", "50"…
## $ HOMEKIDS <chr> "0", "0", "1", "0", "0", "1", "0", "2", "0", "0", "0", "0"…
## $ YOJ <chr> "11", "11", "10", "14", NA, "12", NA, NA, "10", "7", "14",…
## $ INCOME <chr> "67349", "91449", "16039", "", "114986", "125301", "18755"…
## $ PARENT1 <chr> "No", "No", "No", "No", "No", "Yes", "No", "No", "No", "No…
## $ HOME_VAL <chr> "0", "257252", "124191", "306251", "243925", "0", "", "333…
## $ MSTATUS <chr> "No", "No", "Yes", "Yes", "Yes", "No", "Yes", "Yes", "No",…
## $ SEX <chr> "M", "M", "F", "M", "F", "F", "F", "M", "F", "M", "F", "F"…
## $ EDUCATION <chr> "PhD", "High School", "High School", "<High School", "PhD"…
## $ JOB <chr> "Professional", "Blue Collar", "Clerical", "Blue Collar", …
## $ TRAVTIME <chr> "14", "22", "5", "32", "36", "46", "33", "44", "34", "48",…
## $ CAR_USE <chr> "Private", "Commercial", "Private", "Private", "Private", …
## $ BLUEBOOK <chr> "14230", "14940", "4010", "15440", "18000", "17430", "8780…
## $ TIF <chr> "11", "1", "4", "7", "1", "1", "1", "1", "1", "7", "1", "7…
## $ CAR_TYPE <chr> "Minivan", "Minivan", "SUV", "Minivan", "SUV", "Sports Car…
## $ RED_CAR <chr> "yes", "yes", "no", "yes", "no", "no", "no", "yes", "no", …
## $ OLDCLAIM <chr> "4461", "0", "38690", "0", "19217", "0", "0", "2374", "0",…
## $ CLM_FREQ <chr> "2", "0", "2", "0", "2", "0", "0", "1", "0", "0", "0", "0"…
## $ REVOKED <chr> "No", "No", "No", "No", "Yes", "No", "No", "Yes", "No", "N…
## $ MVR_PTS <chr> "3", "0", "3", "0", "3", "0", "0", "10", "0", "1", "0", "0…
## $ CAR_AGE <chr> "18", "1", "10", "6", "17", "7", "1", "7", "1", "17", "11"…
## $ URBANICITY <chr> "Highly Urban/ Urban", "Highly Urban/ Urban", "Highly Urba…Review distinct values
# Count of distinct values for each column
df_ins_raw %>% summarise_all(n_distinct)## TARGET_FLAG TARGET_AMT KIDSDRIV AGE HOMEKIDS YOJ INCOME PARENT1 HOME_VAL
## 1 2 1949 5 61 6 22 6613 2 5107
## MSTATUS SEX EDUCATION JOB TRAVTIME CAR_USE BLUEBOOK TIF CAR_TYPE RED_CAR
## 1 2 2 5 9 97 2 2789 23 6 2
## OLDCLAIM CLM_FREQ REVOKED MVR_PTS CAR_AGE URBANICITY
## 1 2857 6 2 13 31 2df_ins_raw %>% distinct(PARENT1)## PARENT1
## 1 No
## 2 Yesdf_ins_raw %>% distinct(MSTATUS)## MSTATUS
## 1 No
## 2 Yesdf_ins_raw %>% distinct(SEX)## SEX
## 1 M
## 2 Fdf_ins_raw %>% distinct(EDUCATION)## EDUCATION
## 1 PhD
## 2 High School
## 3 <High School
## 4 Bachelors
## 5 Mastersdf_ins_raw %>% distinct(JOB)## JOB
## 1 Professional
## 2 Blue Collar
## 3 Clerical
## 4 Doctor
## 5 Lawyer
## 6 Manager
## 7
## 8 Home Maker
## 9 Studentdf_ins_raw %>% distinct(CAR_USE)## CAR_USE
## 1 Private
## 2 Commercialdf_ins_raw %>% distinct(CAR_TYPE)## CAR_TYPE
## 1 Minivan
## 2 SUV
## 3 Sports Car
## 4 Van
## 5 Panel Truck
## 6 Pickupdf_ins_raw %>% distinct(CLM_FREQ)## CLM_FREQ
## 1 2
## 2 0
## 3 1
## 4 3
## 5 5
## 6 4df_ins_raw %>% distinct(REVOKED)## REVOKED
## 1 No
## 2 Yesdf_ins_raw %>% distinct(URBANICITY)## URBANICITY
## 1 Highly Urban/ Urban
## 2 Highly Rural/ RuralConvert datatypes
# Set data types for variables
df_ins_clean <- df_ins_raw %>% transform(
TARGET_FLAG = as.factor(TARGET_FLAG),
TARGET_AMT = as.numeric(TARGET_AMT),
KIDSDRIV = as.factor(KIDSDRIV),
AGE = as.numeric(AGE),
HOMEKIDS = as.factor(HOMEKIDS),
YOJ = as.numeric(YOJ),
INCOME = as.numeric(INCOME),
PARENT1 = as.factor(PARENT1),
HOME_VAL = as.numeric(HOME_VAL),
MSTATUS = as.factor(MSTATUS),
SEX = as.factor(SEX),
EDUCATION = as.factor(EDUCATION),
JOB = as.factor(JOB),
TRAVTIME = as.numeric(TRAVTIME),
CAR_USE = as.factor(CAR_USE),
BLUEBOOK = as.numeric(BLUEBOOK),
TIF = as.numeric(TIF), # factor or numeric?
CAR_TYPE = as.factor(CAR_TYPE),
RED_CAR = as.factor(RED_CAR),
OLDCLAIM = as.numeric(OLDCLAIM),
CLM_FREQ = as.ordered(CLM_FREQ), # factor or numeric?
REVOKED = as.factor(REVOKED),
MVR_PTS = as.numeric(MVR_PTS),
CAR_AGE = as.numeric(CAR_AGE),
URBANICITY = as.factor(URBANICITY))
# Confirm CLM_FREQ is an ordered factor
is.ordered(df_ins_clean$CLM_FREQ)## [1] TRUEReview NAs
# NA counts for each column
colSums(is.na(df_ins_clean))## TARGET_FLAG TARGET_AMT KIDSDRIV AGE HOMEKIDS YOJ
## 0 0 0 6 0 454
## INCOME PARENT1 HOME_VAL MSTATUS SEX EDUCATION
## 445 0 464 0 0 0
## JOB TRAVTIME CAR_USE BLUEBOOK TIF CAR_TYPE
## 0 0 0 0 0 0
## RED_CAR OLDCLAIM CLM_FREQ REVOKED MVR_PTS CAR_AGE
## 0 0 0 0 0 510
## URBANICITY
## 0# Visualize NA counts for each column
df_ins_clean %>%
summarise_all(list(~is.na(.)))%>%
pivot_longer(everything(),
names_to = "variables", values_to="missing") %>%
count(variables, missing) %>%
ggplot(aes(y=variables,x=n,fill=missing))+
geom_col()
Data imputation
# Impute data by regression:
df_ins_imp <- mice(df_ins_clean, method = "norm.predict", m = 1, remove.collinear=FALSE)##
## iter imp variable
## 1 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 2 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 3 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 4 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 5 1 AGE YOJ INCOME HOME_VAL CAR_AGEdf_ins_imp <- complete(df_ins_imp)
# Confirm no NAs remain
colSums(is.na(df_ins_imp))## TARGET_FLAG TARGET_AMT KIDSDRIV AGE HOMEKIDS YOJ
## 0 0 0 0 0 0
## INCOME PARENT1 HOME_VAL MSTATUS SEX EDUCATION
## 0 0 0 0 0 0
## JOB TRAVTIME CAR_USE BLUEBOOK TIF CAR_TYPE
## 0 0 0 0 0 0
## RED_CAR OLDCLAIM CLM_FREQ REVOKED MVR_PTS CAR_AGE
## 0 0 0 0 0 0
## URBANICITY
## 0DATA EXPLORATION
Summary statistics
describe(df_ins_imp)## df_ins_imp
##
## 25 Variables 8161 Observations
## --------------------------------------------------------------------------------
## TARGET_FLAG
## n missing distinct
## 8161 0 2
##
## Value 0 1
## Frequency 6008 2153
## Proportion 0.736 0.264
## --------------------------------------------------------------------------------
## TARGET_AMT
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 1949 0.601 1504 2574 0 0
## .25 .50 .75 .90 .95
## 0 0 1036 4904 6452
##
## lowest : 0.00000 30.27728 58.53106 95.56732 108.74150
## highest: 73783.46592 77907.43028 78874.19056 85523.65335 107586.13616
## --------------------------------------------------------------------------------
## KIDSDRIV
## n missing distinct
## 8161 0 5
##
## lowest : 0 1 2 3 4, highest: 0 1 2 3 4
##
## Value 0 1 2 3 4
## Frequency 7180 636 279 62 4
## Proportion 0.880 0.078 0.034 0.008 0.000
## --------------------------------------------------------------------------------
## AGE
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 66 0.999 44.78 9.749 30 34
## .25 .50 .75 .90 .95
## 39 45 51 56 59
##
## lowest : 16 17 18 19 20, highest: 72 73 76 80 81
## --------------------------------------------------------------------------------
## HOMEKIDS
## n missing distinct
## 8161 0 6
##
## lowest : 0 1 2 3 4, highest: 1 2 3 4 5
##
## Value 0 1 2 3 4 5
## Frequency 5289 902 1118 674 164 14
## Proportion 0.648 0.111 0.137 0.083 0.020 0.002
## --------------------------------------------------------------------------------
## YOJ
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 475 0.991 10.5 4.2 0 5
## .25 .50 .75 .90 .95
## 9 11 13 14 15
##
## lowest : 0.000000 1.000000 2.000000 2.748179 3.000000
## highest: 16.348246 17.000000 18.000000 19.000000 23.000000
## --------------------------------------------------------------------------------
## INCOME
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 7057 1 61595 51009 0 4362
## .25 .50 .75 .90 .95
## 27940 54216 85472 122744 151663
##
## lowest : -31968.52 -26991.28 -20478.35 -16829.40 -16713.97
## highest: 306277.00 309628.00 320127.00 332339.00 367030.00
## --------------------------------------------------------------------------------
## PARENT1
## n missing distinct
## 8161 0 2
##
## Value No Yes
## Frequency 7084 1077
## Proportion 0.868 0.132
## --------------------------------------------------------------------------------
## HOME_VAL
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 5570 0.978 154934 142397 0 0
## .25 .50 .75 .90 .95
## 0 160953 237604 314151 373031
##
## lowest : -86662.47 -71570.86 -71165.20 -70648.14 -68150.79
## highest: 657804.00 682634.00 738153.00 750455.00 885282.00
## --------------------------------------------------------------------------------
## MSTATUS
## n missing distinct
## 8161 0 2
##
## Value No Yes
## Frequency 3267 4894
## Proportion 0.4 0.6
## --------------------------------------------------------------------------------
## SEX
## n missing distinct
## 8161 0 2
##
## Value F M
## Frequency 4375 3786
## Proportion 0.536 0.464
## --------------------------------------------------------------------------------
## EDUCATION
## n missing distinct
## 8161 0 5
##
## lowest : <High School Bachelors High School Masters PhD
## highest: <High School Bachelors High School Masters PhD
##
## Value <High School Bachelors High School Masters PhD
## Frequency 1203 2242 2330 1658 728
## Proportion 0.147 0.275 0.286 0.203 0.089
## --------------------------------------------------------------------------------
## JOB
## n missing distinct
## 8161 0 9
##
## lowest : Blue Collar Clerical Doctor Home Maker
## highest: Home Maker Lawyer Manager Professional Student
##
## Value Blue Collar Clerical Doctor Home Maker
## Frequency 526 1825 1271 246 641
## Proportion 0.064 0.224 0.156 0.030 0.079
##
## Value Lawyer Manager Professional Student
## Frequency 835 988 1117 712
## Proportion 0.102 0.121 0.137 0.087
## --------------------------------------------------------------------------------
## TRAVTIME
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 97 1 33.49 17.85 7 13
## .25 .50 .75 .90 .95
## 22 33 44 54 60
##
## lowest : 5 6 7 8 9, highest: 103 113 124 134 142
## --------------------------------------------------------------------------------
## CAR_USE
## n missing distinct
## 8161 0 2
##
## Value Commercial Private
## Frequency 3029 5132
## Proportion 0.371 0.629
## --------------------------------------------------------------------------------
## BLUEBOOK
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 2789 1 15710 9354 4900 6000
## .25 .50 .75 .90 .95
## 9280 14440 20850 27460 31110
##
## lowest : 1500 1520 1530 1540 1590, highest: 57970 61050 62240 65970 69740
## --------------------------------------------------------------------------------
## TIF
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 23 0.961 5.351 4.512 1 1
## .25 .50 .75 .90 .95
## 1 4 7 11 13
##
## lowest : 1 2 3 4 5, highest: 19 20 21 22 25
## --------------------------------------------------------------------------------
## CAR_TYPE
## n missing distinct
## 8161 0 6
##
## lowest : Minivan Panel Truck Pickup Sports Car SUV
## highest: Panel Truck Pickup Sports Car SUV Van
##
## Value Minivan Panel Truck Pickup Sports Car SUV
## Frequency 2145 676 1389 907 2294
## Proportion 0.263 0.083 0.170 0.111 0.281
##
## Value Van
## Frequency 750
## Proportion 0.092
## --------------------------------------------------------------------------------
## RED_CAR
## n missing distinct
## 8161 0 2
##
## Value no yes
## Frequency 5783 2378
## Proportion 0.709 0.291
## --------------------------------------------------------------------------------
## OLDCLAIM
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 2857 0.769 4037 6563 0 0
## .25 .50 .75 .90 .95
## 0 0 4636 9583 27090
##
## lowest : 0 502 506 518 519, highest: 52507 53477 53568 53986 57037
## --------------------------------------------------------------------------------
## CLM_FREQ
## n missing distinct
## 8161 0 6
##
## lowest : 0 1 2 3 4, highest: 1 2 3 4 5
##
## Value 0 1 2 3 4 5
## Frequency 5009 997 1171 776 190 18
## Proportion 0.614 0.122 0.143 0.095 0.023 0.002
## --------------------------------------------------------------------------------
## REVOKED
## n missing distinct
## 8161 0 2
##
## Value No Yes
## Frequency 7161 1000
## Proportion 0.877 0.123
## --------------------------------------------------------------------------------
## MVR_PTS
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 13 0.9 1.696 2.187 0 0
## .25 .50 .75 .90 .95
## 0 1 3 5 6
##
## lowest : 0 1 2 3 4, highest: 8 9 10 11 13
##
## Value 0 1 2 3 4 5 6 7 8 9 10
## Frequency 3712 1157 948 758 599 399 266 167 84 45 13
## Proportion 0.455 0.142 0.116 0.093 0.073 0.049 0.033 0.020 0.010 0.006 0.002
##
## Value 11 13
## Frequency 11 2
## Proportion 0.001 0.000
## --------------------------------------------------------------------------------
## CAR_AGE
## n missing distinct Info Mean Gmd .05 .10
## 8161 0 540 0.985 8.347 6.374 1.000 1.000
## .25 .50 .75 .90 .95
## 3.514 8.000 12.000 16.000 18.000
##
## lowest : -3.0000000 -1.1184462 -0.9423218 0.0000000 1.0000000
## highest: 24.0000000 25.0000000 26.0000000 27.0000000 28.0000000
## --------------------------------------------------------------------------------
## URBANICITY
## n missing distinct
## 8161 0 2
##
## Value Highly Rural/ Rural Highly Urban/ Urban
## Frequency 1669 6492
## Proportion 0.205 0.795
## --------------------------------------------------------------------------------Distributions of variables
# Histograms
df_ins_imp %>%
keep(is.numeric) %>%
gather() %>%
ggplot(aes(value)) +
facet_wrap(~ key, scales = "free") +
geom_density(fill = "steelblue", alpha=0.9, color="steelblue") +
geom_histogram(aes(y=..density..), alpha=0.5, fill = "lightblue", color="lightblue", position="identity")
# Boxplots
df_ins_imp %>%
keep(is.numeric) %>%
gather() %>%
ggplot(aes(value)) +
facet_wrap(~ key, scales = "free") +
geom_boxplot(fill = "steelblue", color="black", outlier.colour="red", outlier.shape=16,
outlier.size=2, notch=FALSE)
Distributions of log-transformed variables
# Log transformation
df_ins_imp_log <- df_ins_imp %>% keep(is.numeric)
df_ins_imp_log <- log(df_ins_imp_log + 1)
# Histograms of log transformed numeric variables
df_ins_imp_log %>%
gather(variable, value, TARGET_AMT:CAR_AGE) %>%
ggplot(., aes(value)) +
geom_density(fill = "steelblue", color="steelblue") +
facet_wrap(~variable, scales ="free", ncol = 4) +
labs(x = element_blank(), y = element_blank())
# Test for normality
shapiro.test(df_ins_imp_log$AGE[0:5000])##
## Shapiro-Wilk normality test
##
## data: df_ins_imp_log$AGE[0:5000]
## W = 0.97949, p-value < 2.2e-16# Visual inspection of one variable (age) for normality
qqnorm(df_ins_imp_log$AGE, pch = 1, frame = FALSE)
qqline(df_ins_imp_log$AGE, col = "steelblue", lwd = 2)
Distributions of square root-transformed variables
# Square root transformation
df_ins_imp_sqrt <- sqrt(df_ins_imp %>% keep(is.numeric))
# Histograms of square root transformed numeric variables
df_ins_imp_sqrt %>%
gather(variable, value, TARGET_AMT:CAR_AGE) %>%
ggplot(., aes(value)) +
geom_density(fill = "steelblue", color="steelblue") +
facet_wrap(~variable, scales ="free", ncol = 4) +
labs(x = element_blank(), y = element_blank())
# Test for normality
shapiro.test(df_ins_imp_sqrt$AGE[0:5000])##
## Shapiro-Wilk normality test
##
## data: df_ins_imp_sqrt$AGE[0:5000]
## W = 0.99371, p-value = 5.047e-14# Visual inspection of one variable (age) for normality
qqnorm(df_ins_imp_sqrt$AGE, pch = 1, frame = FALSE)
qqline(df_ins_imp_sqrt$AGE, col = "steelblue", lwd = 2)
Distributions of cube root-transformed variables
# Cube root transformation
df_ins_imp_cube <- (df_ins_imp %>% keep(is.numeric))^(1/3)
# Histograms of cube root transformed numeric variables
df_ins_imp_cube %>%
gather(variable, value, TARGET_AMT:CAR_AGE) %>%
ggplot(., aes(value)) +
geom_density(fill = "steelblue", color="steelblue") +
facet_wrap(~variable, scales ="free", ncol = 4) +
labs(x = element_blank(), y = element_blank())
# Test for normality
shapiro.test(df_ins_imp_cube$AGE[0:5000])##
## Shapiro-Wilk normality test
##
## data: df_ins_imp_cube$AGE[0:5000]
## W = 0.98989, p-value < 2.2e-16# Visual inspection of one variable (age) for normality
qqnorm(df_ins_imp_cube$AGE, pch = 1, frame = FALSE)
qqline(df_ins_imp_cube$AGE, col = "steelblue", lwd = 2)
Create new columns with transformed variables
df_ins <- df_ins_imp %>%
mutate(across(c(TARGET_AMT, AGE, YOJ, INCOME, HOME_VAL, TRAVTIME, BLUEBOOK,
TIF, OLDCLAIM, MVR_PTS, CAR_AGE), .fns = list(log = ~ log(. + 1))))
df_ins <- df_ins %>%
mutate(across(c(TARGET_AMT, AGE, YOJ, INCOME, HOME_VAL, TRAVTIME, BLUEBOOK,
TIF, OLDCLAIM, MVR_PTS, CAR_AGE), .fns = list(sqrt = sqrt)))
df_ins <- df_ins %>%
mutate(across(c(TARGET_AMT, AGE, YOJ, INCOME, HOME_VAL, TRAVTIME, BLUEBOOK,
TIF, OLDCLAIM, MVR_PTS, CAR_AGE), .fns = list(cbrt = ~ .^(1/3))))
glimpse(df_ins)## Rows: 8,161
## Columns: 58
## $ TARGET_FLAG <fct> 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, …
## $ TARGET_AMT <dbl> 0.000, 0.000, 0.000, 0.000, 0.000, 2946.000, 0.000, 40…
## $ KIDSDRIV <fct> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ AGE <dbl> 60, 43, 35, 51, 50, 34, 54, 37, 34, 50, 53, 43, 55, 53…
## $ HOMEKIDS <fct> 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, …
## $ YOJ <dbl> 11.00000, 11.00000, 10.00000, 14.00000, 11.34200, 12.0…
## $ INCOME <dbl> 67349.00, 91449.00, 16039.00, 67185.86, 114986.00, 125…
## $ PARENT1 <fct> No, No, No, No, No, Yes, No, No, No, No, No, No, No, N…
## $ HOME_VAL <dbl> 0.0, 257252.0, 124191.0, 306251.0, 243925.0, 0.0, 1654…
## $ MSTATUS <fct> No, No, Yes, Yes, Yes, No, Yes, Yes, No, No, No, Yes, …
## $ SEX <fct> M, M, F, M, F, F, F, M, F, M, F, F, M, M, F, F, M, F, …
## $ EDUCATION <fct> PhD, High School, High School, <High School, PhD, Bach…
## $ JOB <fct> Professional, Blue Collar, Clerical, Blue Collar, Doct…
## $ TRAVTIME <dbl> 14, 22, 5, 32, 36, 46, 33, 44, 34, 48, 15, 36, 25, 64,…
## $ CAR_USE <fct> Private, Commercial, Private, Private, Private, Commer…
## $ BLUEBOOK <dbl> 14230, 14940, 4010, 15440, 18000, 17430, 8780, 16970, …
## $ TIF <dbl> 11, 1, 4, 7, 1, 1, 1, 1, 1, 7, 1, 7, 7, 6, 1, 6, 6, 7,…
## $ CAR_TYPE <fct> Minivan, Minivan, SUV, Minivan, SUV, Sports Car, SUV, …
## $ RED_CAR <fct> yes, yes, no, yes, no, no, no, yes, no, no, no, no, ye…
## $ OLDCLAIM <dbl> 4461, 0, 38690, 0, 19217, 0, 0, 2374, 0, 0, 0, 0, 5028…
## $ CLM_FREQ <ord> 2, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, …
## $ REVOKED <fct> No, No, No, No, Yes, No, No, Yes, No, No, No, No, Yes,…
## $ MVR_PTS <dbl> 3, 0, 3, 0, 3, 0, 0, 10, 0, 1, 0, 0, 3, 3, 3, 0, 0, 0,…
## $ CAR_AGE <dbl> 18, 1, 10, 6, 17, 7, 1, 7, 1, 17, 11, 1, 9, 10, 5, 13,…
## $ URBANICITY <fct> Highly Urban/ Urban, Highly Urban/ Urban, Highly Urban…
## $ TARGET_AMT_log <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 7.98…
## $ AGE_log <dbl> 4.110874, 3.784190, 3.583519, 3.951244, 3.931826, 3.55…
## $ YOJ_log <dbl> 2.484907, 2.484907, 2.397895, 2.708050, 2.513008, 2.56…
## $ INCOME_log <dbl> 11.117658, 11.423548, 9.682841, 11.115233, 11.652574, …
## $ HOME_VAL_log <dbl> 0.00000, 12.45782, 11.72958, 12.63216, 12.40462, 0.000…
## $ TRAVTIME_log <dbl> 2.708050, 3.135494, 1.791759, 3.496508, 3.610918, 3.85…
## $ BLUEBOOK_log <dbl> 9.563178, 9.611864, 8.296796, 9.644782, 9.798183, 9.76…
## $ TIF_log <dbl> 2.4849066, 0.6931472, 1.6094379, 2.0794415, 0.6931472,…
## $ OLDCLAIM_log <dbl> 8.403352, 0.000000, 10.563362, 0.000000, 9.863603, 0.0…
## $ MVR_PTS_log <dbl> 1.3862944, 0.0000000, 1.3862944, 0.0000000, 1.3862944,…
## $ CAR_AGE_log <dbl> 2.9444390, 0.6931472, 2.3978953, 1.9459101, 2.8903718,…
## $ TARGET_AMT_sqrt <dbl> 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 54.27707,…
## $ AGE_sqrt <dbl> 7.745967, 6.557439, 5.916080, 7.141428, 7.071068, 5.83…
## $ YOJ_sqrt <dbl> 3.316625, 3.316625, 3.162278, 3.741657, 3.367789, 3.46…
## $ INCOME_sqrt <dbl> 259.5169, 302.4054, 126.6452, 259.2024, 339.0959, 353.…
## $ HOME_VAL_sqrt <dbl> 0.0000, 507.2002, 352.4074, 553.3995, 493.8876, 0.0000…
## $ TRAVTIME_sqrt <dbl> 3.741657, 4.690416, 2.236068, 5.656854, 6.000000, 6.78…
## $ BLUEBOOK_sqrt <dbl> 119.28956, 122.22929, 63.32456, 124.25780, 134.16408, …
## $ TIF_sqrt <dbl> 3.316625, 1.000000, 2.000000, 2.645751, 1.000000, 1.00…
## $ OLDCLAIM_sqrt <dbl> 66.79072, 0.00000, 196.69774, 0.00000, 138.62539, 0.00…
## $ MVR_PTS_sqrt <dbl> 1.732051, 0.000000, 1.732051, 0.000000, 1.732051, 0.00…
## $ CAR_AGE_sqrt <dbl> 4.242641, 1.000000, 3.162278, 2.449490, 4.123106, 2.64…
## $ TARGET_AMT_cbrt <dbl> 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 14.33544,…
## $ AGE_cbrt <dbl> 3.914868, 3.503398, 3.271066, 3.708430, 3.684031, 3.23…
## $ YOJ_cbrt <dbl> 2.223980, 2.223980, 2.154435, 2.410142, 2.246794, 2.28…
## $ INCOME_cbrt <dbl> 40.68588, 45.05327, 25.21888, 40.65300, 48.62747, 50.0…
## $ HOME_VAL_cbrt <dbl> 0.00000, 63.59939, 49.89190, 67.40506, 62.48159, 0.000…
## $ TRAVTIME_cbrt <dbl> 2.410142, 2.802039, 1.709976, 3.174802, 3.301927, 3.58…
## $ BLUEBOOK_cbrt <dbl> 24.23269, 24.62919, 15.88723, 24.90094, 26.20741, 25.9…
## $ TIF_cbrt <dbl> 2.223980, 1.000000, 1.587401, 1.912931, 1.000000, 1.00…
## $ OLDCLAIM_cbrt <dbl> 16.46180, 0.00000, 33.82202, 0.00000, 26.78522, 0.0000…
## $ MVR_PTS_cbrt <dbl> 1.442250, 0.000000, 1.442250, 0.000000, 1.442250, 0.00…
## $ CAR_AGE_cbrt <dbl> 2.620741, 1.000000, 2.154435, 1.817121, 2.571282, 1.91…Create new variables
df_ins$HV_INC_RATIO <- df_ins$HOME_VAL / df_ins$INCOME
df_ins$TRT_MVR_PRODUCT <- df_ins$TRAVTIME * df_ins$MVR_PTS
df_ins$HV_INC_RATIO[is.nan(df_ins$HV_INC_RATIO)] <- 0
df_ins$HV_INC_RATIO[is.infinite(df_ins$HV_INC_RATIO)] <- 0Data imputation again
# Impute data by regression:
df_ins <- mice(df_ins, method = "norm.predict", m = 1, remove.collinear=FALSE)##
## iter imp variable
## 1 1 INCOME_log* HOME_VAL_log* CAR_AGE_log* INCOME_sqrt* HOME_VAL_sqrt* CAR_AGE_sqrt* INCOME_cbrt* HOME_VAL_cbrt* CAR_AGE_cbrt*
## 2 1 INCOME_log HOME_VAL_log* CAR_AGE_log* INCOME_sqrt HOME_VAL_sqrt* CAR_AGE_sqrt* INCOME_cbrt* HOME_VAL_cbrt* CAR_AGE_cbrt*
## 3 1 INCOME_log* HOME_VAL_log* CAR_AGE_log* INCOME_sqrt HOME_VAL_sqrt* CAR_AGE_sqrt* INCOME_cbrt* HOME_VAL_cbrt* CAR_AGE_cbrt*
## 4 1 INCOME_log* HOME_VAL_log* CAR_AGE_log* INCOME_sqrt HOME_VAL_sqrt* CAR_AGE_sqrt* INCOME_cbrt* HOME_VAL_cbrt* CAR_AGE_cbrt*
## 5 1 INCOME_log* HOME_VAL_log* CAR_AGE_log* INCOME_sqrt HOME_VAL_sqrt* CAR_AGE_sqrt* INCOME_cbrt* HOME_VAL_cbrt* CAR_AGE_cbrt*## Warning: Number of logged events: 85df_ins <- complete(df_ins)
# Confirm no NAs remain
colSums(is.na(df_ins))## TARGET_FLAG TARGET_AMT KIDSDRIV AGE HOMEKIDS
## 0 0 0 0 0
## YOJ INCOME PARENT1 HOME_VAL MSTATUS
## 0 0 0 0 0
## SEX EDUCATION JOB TRAVTIME CAR_USE
## 0 0 0 0 0
## BLUEBOOK TIF CAR_TYPE RED_CAR OLDCLAIM
## 0 0 0 0 0
## CLM_FREQ REVOKED MVR_PTS CAR_AGE URBANICITY
## 0 0 0 0 0
## TARGET_AMT_log AGE_log YOJ_log INCOME_log HOME_VAL_log
## 0 0 0 0 0
## TRAVTIME_log BLUEBOOK_log TIF_log OLDCLAIM_log MVR_PTS_log
## 0 0 0 0 0
## CAR_AGE_log TARGET_AMT_sqrt AGE_sqrt YOJ_sqrt INCOME_sqrt
## 0 0 0 0 0
## HOME_VAL_sqrt TRAVTIME_sqrt BLUEBOOK_sqrt TIF_sqrt OLDCLAIM_sqrt
## 0 0 0 0 0
## MVR_PTS_sqrt CAR_AGE_sqrt TARGET_AMT_cbrt AGE_cbrt YOJ_cbrt
## 0 0 0 0 0
## INCOME_cbrt HOME_VAL_cbrt TRAVTIME_cbrt BLUEBOOK_cbrt TIF_cbrt
## 0 0 0 0 0
## OLDCLAIM_cbrt MVR_PTS_cbrt CAR_AGE_cbrt HV_INC_RATIO TRT_MVR_PRODUCT
## 0 0 0 0 0Correlation of variables
# Visualize correlation between variables
corrplot(cor(df_ins_imp %>% keep(is.numeric)), method="shade", shade.col=NA, tl.col="black", tl.srt=45)
# Reshape correlation results
flattenCorrMatrix <- function(cormat, pmat) {
ut <- upper.tri(cormat)
data.frame(
row = rownames(cormat)[row(cormat)[ut]],
column = rownames(cormat)[col(cormat)[ut]],
cor =(cormat)[ut],
p = pmat[ut]
)
}
# Closer look at correlations of variables
corr_results <- rcorr(as.matrix(df_ins_imp %>% keep(is.numeric)))
df_corr <- flattenCorrMatrix(corr_results$r, corr_results$P)
# Noteworthy positive correlations
df_corr %>% filter(cor > 0.4)## row column cor p
## 1 INCOME HOME_VAL 0.5905965 0
## 2 INCOME BLUEBOOK 0.4347123 0
## 3 INCOME CAR_AGE 0.4259208 0# Noteworthy negative correlations
df_corr %>% filter(cor < -0.4)## [1] row column cor p
## <0 rows> (or 0-length row.names)# Pair plot
pairs(df_ins_imp %>% keep(is.numeric), lower.panel = NULL, col = "steelblue")
Check for multicollinearity
model <- glm(TARGET_AMT ~ KIDSDRIV + AGE + YOJ + INCOME + HOME_VAL + TRAVTIME + BLUEBOOK +
TIF + OLDCLAIM + MVR_PTS + CAR_AGE, data = df_ins, family = "quasipoisson")
vif(model)## GVIF Df GVIF^(1/(2*Df))
## KIDSDRIV 1.024923 4 1.003082
## AGE 1.094997 1 1.046421
## YOJ 1.182086 1 1.087238
## INCOME 1.821524 1 1.349639
## HOME_VAL 1.330630 1 1.153529
## TRAVTIME 1.004598 1 1.002296
## BLUEBOOK 1.229378 1 1.108773
## TIF 1.004250 1 1.002123
## OLDCLAIM 1.080919 1 1.039673
## MVR_PTS 1.097636 1 1.047681
## CAR_AGE 1.252012 1 1.118933Bucket select variables (by quantiles)
# 0-.25, .25-.75, .75-1
df_ins$CAR_AGE_fact <- cut(x = df_ins$CAR_AGE, breaks = c(-4, 3.5, 12, 28), labels = c("New", "Moderate", "Old"))
# -.5, .5-.9, .9+
df_ins$HOME_VAL_fact <- cut(x = df_ins$HOME_VAL, breaks = c(-86567, 160953, 314151, 885283), labels = c("No or Low", "Moderate", "High"))
# 0-.25, .25-.75, .75-1
df_ins$INCOME_fact <- cut(x = df_ins$INCOME, breaks = c(-31969, 27940, 85472, 367031), labels = c("Low", "Moderate", "High"))
# 0-.5, .50-.75, .75-1
df_ins$MVR_PTS_fact <- cut(x = df_ins$MVR_PTS, breaks = c(-1, 1, 3, 14), labels = c("Low", "Moderate", "High"))
# 0-.75, .75-1
df_ins$OLDCLAIM_fact <- cut(x = df_ins$OLDCLAIM, breaks = c(-1, 4636, 57038), labels = c("Low", "High"))
# 0-.25, .25-.75, .75-1
df_ins$TIF_fact <- cut(x = df_ins$TIF, breaks = c(-1, 1, 7, 26), labels = c("Low", "Moderate", "High"))
# 0-.25, .25-.75, .75-1
df_ins$TRAVTIME_fact <- cut(x = df_ins$TRAVTIME, breaks = c(4, 22, 44, 143), labels = c("Short", "Moderate", "Long"))
# 0-.25, .25-.75, .75-1
df_ins$YOJ_fact <- cut(x = df_ins$YOJ, breaks = c(-1, 9, 13, 24), labels = c("Low", "Moderate", "High"))Binary Logistic Regression
Binomial NULL Model
# Remove the Target Columns and create new data frame
data_train <- df_ins %>% dplyr::select(-starts_with("TARGET"))
data_train$TARGET_FLAG <- df_ins$TARGET_FLAG# Show new data frame
head(data_train)## KIDSDRIV AGE HOMEKIDS YOJ INCOME PARENT1 HOME_VAL MSTATUS SEX
## 1 0 60 0 11.000 67349.00 No 0 No M
## 2 0 43 0 11.000 91449.00 No 257252 No M
## 3 0 35 1 10.000 16039.00 No 124191 Yes F
## 4 0 51 0 14.000 67185.86 No 306251 Yes M
## 5 0 50 0 11.342 114986.00 No 243925 Yes F
## 6 0 34 1 12.000 125301.00 Yes 0 No F
## EDUCATION JOB TRAVTIME CAR_USE BLUEBOOK TIF CAR_TYPE RED_CAR
## 1 PhD Professional 14 Private 14230 11 Minivan yes
## 2 High School Blue Collar 22 Commercial 14940 1 Minivan yes
## 3 High School Clerical 5 Private 4010 4 SUV no
## 4 <High School Blue Collar 32 Private 15440 7 Minivan yes
## 5 PhD Doctor 36 Private 18000 1 SUV no
## 6 Bachelors Blue Collar 46 Commercial 17430 1 Sports Car no
## OLDCLAIM CLM_FREQ REVOKED MVR_PTS CAR_AGE URBANICITY AGE_log
## 1 4461 2 No 3 18 Highly Urban/ Urban 4.110874
## 2 0 0 No 0 1 Highly Urban/ Urban 3.784190
## 3 38690 2 No 3 10 Highly Urban/ Urban 3.583519
## 4 0 0 No 0 6 Highly Urban/ Urban 3.951244
## 5 19217 2 Yes 3 17 Highly Urban/ Urban 3.931826
## 6 0 0 No 0 7 Highly Urban/ Urban 3.555348
## YOJ_log INCOME_log HOME_VAL_log TRAVTIME_log BLUEBOOK_log TIF_log
## 1 2.484907 11.117658 0.00000 2.708050 9.563178 2.4849066
## 2 2.484907 11.423548 12.45782 3.135494 9.611864 0.6931472
## 3 2.397895 9.682841 11.72958 1.791759 8.296796 1.6094379
## 4 2.708050 11.115233 12.63216 3.496508 9.644782 2.0794415
## 5 2.513008 11.652574 12.40462 3.610918 9.798183 0.6931472
## 6 2.564949 11.738482 0.00000 3.850148 9.766006 0.6931472
## OLDCLAIM_log MVR_PTS_log CAR_AGE_log AGE_sqrt YOJ_sqrt INCOME_sqrt
## 1 8.403352 1.386294 2.9444390 7.745967 3.316625 259.5169
## 2 0.000000 0.000000 0.6931472 6.557439 3.316625 302.4054
## 3 10.563362 1.386294 2.3978953 5.916080 3.162278 126.6452
## 4 0.000000 0.000000 1.9459101 7.141428 3.741657 259.2024
## 5 9.863603 1.386294 2.8903718 7.071068 3.367789 339.0959
## 6 0.000000 0.000000 2.0794415 5.830952 3.464102 353.9788
## HOME_VAL_sqrt TRAVTIME_sqrt BLUEBOOK_sqrt TIF_sqrt OLDCLAIM_sqrt MVR_PTS_sqrt
## 1 0.0000 3.741657 119.28956 3.316625 66.79072 1.732051
## 2 507.2002 4.690416 122.22929 1.000000 0.00000 0.000000
## 3 352.4074 2.236068 63.32456 2.000000 196.69774 1.732051
## 4 553.3995 5.656854 124.25780 2.645751 0.00000 0.000000
## 5 493.8876 6.000000 134.16408 1.000000 138.62539 1.732051
## 6 0.0000 6.782330 132.02273 1.000000 0.00000 0.000000
## CAR_AGE_sqrt AGE_cbrt YOJ_cbrt INCOME_cbrt HOME_VAL_cbrt TRAVTIME_cbrt
## 1 4.242641 3.914868 2.223980 40.68588 0.00000 2.410142
## 2 1.000000 3.503398 2.223980 45.05327 63.59939 2.802039
## 3 3.162278 3.271066 2.154435 25.21888 49.89190 1.709976
## 4 2.449490 3.708430 2.410142 40.65300 67.40506 3.174802
## 5 4.123106 3.684031 2.246794 48.62747 62.48159 3.301927
## 6 2.645751 3.239612 2.289428 50.04010 0.00000 3.583048
## BLUEBOOK_cbrt TIF_cbrt OLDCLAIM_cbrt MVR_PTS_cbrt CAR_AGE_cbrt HV_INC_RATIO
## 1 24.23269 2.223980 16.46180 1.44225 2.620741 0.000000
## 2 24.62919 1.000000 0.00000 0.00000 1.000000 2.813065
## 3 15.88723 1.587401 33.82202 1.44225 2.154435 7.743064
## 4 24.90094 1.912931 0.00000 0.00000 1.817121 4.558265
## 5 26.20741 1.000000 26.78522 1.44225 2.571282 2.121345
## 6 25.92781 1.000000 0.00000 0.00000 1.912931 0.000000
## TRT_MVR_PRODUCT CAR_AGE_fact HOME_VAL_fact INCOME_fact MVR_PTS_fact
## 1 42 Old No or Low Moderate Moderate
## 2 0 New Moderate High Low
## 3 15 Moderate No or Low Low Moderate
## 4 0 Moderate Moderate Moderate Low
## 5 108 Old Moderate High Moderate
## 6 0 Moderate No or Low High Low
## OLDCLAIM_fact TIF_fact TRAVTIME_fact YOJ_fact TARGET_FLAG
## 1 Low High Short Moderate 0
## 2 Low Low Short Moderate 0
## 3 High Moderate Short Moderate 0
## 4 Low Moderate Moderate High 0
## 5 High Low Moderate Moderate 0
## 6 Low Low Long Moderate 1Build a Binary Logistic Regression Null model utilizing all the variables and data
# Build the binomial null regression
model1 <- glm(TARGET_FLAG ~ 1, data = data_train, family = binomial(link ="logit"))
summary(model1)##
## Call:
## glm(formula = TARGET_FLAG ~ 1, family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7827 -0.7827 -0.7827 1.6325 1.6325
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.02623 0.02512 -40.86 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 9418 on 8160 degrees of freedom
## Residual deviance: 9418 on 8160 degrees of freedom
## AIC: 9420
##
## Number of Fisher Scoring iterations: 4Binomial FULL Model
Binary Logistic Regression Full model utilizing all the variables and data, This model will be considered to be valid..
# Binomial FULL Model
model2 <- glm(TARGET_FLAG ~ ., data = data_train, family = binomial(link ="logit"))
summary(model2)##
## Call:
## glm(formula = TARGET_FLAG ~ ., family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.7570 -0.6937 -0.3802 0.5595 3.0348
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.644e+03 1.674e+03 1.580 0.114153
## KIDSDRIV1 7.110e-01 1.213e-01 5.861 4.60e-09 ***
## KIDSDRIV2 9.772e-01 1.694e-01 5.768 8.03e-09 ***
## KIDSDRIV3 1.202e+00 3.188e-01 3.770 0.000164 ***
## KIDSDRIV4 -1.375e+01 3.050e+02 -0.045 0.964048
## AGE -1.146e+01 8.468e+00 -1.354 0.175888
## HOMEKIDS1 1.227e-01 1.259e-01 0.975 0.329726
## HOMEKIDS2 6.168e-02 1.251e-01 0.493 0.622067
## HOMEKIDS3 2.502e-03 1.466e-01 0.017 0.986378
## HOMEKIDS4 -2.590e-01 2.307e-01 -1.123 0.261453
## HOMEKIDS5 -1.711e-01 7.107e-01 -0.241 0.809709
## YOJ 1.154e+00 1.007e+00 1.146 0.251735
## INCOME -3.919e-06 4.591e-06 -0.854 0.393345
## PARENT1Yes 2.048e-01 1.248e-01 1.642 0.100602
## HOME_VAL 1.900e-05 1.223e-05 1.554 0.120168
## MSTATUSYes -5.403e-01 9.374e-02 -5.764 8.20e-09 ***
## SEXM 5.289e-02 1.154e-01 0.458 0.646660
## EDUCATIONBachelors -3.945e-01 1.279e-01 -3.084 0.002044 **
## EDUCATIONHigh School 8.298e-03 1.013e-01 0.082 0.934687
## EDUCATIONMasters -2.597e-01 1.937e-01 -1.341 0.179911
## EDUCATIONPhD -2.523e-01 2.278e-01 -1.107 0.268153
## JOBBlue Collar 3.797e-01 1.893e-01 2.006 0.044842 *
## JOBClerical 4.460e-01 2.011e-01 2.217 0.026612 *
## JOBDoctor -4.007e-01 2.715e-01 -1.476 0.139994
## JOBHome Maker 1.144e-01 2.338e-01 0.489 0.624562
## JOBLawyer 1.250e-01 1.725e-01 0.725 0.468677
## JOBManager -5.487e-01 1.735e-01 -3.162 0.001565 **
## JOBProfessional 1.953e-01 1.815e-01 1.076 0.281725
## JOBStudent -8.114e-03 2.429e-01 -0.033 0.973357
## TRAVTIME -1.433e+00 1.940e+00 -0.739 0.460070
## CAR_USEPrivate -7.496e-01 9.385e-02 -7.988 1.38e-15 ***
## BLUEBOOK -3.345e-05 3.844e-04 -0.087 0.930651
## TIF -1.378e-01 1.331e+00 -0.104 0.917545
## CAR_TYPEPanel Truck 5.300e-01 1.721e-01 3.080 0.002068 **
## CAR_TYPEPickup 5.651e-01 1.053e-01 5.365 8.10e-08 ***
## CAR_TYPESports Car 8.811e-01 1.356e-01 6.498 8.15e-11 ***
## CAR_TYPESUV 7.117e-01 1.153e-01 6.174 6.65e-10 ***
## CAR_TYPEVan 7.202e-01 1.299e-01 5.544 2.95e-08 ***
## RED_CARyes -4.457e-02 8.857e-02 -0.503 0.614837
## OLDCLAIM 1.268e-04 2.986e-04 0.425 0.670998
## CLM_FREQ.L 2.013e+00 7.812e+00 0.258 0.796678
## CLM_FREQ.Q -1.377e+00 7.129e+00 -0.193 0.846812
## CLM_FREQ.C 1.141e+00 4.875e+00 0.234 0.814877
## CLM_FREQ^4 -5.284e-01 2.466e+00 -0.214 0.830376
## CLM_FREQ^5 1.345e-01 8.298e-01 0.162 0.871225
## REVOKEDYes 9.734e-01 9.681e-02 10.055 < 2e-16 ***
## MVR_PTS 4.336e+00 3.281e+00 1.321 0.186409
## CAR_AGE -6.396e-01 6.930e-01 -0.923 0.356053
## URBANICITYHighly Urban/ Urban 2.381e+00 1.154e-01 20.623 < 2e-16 ***
## AGE_log 1.438e+03 9.255e+02 1.554 0.120232
## YOJ_log 1.343e+01 9.797e+00 1.371 0.170480
## INCOME_log -1.503e-01 8.356e-02 -1.799 0.072026 .
## HOME_VAL_log -1.422e-01 5.284e-01 -0.269 0.787768
## TRAVTIME_log 1.359e+02 1.974e+02 0.689 0.491027
## BLUEBOOK_log 2.529e+00 8.014e+00 0.316 0.752282
## TIF_log -2.048e+01 7.802e+01 -0.262 0.792939
## OLDCLAIM_log -1.535e+00 4.854e+00 -0.316 0.751885
## MVR_PTS_log 2.054e+01 1.921e+01 1.069 0.284921
## CAR_AGE_log -2.100e+01 2.213e+01 -0.949 0.342598
## AGE_sqrt 1.421e+03 9.606e+02 1.479 0.139108
## YOJ_sqrt -1.754e+01 1.509e+01 -1.162 0.245089
## INCOME_sqrt -3.440e-03 1.956e-03 -1.758 0.078730 .
## HOME_VAL_sqrt -4.139e-02 4.380e-02 -0.945 0.344630
## TRAVTIME_sqrt 1.501e+02 2.127e+02 0.706 0.480497
## BLUEBOOK_sqrt 1.487e-01 6.558e-01 0.227 0.820649
## TIF_sqrt -1.173e+01 4.618e+01 -0.254 0.799425
## OLDCLAIM_sqrt -2.079e-01 4.642e-01 -0.448 0.654196
## MVR_PTS_sqrt -5.085e+01 4.230e+01 -1.202 0.229380
## CAR_AGE_sqrt -1.744e-01 4.768e+00 -0.037 0.970817
## AGE_cbrt -4.771e+03 3.160e+03 -1.510 0.131055
## YOJ_cbrt 5.497e+00 6.919e+00 0.794 0.426921
## INCOME_cbrt 5.352e-02 2.965e-02 1.805 0.071055 .
## HOME_VAL_cbrt 2.710e-01 4.025e-01 0.673 0.500699
## TRAVTIME_cbrt -4.819e+02 6.908e+02 -0.698 0.485390
## BLUEBOOK_cbrt -1.398e+00 5.152e+00 -0.271 0.786099
## TIF_cbrt 5.336e+01 2.051e+02 0.260 0.794764
## OLDCLAIM_cbrt 1.458e+00 3.494e+00 0.417 0.676425
## MVR_PTS_cbrt 3.238e+01 2.575e+01 1.257 0.208662
## CAR_AGE_cbrt 3.638e+01 3.933e+01 0.925 0.354938
## HV_INC_RATIO -1.182e-04 5.476e-04 -0.216 0.829104
## TRT_MVR_PRODUCT 8.584e-04 8.556e-04 1.003 0.315729
## CAR_AGE_factModerate -7.225e-02 3.757e-01 -0.192 0.847514
## CAR_AGE_factOld -2.669e-01 3.712e-01 -0.719 0.472177
## HOME_VAL_factModerate 2.404e-01 1.419e-01 1.694 0.090201 .
## HOME_VAL_factHigh -2.757e-02 2.661e-01 -0.104 0.917490
## INCOME_factModerate -2.045e-02 1.419e-01 -0.144 0.885450
## INCOME_factHigh -2.882e-01 2.151e-01 -1.340 0.180276
## MVR_PTS_factModerate 1.127e-01 3.666e-01 0.307 0.758483
## MVR_PTS_factHigh -1.842e-02 4.533e-01 -0.041 0.967586
## OLDCLAIM_factHigh -1.771e-01 1.808e-01 -0.980 0.327165
## TIF_factModerate -6.625e-01 3.786e+00 -0.175 0.861082
## TIF_factHigh -6.525e-01 3.807e+00 -0.171 0.863910
## TRAVTIME_factModerate 1.851e-02 1.624e-01 0.114 0.909253
## TRAVTIME_factLong 1.175e-01 2.181e-01 0.539 0.589975
## YOJ_factModerate -3.923e-02 1.515e-01 -0.259 0.795659
## YOJ_factHigh -1.672e-02 2.262e-01 -0.074 0.941091
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 9417.3 on 8159 degrees of freedom
## Residual deviance: 7093.4 on 8064 degrees of freedom
## (1 observation deleted due to missingness)
## AIC: 7285.4
##
## Number of Fisher Scoring iterations: 9plot(model2)
we notice how some variables are not statistically significant; for study purposes, I will assume that this is a valid model.
# Generate confidence intervals for regression slope
confint.default(model2)## 2.5 % 97.5 %
## (Intercept) -6.362180e+02 5.923872e+03
## KIDSDRIV1 4.732045e-01 9.487048e-01
## KIDSDRIV2 6.451129e-01 1.309201e+00
## KIDSDRIV3 5.768796e-01 1.826525e+00
## KIDSDRIV4 -6.114412e+02 5.839504e+02
## AGE -2.805961e+01 5.135498e+00
## HOMEKIDS1 -1.240693e-01 3.695306e-01
## HOMEKIDS2 -1.835730e-01 3.069332e-01
## HOMEKIDS3 -2.847629e-01 2.897677e-01
## HOMEKIDS4 -7.111246e-01 1.930671e-01
## HOMEKIDS5 -1.564175e+00 1.221881e+00
## YOJ -8.191140e-01 3.126319e+00
## INCOME -1.291731e-05 5.079623e-06
## PARENT1Yes -3.967547e-02 4.493644e-01
## HOME_VAL -4.962223e-06 4.296018e-05
## MSTATUSYes -7.240485e-01 -3.566076e-01
## SEXM -1.732516e-01 2.790348e-01
## EDUCATIONBachelors -6.452560e-01 -1.437693e-01
## EDUCATIONHigh School -1.901580e-01 2.067536e-01
## EDUCATIONMasters -6.393571e-01 1.198794e-01
## EDUCATIONPhD -6.988592e-01 1.942674e-01
## JOBBlue Collar 8.738496e-03 7.506131e-01
## JOBClerical 5.173186e-02 8.401688e-01
## JOBDoctor -9.328680e-01 1.314544e-01
## JOBHome Maker -3.437751e-01 5.725869e-01
## JOBLawyer -2.130477e-01 4.629916e-01
## JOBManager -8.887088e-01 -2.086209e-01
## JOBProfessional -1.603255e-01 5.509992e-01
## JOBStudent -4.842851e-01 4.680568e-01
## TRAVTIME -5.236229e+00 2.369533e+00
## CAR_USEPrivate -9.335890e-01 -5.656976e-01
## BLUEBOOK -7.867878e-04 7.198887e-04
## TIF -2.746682e+00 2.471076e+00
## CAR_TYPEPanel Truck 1.927642e-01 8.671991e-01
## CAR_TYPEPickup 3.586461e-01 7.715495e-01
## CAR_TYPESports Car 6.153094e-01 1.146841e+00
## CAR_TYPESUV 4.857723e-01 9.376192e-01
## CAR_TYPEVan 4.656173e-01 9.748397e-01
## RED_CARyes -2.181687e-01 1.290319e-01
## OLDCLAIM -4.583689e-04 7.120259e-04
## CLM_FREQ.L -1.329815e+01 1.732355e+01
## CLM_FREQ.Q -1.534988e+01 1.259540e+01
## CLM_FREQ.C -8.413659e+00 1.069658e+01
## CLM_FREQ^4 -5.362575e+00 4.305839e+00
## CLM_FREQ^5 -1.491954e+00 1.760994e+00
## REVOKEDYes 7.836792e-01 1.163151e+00
## MVR_PTS -2.095844e+00 1.076738e+01
## CAR_AGE -1.997767e+00 7.186538e-01
## URBANICITYHighly Urban/ Urban 2.154584e+00 2.607123e+00
## AGE_log -3.759087e+02 3.252025e+03
## YOJ_log -5.773360e+00 3.263004e+01
## INCOME_log -3.140847e-01 1.345350e-02
## HOME_VAL_log -1.177879e+00 8.933819e-01
## TRAVTIME_log -2.509451e+02 5.228265e+02
## BLUEBOOK_log -1.317696e+01 1.823564e+01
## TIF_log -1.733964e+02 1.324364e+02
## OLDCLAIM_log -1.104889e+01 7.979491e+00
## MVR_PTS_log -1.710714e+01 5.818621e+01
## CAR_AGE_log -6.436881e+01 2.236902e+01
## AGE_sqrt -4.618867e+02 3.303507e+03
## YOJ_sqrt -4.710987e+01 1.203428e+01
## INCOME_sqrt -7.274239e-03 3.949321e-04
## HOME_VAL_sqrt -1.272442e-01 4.445449e-02
## TRAVTIME_sqrt -2.668314e+02 5.669610e+02
## BLUEBOOK_sqrt -1.136608e+00 1.433944e+00
## TIF_sqrt -1.022459e+02 7.877784e+01
## OLDCLAIM_sqrt -1.117782e+00 7.019014e-01
## MVR_PTS_sqrt -1.337636e+02 3.206705e+01
## CAR_AGE_sqrt -9.519973e+00 9.171098e+00
## AGE_cbrt -1.096350e+04 1.421850e+03
## YOJ_cbrt -8.064150e+00 1.905819e+01
## INCOME_cbrt -4.590843e-03 1.116302e-01
## HOME_VAL_cbrt -5.178084e-01 1.059848e+00
## TRAVTIME_cbrt -1.835801e+03 8.719587e+02
## BLUEBOOK_cbrt -1.149641e+01 8.699986e+00
## TIF_cbrt -3.487044e+02 4.554305e+02
## OLDCLAIM_cbrt -5.390425e+00 8.307127e+00
## MVR_PTS_cbrt -1.809788e+01 8.285727e+01
## CAR_AGE_cbrt -4.070100e+01 1.134621e+02
## HV_INC_RATIO -1.191545e-03 9.551320e-04
## TRT_MVR_PRODUCT -8.185625e-04 2.535400e-03
## CAR_AGE_factModerate -8.086301e-01 6.641377e-01
## CAR_AGE_factOld -9.944909e-01 4.607052e-01
## HOME_VAL_factModerate -3.769382e-02 5.185653e-01
## HOME_VAL_factHigh -5.491165e-01 4.939827e-01
## INCOME_factModerate -2.986477e-01 2.577507e-01
## INCOME_factHigh -7.098153e-01 1.333773e-01
## MVR_PTS_factModerate -6.057647e-01 8.311897e-01
## MVR_PTS_factHigh -9.068555e-01 8.700156e-01
## OLDCLAIM_factHigh -5.313949e-01 1.771656e-01
## TIF_factModerate -8.082005e+00 6.757083e+00
## TIF_factHigh -8.114162e+00 6.809118e+00
## TRAVTIME_factModerate -2.998275e-01 3.368535e-01
## TRAVTIME_factLong -3.099097e-01 5.449424e-01
## YOJ_factModerate -3.360938e-01 2.576436e-01
## YOJ_factHigh -4.600438e-01 4.266133e-01# Generate the odds ratios
exp(coef(model2))## (Intercept) KIDSDRIV1
## Inf 2.035934e+00
## KIDSDRIV2 KIDSDRIV3
## 2.656892e+00 3.325774e+00
## KIDSDRIV4 AGE
## 1.072606e-06 1.052188e-05
## HOMEKIDS1 HOMEKIDS2
## 1.130580e+00 1.063622e+00
## HOMEKIDS3 HOMEKIDS4
## 1.002506e+00 7.718008e-01
## HOMEKIDS5 YOJ
## 8.426974e-01 3.169591e+00
## INCOME PARENT1Yes
## 9.999961e-01 1.227334e+00
## HOME_VAL MSTATUSYes
## 1.000019e+00 5.825571e-01
## SEXM EDUCATIONBachelors
## 1.054315e+00 6.740085e-01
## EDUCATIONHigh School EDUCATIONMasters
## 1.008332e+00 7.712530e-01
## EDUCATIONPhD JOBBlue Collar
## 7.770148e-01 1.461811e+00
## JOBClerical JOBDoctor
## 1.561974e+00 6.698464e-01
## JOBHome Maker JOBLawyer
## 1.121207e+00 1.133117e+00
## JOBManager JOBProfessional
## 5.777206e-01 1.215720e+00
## JOBStudent TRAVTIME
## 9.919187e-01 2.385091e-01
## CAR_USEPrivate BLUEBOOK
## 4.725351e-01 9.999666e-01
## TIF CAR_TYPEPanel Truck
## 8.712705e-01 1.698901e+00
## CAR_TYPEPickup CAR_TYPESports Car
## 1.759620e+00 2.413493e+00
## CAR_TYPESUV CAR_TYPEVan
## 2.037443e+00 2.054903e+00
## RED_CARyes OLDCLAIM
## 9.564102e-01 1.000127e+00
## CLM_FREQ.L CLM_FREQ.Q
## 7.483492e+00 2.522747e-01
## CLM_FREQ.C CLM_FREQ^4
## 3.131345e+00 5.895664e-01
## CLM_FREQ^5 REVOKEDYes
## 1.143988e+00 2.646968e+00
## MVR_PTS CAR_AGE
## 7.638360e+01 5.275264e-01
## URBANICITYHighly Urban/ Urban AGE_log
## 1.081413e+01 Inf
## YOJ_log INCOME_log
## 6.789740e+05 8.604364e-01
## HOME_VAL_log TRAVTIME_log
## 8.674056e-01 1.092162e+59
## BLUEBOOK_log TIF_log
## 1.254522e+01 1.275433e-09
## OLDCLAIM_log MVR_PTS_log
## 2.155206e-01 8.321629e+08
## CAR_AGE_log AGE_sqrt
## 7.583379e-10 Inf
## YOJ_sqrt INCOME_sqrt
## 2.417865e-08 9.965663e-01
## HOME_VAL_sqrt TRAVTIME_sqrt
## 9.594502e-01 1.487050e+65
## BLUEBOOK_sqrt TIF_sqrt
## 1.160288e+00 8.016185e-06
## OLDCLAIM_sqrt MVR_PTS_sqrt
## 8.122554e-01 8.258207e-23
## CAR_AGE_sqrt AGE_cbrt
## 8.399296e-01 0.000000e+00
## YOJ_cbrt INCOME_cbrt
## 2.439635e+02 1.054978e+00
## HOME_VAL_cbrt TRAVTIME_cbrt
## 1.311301e+00 5.060917e-210
## BLUEBOOK_cbrt TIF_cbrt
## 2.470385e-01 1.497195e+23
## OLDCLAIM_cbrt MVR_PTS_cbrt
## 4.298866e+00 1.154309e+14
## CAR_AGE_cbrt HV_INC_RATIO
## 6.307658e+15 9.998818e-01
## TRT_MVR_PRODUCT CAR_AGE_factModerate
## 1.000859e+00 9.303018e-01
## CAR_AGE_factOld HOME_VAL_factModerate
## 7.657551e-01 1.271803e+00
## HOME_VAL_factHigh INCOME_factModerate
## 9.728096e-01 9.797592e-01
## INCOME_factHigh MVR_PTS_factModerate
## 7.495974e-01 1.119310e+00
## MVR_PTS_factHigh OLDCLAIM_factHigh
## 9.817487e-01 8.376837e-01
## TIF_factModerate TIF_factHigh
## 5.155811e-01 5.207307e-01
## TRAVTIME_factModerate TRAVTIME_factLong
## 1.018685e+00 1.124700e+00
## YOJ_factModerate YOJ_factHigh
## 9.615343e-01 9.834237e-01# Generate confidence intervals for regression slope
confint.default(model2)## 2.5 % 97.5 %
## (Intercept) -6.362180e+02 5.923872e+03
## KIDSDRIV1 4.732045e-01 9.487048e-01
## KIDSDRIV2 6.451129e-01 1.309201e+00
## KIDSDRIV3 5.768796e-01 1.826525e+00
## KIDSDRIV4 -6.114412e+02 5.839504e+02
## AGE -2.805961e+01 5.135498e+00
## HOMEKIDS1 -1.240693e-01 3.695306e-01
## HOMEKIDS2 -1.835730e-01 3.069332e-01
## HOMEKIDS3 -2.847629e-01 2.897677e-01
## HOMEKIDS4 -7.111246e-01 1.930671e-01
## HOMEKIDS5 -1.564175e+00 1.221881e+00
## YOJ -8.191140e-01 3.126319e+00
## INCOME -1.291731e-05 5.079623e-06
## PARENT1Yes -3.967547e-02 4.493644e-01
## HOME_VAL -4.962223e-06 4.296018e-05
## MSTATUSYes -7.240485e-01 -3.566076e-01
## SEXM -1.732516e-01 2.790348e-01
## EDUCATIONBachelors -6.452560e-01 -1.437693e-01
## EDUCATIONHigh School -1.901580e-01 2.067536e-01
## EDUCATIONMasters -6.393571e-01 1.198794e-01
## EDUCATIONPhD -6.988592e-01 1.942674e-01
## JOBBlue Collar 8.738496e-03 7.506131e-01
## JOBClerical 5.173186e-02 8.401688e-01
## JOBDoctor -9.328680e-01 1.314544e-01
## JOBHome Maker -3.437751e-01 5.725869e-01
## JOBLawyer -2.130477e-01 4.629916e-01
## JOBManager -8.887088e-01 -2.086209e-01
## JOBProfessional -1.603255e-01 5.509992e-01
## JOBStudent -4.842851e-01 4.680568e-01
## TRAVTIME -5.236229e+00 2.369533e+00
## CAR_USEPrivate -9.335890e-01 -5.656976e-01
## BLUEBOOK -7.867878e-04 7.198887e-04
## TIF -2.746682e+00 2.471076e+00
## CAR_TYPEPanel Truck 1.927642e-01 8.671991e-01
## CAR_TYPEPickup 3.586461e-01 7.715495e-01
## CAR_TYPESports Car 6.153094e-01 1.146841e+00
## CAR_TYPESUV 4.857723e-01 9.376192e-01
## CAR_TYPEVan 4.656173e-01 9.748397e-01
## RED_CARyes -2.181687e-01 1.290319e-01
## OLDCLAIM -4.583689e-04 7.120259e-04
## CLM_FREQ.L -1.329815e+01 1.732355e+01
## CLM_FREQ.Q -1.534988e+01 1.259540e+01
## CLM_FREQ.C -8.413659e+00 1.069658e+01
## CLM_FREQ^4 -5.362575e+00 4.305839e+00
## CLM_FREQ^5 -1.491954e+00 1.760994e+00
## REVOKEDYes 7.836792e-01 1.163151e+00
## MVR_PTS -2.095844e+00 1.076738e+01
## CAR_AGE -1.997767e+00 7.186538e-01
## URBANICITYHighly Urban/ Urban 2.154584e+00 2.607123e+00
## AGE_log -3.759087e+02 3.252025e+03
## YOJ_log -5.773360e+00 3.263004e+01
## INCOME_log -3.140847e-01 1.345350e-02
## HOME_VAL_log -1.177879e+00 8.933819e-01
## TRAVTIME_log -2.509451e+02 5.228265e+02
## BLUEBOOK_log -1.317696e+01 1.823564e+01
## TIF_log -1.733964e+02 1.324364e+02
## OLDCLAIM_log -1.104889e+01 7.979491e+00
## MVR_PTS_log -1.710714e+01 5.818621e+01
## CAR_AGE_log -6.436881e+01 2.236902e+01
## AGE_sqrt -4.618867e+02 3.303507e+03
## YOJ_sqrt -4.710987e+01 1.203428e+01
## INCOME_sqrt -7.274239e-03 3.949321e-04
## HOME_VAL_sqrt -1.272442e-01 4.445449e-02
## TRAVTIME_sqrt -2.668314e+02 5.669610e+02
## BLUEBOOK_sqrt -1.136608e+00 1.433944e+00
## TIF_sqrt -1.022459e+02 7.877784e+01
## OLDCLAIM_sqrt -1.117782e+00 7.019014e-01
## MVR_PTS_sqrt -1.337636e+02 3.206705e+01
## CAR_AGE_sqrt -9.519973e+00 9.171098e+00
## AGE_cbrt -1.096350e+04 1.421850e+03
## YOJ_cbrt -8.064150e+00 1.905819e+01
## INCOME_cbrt -4.590843e-03 1.116302e-01
## HOME_VAL_cbrt -5.178084e-01 1.059848e+00
## TRAVTIME_cbrt -1.835801e+03 8.719587e+02
## BLUEBOOK_cbrt -1.149641e+01 8.699986e+00
## TIF_cbrt -3.487044e+02 4.554305e+02
## OLDCLAIM_cbrt -5.390425e+00 8.307127e+00
## MVR_PTS_cbrt -1.809788e+01 8.285727e+01
## CAR_AGE_cbrt -4.070100e+01 1.134621e+02
## HV_INC_RATIO -1.191545e-03 9.551320e-04
## TRT_MVR_PRODUCT -8.185625e-04 2.535400e-03
## CAR_AGE_factModerate -8.086301e-01 6.641377e-01
## CAR_AGE_factOld -9.944909e-01 4.607052e-01
## HOME_VAL_factModerate -3.769382e-02 5.185653e-01
## HOME_VAL_factHigh -5.491165e-01 4.939827e-01
## INCOME_factModerate -2.986477e-01 2.577507e-01
## INCOME_factHigh -7.098153e-01 1.333773e-01
## MVR_PTS_factModerate -6.057647e-01 8.311897e-01
## MVR_PTS_factHigh -9.068555e-01 8.700156e-01
## OLDCLAIM_factHigh -5.313949e-01 1.771656e-01
## TIF_factModerate -8.082005e+00 6.757083e+00
## TIF_factHigh -8.114162e+00 6.809118e+00
## TRAVTIME_factModerate -2.998275e-01 3.368535e-01
## TRAVTIME_factLong -3.099097e-01 5.449424e-01
## YOJ_factModerate -3.360938e-01 2.576436e-01
## YOJ_factHigh -4.600438e-01 4.266133e-01# Generate the odds ratios
exp(coef(model2))## (Intercept) KIDSDRIV1
## Inf 2.035934e+00
## KIDSDRIV2 KIDSDRIV3
## 2.656892e+00 3.325774e+00
## KIDSDRIV4 AGE
## 1.072606e-06 1.052188e-05
## HOMEKIDS1 HOMEKIDS2
## 1.130580e+00 1.063622e+00
## HOMEKIDS3 HOMEKIDS4
## 1.002506e+00 7.718008e-01
## HOMEKIDS5 YOJ
## 8.426974e-01 3.169591e+00
## INCOME PARENT1Yes
## 9.999961e-01 1.227334e+00
## HOME_VAL MSTATUSYes
## 1.000019e+00 5.825571e-01
## SEXM EDUCATIONBachelors
## 1.054315e+00 6.740085e-01
## EDUCATIONHigh School EDUCATIONMasters
## 1.008332e+00 7.712530e-01
## EDUCATIONPhD JOBBlue Collar
## 7.770148e-01 1.461811e+00
## JOBClerical JOBDoctor
## 1.561974e+00 6.698464e-01
## JOBHome Maker JOBLawyer
## 1.121207e+00 1.133117e+00
## JOBManager JOBProfessional
## 5.777206e-01 1.215720e+00
## JOBStudent TRAVTIME
## 9.919187e-01 2.385091e-01
## CAR_USEPrivate BLUEBOOK
## 4.725351e-01 9.999666e-01
## TIF CAR_TYPEPanel Truck
## 8.712705e-01 1.698901e+00
## CAR_TYPEPickup CAR_TYPESports Car
## 1.759620e+00 2.413493e+00
## CAR_TYPESUV CAR_TYPEVan
## 2.037443e+00 2.054903e+00
## RED_CARyes OLDCLAIM
## 9.564102e-01 1.000127e+00
## CLM_FREQ.L CLM_FREQ.Q
## 7.483492e+00 2.522747e-01
## CLM_FREQ.C CLM_FREQ^4
## 3.131345e+00 5.895664e-01
## CLM_FREQ^5 REVOKEDYes
## 1.143988e+00 2.646968e+00
## MVR_PTS CAR_AGE
## 7.638360e+01 5.275264e-01
## URBANICITYHighly Urban/ Urban AGE_log
## 1.081413e+01 Inf
## YOJ_log INCOME_log
## 6.789740e+05 8.604364e-01
## HOME_VAL_log TRAVTIME_log
## 8.674056e-01 1.092162e+59
## BLUEBOOK_log TIF_log
## 1.254522e+01 1.275433e-09
## OLDCLAIM_log MVR_PTS_log
## 2.155206e-01 8.321629e+08
## CAR_AGE_log AGE_sqrt
## 7.583379e-10 Inf
## YOJ_sqrt INCOME_sqrt
## 2.417865e-08 9.965663e-01
## HOME_VAL_sqrt TRAVTIME_sqrt
## 9.594502e-01 1.487050e+65
## BLUEBOOK_sqrt TIF_sqrt
## 1.160288e+00 8.016185e-06
## OLDCLAIM_sqrt MVR_PTS_sqrt
## 8.122554e-01 8.258207e-23
## CAR_AGE_sqrt AGE_cbrt
## 8.399296e-01 0.000000e+00
## YOJ_cbrt INCOME_cbrt
## 2.439635e+02 1.054978e+00
## HOME_VAL_cbrt TRAVTIME_cbrt
## 1.311301e+00 5.060917e-210
## BLUEBOOK_cbrt TIF_cbrt
## 2.470385e-01 1.497195e+23
## OLDCLAIM_cbrt MVR_PTS_cbrt
## 4.298866e+00 1.154309e+14
## CAR_AGE_cbrt HV_INC_RATIO
## 6.307658e+15 9.998818e-01
## TRT_MVR_PRODUCT CAR_AGE_factModerate
## 1.000859e+00 9.303018e-01
## CAR_AGE_factOld HOME_VAL_factModerate
## 7.657551e-01 1.271803e+00
## HOME_VAL_factHigh INCOME_factModerate
## 9.728096e-01 9.797592e-01
## INCOME_factHigh MVR_PTS_factModerate
## 7.495974e-01 1.119310e+00
## MVR_PTS_factHigh OLDCLAIM_factHigh
## 9.817487e-01 8.376837e-01
## TIF_factModerate TIF_factHigh
## 5.155811e-01 5.207307e-01
## TRAVTIME_factModerate TRAVTIME_factLong
## 1.018685e+00 1.124700e+00
## YOJ_factModerate YOJ_factHigh
## 9.615343e-01 9.834237e-01I will select the variables using the stepwise method
The ‘stepAIC’ function in R performs a stepwise model selection with an objective to minimize the AIC value.
Using Step in both direction
create multiple models using the STEP function from R.
Let’s check an ANOVA table based on the above testing results.
step_b$anova## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 NA NA 8160 9417.962 9419.962
## 2 + URBANICITY -1 502.103089 8159 8915.859 8919.859
## 3 + JOB -8 523.306410 8151 8392.553 8412.553
## 4 + TRT_MVR_PRODUCT -1 225.402921 8150 8167.150 8189.150
## 5 + HOME_VAL_sqrt -1 183.181057 8149 7983.969 8007.969
## 6 + CAR_TYPE -5 164.006081 8144 7819.963 7853.963
## 7 + REVOKED -1 103.395598 8143 7716.567 7752.567
## 8 + PARENT1 -1 75.136156 8142 7641.431 7679.431
## 9 + CAR_USE -1 65.145841 8141 7576.285 7616.285
## 10 + TIF_cbrt -1 62.057877 8140 7514.227 7556.227
## 11 + KIDSDRIV -4 52.579316 8136 7461.648 7511.648
## 12 + BLUEBOOK_cbrt -1 47.416795 8135 7414.231 7466.231
## 13 + CLM_FREQ -5 44.954091 8130 7369.277 7431.277
## 14 + INCOME_sqrt -1 28.595953 8129 7340.681 7404.681
## 15 + MSTATUS -1 25.603899 8128 7315.077 7381.077
## 16 + OLDCLAIM -1 24.623660 8127 7290.454 7358.454
## 17 + TRAVTIME_cbrt -1 23.079405 8126 7267.374 7337.374
## 18 + EDUCATION -4 20.765533 8122 7246.609 7324.609
## 19 + MVR_PTS -1 5.403444 8121 7241.205 7321.205
## 20 + MVR_PTS_fact -2 12.618083 8119 7228.587 7312.587
## 21 + AGE_log -1 3.752757 8118 7224.834 7310.834
## 22 + AGE -1 53.395704 8117 7171.439 7259.439
## 23 + AGE_cbrt -1 10.081550 8116 7161.357 7251.357
## 24 - TRT_MVR_PRODUCT 1 1.098658 8117 7162.456 7250.456
## 25 + INCOME_fact -2 4.657489 8115 7157.798 7249.798
## 26 + INCOME -1 4.462656 8114 7153.336 7247.336
## 27 + AGE_sqrt -1 2.892799 8113 7150.443 7246.443From the above results, it shows that the best model is as follows:
summary(step_b)##
## Call:
## glm(formula = TARGET_FLAG ~ URBANICITY + JOB + HOME_VAL_sqrt +
## CAR_TYPE + REVOKED + PARENT1 + CAR_USE + TIF_cbrt + KIDSDRIV +
## BLUEBOOK_cbrt + CLM_FREQ + INCOME_sqrt + MSTATUS + OLDCLAIM +
## TRAVTIME_cbrt + EDUCATION + MVR_PTS + MVR_PTS_fact + AGE_log +
## AGE + AGE_cbrt + INCOME_fact + INCOME + AGE_sqrt, family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5191 -0.6983 -0.3852 0.5951 3.0129
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.708e+03 1.588e+03 1.705 0.088128 .
## URBANICITYHighly Urban/ Urban 2.372e+00 1.137e-01 20.852 < 2e-16 ***
## JOBBlue Collar 3.654e-01 1.880e-01 1.943 0.051995 .
## JOBClerical 4.164e-01 1.996e-01 2.087 0.036899 *
## JOBDoctor -4.017e-01 2.690e-01 -1.493 0.135354
## JOBHome Maker 1.373e-01 2.248e-01 0.611 0.541503
## JOBLawyer 1.282e-01 1.714e-01 0.748 0.454564
## JOBManager -5.466e-01 1.725e-01 -3.169 0.001530 **
## JOBProfessional 2.012e-01 1.803e-01 1.116 0.264294
## JOBStudent -1.414e-02 2.325e-01 -0.061 0.951493
## HOME_VAL_sqrt -7.470e-04 1.880e-04 -3.975 7.05e-05 ***
## CAR_TYPEPanel Truck 5.933e-01 1.487e-01 3.989 6.62e-05 ***
## CAR_TYPEPickup 5.563e-01 1.019e-01 5.458 4.83e-08 ***
## CAR_TYPESports Car 8.839e-01 1.102e-01 8.023 1.03e-15 ***
## CAR_TYPESUV 6.899e-01 8.727e-02 7.906 2.66e-15 ***
## CAR_TYPEVan 7.075e-01 1.241e-01 5.702 1.18e-08 ***
## REVOKEDYes 9.525e-01 9.389e-02 10.146 < 2e-16 ***
## PARENT1Yes 2.599e-01 1.030e-01 2.523 0.011650 *
## CAR_USEPrivate -7.653e-01 9.293e-02 -8.235 < 2e-16 ***
## TIF_cbrt -4.841e-01 6.173e-02 -7.842 4.42e-15 ***
## KIDSDRIV1 7.536e-01 1.087e-01 6.930 4.20e-12 ***
## KIDSDRIV2 9.728e-01 1.549e-01 6.281 3.37e-10 ***
## KIDSDRIV3 1.123e+00 3.060e-01 3.669 0.000244 ***
## KIDSDRIV4 1.294e+00 1.180e+00 1.097 0.272683
## BLUEBOOK_cbrt -4.484e-02 8.006e-03 -5.600 2.14e-08 ***
## CLM_FREQ.L 6.637e-01 3.319e-01 1.999 0.045561 *
## CLM_FREQ.Q -1.503e-01 3.024e-01 -0.497 0.619125
## CLM_FREQ.C 2.802e-01 2.265e-01 1.237 0.216040
## CLM_FREQ^4 -1.117e-01 1.516e-01 -0.737 0.460942
## CLM_FREQ^5 -5.681e-03 9.494e-02 -0.060 0.952291
## INCOME_sqrt -3.601e-03 1.050e-03 -3.428 0.000609 ***
## MSTATUSYes -5.321e-01 8.646e-02 -6.154 7.55e-10 ***
## OLDCLAIM -1.982e-05 4.251e-06 -4.662 3.13e-06 ***
## TRAVTIME_cbrt 4.332e-01 5.460e-02 7.933 2.13e-15 ***
## EDUCATIONBachelors -3.775e-01 1.131e-01 -3.338 0.000845 ***
## EDUCATIONHigh School 1.308e-02 9.831e-02 0.133 0.894120
## EDUCATIONMasters -2.531e-01 1.648e-01 -1.536 0.124610
## EDUCATIONPhD -2.449e-01 2.057e-01 -1.190 0.233993
## MVR_PTS 1.856e-01 3.556e-02 5.220 1.79e-07 ***
## MVR_PTS_factModerate -1.349e-01 1.077e-01 -1.252 0.210410
## MVR_PTS_factHigh -5.803e-01 1.958e-01 -2.964 0.003041 **
## AGE_log 1.591e+03 8.996e+02 1.769 0.076909 .
## AGE -1.276e+01 8.240e+00 -1.549 0.121400
## AGE_cbrt -5.283e+03 3.072e+03 -1.720 0.085514 .
## INCOME_factModerate 7.850e-02 1.190e-01 0.660 0.509474
## INCOME_factHigh -2.549e-01 1.924e-01 -1.325 0.185215
## INCOME 5.155e-06 2.416e-06 2.134 0.032828 *
## AGE_sqrt 1.575e+03 9.342e+02 1.685 0.091897 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 9418.0 on 8160 degrees of freedom
## Residual deviance: 7150.4 on 8113 degrees of freedom
## AIC: 7246.4
##
## Number of Fisher Scoring iterations: 5We see how all the predictors are statistical significant, also, noticing how the HOME_VAL and the INCOME are not as statistical significant compared to other variables.
The below plot shows our fitted models vs Density.
hist(step_b$fitted.values, main = " Histogram ",xlab = "Fitted models", col = 'skyblue3')
Show the predicted values
data_train$Predict <- ifelse(step_b$fitted.values >0.5,"pos","neg")
head(data_train$Predict)## [1] "neg" "neg" "neg" "neg" "neg" "pos"Confusion Matrix
Building a confusion matrix to get more insights.
step_c <- data_train
step_c$Predict = predict(step_b,type="response")
step_c$TARGET_FLAG_Predict <- round(step_c$Predict)cMatrix <- confusionMatrix(data = as.factor(step_c$TARGET_FLAG_Predict),
reference = as.factor(step_c$TARGET_FLAG),
positive = '1')
cMatrix## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 5546 1186
## 1 462 967
##
## Accuracy : 0.7981
## 95% CI : (0.7892, 0.8067)
## No Information Rate : 0.7362
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.4173
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Sensitivity : 0.4491
## Specificity : 0.9231
## Pos Pred Value : 0.6767
## Neg Pred Value : 0.8238
## Prevalence : 0.2638
## Detection Rate : 0.1185
## Detection Prevalence : 0.1751
## Balanced Accuracy : 0.6861
##
## 'Positive' Class : 1
## We can see the accuracy is 0.7981
data.frame(Value = cMatrix$byClass)## Value
## Sensitivity 0.4491407
## Specificity 0.9231025
## Pos Pred Value 0.6766970
## Neg Pred Value 0.8238265
## Precision 0.6766970
## Recall 0.4491407
## F1 0.5399218
## Prevalence 0.2638157
## Detection Rate 0.1184904
## Detection Prevalence 0.1751011
## Balanced Accuracy 0.6861216Binary STEP MODIFIED Model
For the following variables I will add 1 and calculate the log, to avoid errors since some entries reported 0 and log(0) will produce errors, also I will remove the variable HOMEKIDS and KIDSDRIV
- Log(1 + INCOME) - Log(1 + HOME_VAL) - Log(1 + BLUEBOOK) - Log(1 + OLDCLAIM) - HOMEKIDS Remove - KIDSDRIV Remove
step_modified <- glm(formula = TARGET_FLAG ~ KIDSDRIV +AGE+HOMEKIDS+YOJ+log(1 + INCOME)+PARENT1+ log(1+HOME_VAL) + MSTATUS+SEX+EDUCATION+JOB+TRAVTIME+CAR_USE+ log(1+BLUEBOOK) + TIF + CAR_TYPE + RED_CAR + log(1 + OLDCLAIM)+CLM_FREQ+REVOKED+URBANICITY+CAR_AGE, family = binomial(link = "logit"), data = data_train)## Warning in log(1 + INCOME): NaNs produced## Warning in log(1 + HOME_VAL): NaNs producedLet’s see the summary:
summary(step_modified)##
## Call:
## glm(formula = TARGET_FLAG ~ KIDSDRIV + AGE + HOMEKIDS + YOJ +
## log(1 + INCOME) + PARENT1 + log(1 + HOME_VAL) + MSTATUS +
## SEX + EDUCATION + JOB + TRAVTIME + CAR_USE + log(1 + BLUEBOOK) +
## TIF + CAR_TYPE + RED_CAR + log(1 + OLDCLAIM) + CLM_FREQ +
## REVOKED + URBANICITY + CAR_AGE, family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4049 -0.7144 -0.4006 0.6510 3.1601
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.974062 0.737363 2.677 0.007424 **
## KIDSDRIV1 0.465540 0.114462 4.067 4.76e-05 ***
## KIDSDRIV2 0.774529 0.164434 4.710 2.47e-06 ***
## KIDSDRIV3 1.017934 0.316353 3.218 0.001292 **
## KIDSDRIV4 1.306006 1.127510 1.158 0.246738
## AGE -0.002913 0.004220 -0.690 0.489941
## HOMEKIDS1 0.336324 0.118736 2.833 0.004618 **
## HOMEKIDS2 0.186599 0.117836 1.584 0.113296
## HOMEKIDS3 0.138269 0.137396 1.006 0.314245
## HOMEKIDS4 -0.064806 0.222983 -0.291 0.771333
## HOMEKIDS5 0.391761 0.655364 0.598 0.549990
## YOJ 0.023942 0.011540 2.075 0.038010 *
## log(1 + INCOME) -0.110011 0.019108 -5.757 8.54e-09 ***
## PARENT1Yes 0.230930 0.121109 1.907 0.056546 .
## log(1 + HOME_VAL) -0.029475 0.007051 -4.181 2.91e-05 ***
## MSTATUSYes -0.551157 0.091142 -6.047 1.47e-09 ***
## SEXM 0.123201 0.108533 1.135 0.256314
## EDUCATIONBachelors -0.403709 0.116647 -3.461 0.000538 ***
## EDUCATIONHigh School 0.011904 0.095893 0.124 0.901205
## EDUCATIONMasters -0.308092 0.181943 -1.693 0.090390 .
## EDUCATIONPhD -0.333824 0.210341 -1.587 0.112498
## JOBBlue Collar 0.388576 0.184997 2.100 0.035690 *
## JOBClerical 0.517336 0.194101 2.665 0.007692 **
## JOBDoctor -0.399476 0.264143 -1.512 0.130446
## JOBHome Maker 0.008411 0.220423 0.038 0.969562
## JOBLawyer 0.151671 0.168561 0.900 0.368227
## JOBManager -0.532654 0.169874 -3.136 0.001715 **
## JOBProfessional 0.227576 0.177783 1.280 0.200518
## JOBStudent -0.089603 0.226668 -0.395 0.692618
## TRAVTIME 0.015232 0.001894 8.041 8.94e-16 ***
## CAR_USEPrivate -0.776008 0.092521 -8.387 < 2e-16 ***
## log(1 + BLUEBOOK) -0.283129 0.059411 -4.766 1.88e-06 ***
## TIF -0.056250 0.007385 -7.616 2.61e-14 ***
## CAR_TYPEPanel Truck 0.441112 0.150483 2.931 0.003375 **
## CAR_TYPEPickup 0.597242 0.100732 5.929 3.05e-09 ***
## CAR_TYPESports Car 1.065882 0.128519 8.294 < 2e-16 ***
## CAR_TYPESUV 0.825548 0.108027 7.642 2.14e-14 ***
## CAR_TYPEVan 0.628435 0.125415 5.011 5.42e-07 ***
## RED_CARyes -0.004075 0.086455 -0.047 0.962408
## log(1 + OLDCLAIM) -0.161334 0.045645 -3.535 0.000409 ***
## CLM_FREQ.L 1.529063 0.412015 3.711 0.000206 ***
## CLM_FREQ.Q -0.907783 0.373831 -2.428 0.015169 *
## CLM_FREQ.C 0.784731 0.272593 2.879 0.003992 **
## CLM_FREQ^4 -0.412620 0.169157 -2.439 0.014717 *
## CLM_FREQ^5 0.086024 0.097661 0.881 0.378402
## REVOKEDYes 0.848297 0.088907 9.541 < 2e-16 ***
## URBANICITYHighly Urban/ Urban 2.383108 0.114552 20.804 < 2e-16 ***
## CAR_AGE -0.004613 0.007804 -0.591 0.554515
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 9337.1 on 8095 degrees of freedom
## Residual deviance: 7247.3 on 8048 degrees of freedom
## (65 observations deleted due to missingness)
## AIC: 7343.3
##
## Number of Fisher Scoring iterations: 5With the transformation it looks slightly better the AIC is lower than the automatically selected model by the STEP procedure.
Plot of standardized residuals
The below plot shows our fitted models vs the deviance standardized residuals.
plot(fitted(step_modified),
rstandard(step_modified),
main = 'Standarize residuals',
xlab = 'Fitted values',
ylab = ' Residuals',
col = 'blue')
Confusion Matrix
Let’s check teh confusion matrix.
step_modified_b <- step_modified
step_modified_b$Predict = predict(step_modified,type="response")
step_modified_b$TARGET_FLAG_Predict <- round(step_modified_b$Predict)cMatrix <- confusionMatrix(data = as.factor(step_modified_b$TARGET_FLAG_Predict),
reference = as.factor(step_modified_b$TARGET_FLAG),
positive = '1')
cMatrix## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 6769 0
## 1 0 1327
##
## Accuracy : 1
## 95% CI : (0.9995, 1)
## No Information Rate : 0.8361
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 1
##
## Mcnemar's Test P-Value : NA
##
## Sensitivity : 1.0000
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 1.0000
## Prevalence : 0.1639
## Detection Rate : 0.1639
## Detection Prevalence : 0.1639
## Balanced Accuracy : 1.0000
##
## 'Positive' Class : 1
## Is interesting to note that the reported Accuracy is
From the above results, we obtain as follows:
data.frame(Value = cMatrix$byClass)## Value
## Sensitivity 1.0000000
## Specificity 1.0000000
## Pos Pred Value 1.0000000
## Neg Pred Value 1.0000000
## Precision 1.0000000
## Recall 1.0000000
## F1 1.0000000
## Prevalence 0.1639081
## Detection Rate 0.1639081
## Detection Prevalence 0.1639081
## Balanced Accuracy 1.0000000