Table of Contents
Car Insurance
Data Preparatation
Philippe De Brouwer
2024-10-01
1 Executive Summary
This is part 1 on the analysis that demonstrate bias in data and the possibilities to de-bias data. In this document we show how to clean the data and prepare it.
2 Introduction
The car insurance data is provides a wealth of information and points to discuss. What is fair? What is ethical. We will explore questions like:
- Is it fair to use gender?
- No? Well can we use age then? That is a good indicator proxy for driving experience, maturity, etc. and indeed has a high information value.
- Also not? Well, let’s just look at past track record then (did the person have an accident in the last 5 years)
- But wait, that is somehow discriminatory for people that drive at least 5 years, because only they could build up such track record?
- That leaves us wealth related parameters such as income, value of the car, etc. They do the same … but isn’t that discriminatory for poor people?
- So, we have left things related to car use (private or commercial use, daily average travel time)
- This model won’t be that strong. The insurance company now need to increase prices … which will impact the poor …
The dilemma is that when we believe that there is a protected feature \(S\) (say income), then there are at least two groups for which using the feature will results in more desirable outcome or less desirable outcome. Leaving out the feature will make the model weaker and increase prices for all … impacting the hardest the group that we set out to protect.
Workflow
The work-flow is inspired by: (De Brouwer 2020) and is prepared by Philippe De Brouwer to illustrate the concepts explained in the book.
We will approach the problem in a few phases
- Prepare the data: this file
- Build a naive model
- Build a classification model based with
CLAIM_FLAGas dependent variable (this variable is 0 of no claim was filed) - Now we need to find a price for the insurance policy. We can use a
simple average or build a model. We will build a regression model to
determine the fee that the customer should pay based on
CLM_AMT(the amount claimed) of those customers that are expected to have an accident - Decide on Protected Features
- Remove protected features and proxy features
- repeat both models
- Draw conclusions
3 Loading the Data
First we need to read in data and some custom functions.
setwd("/home/philippe/Documents/courses/lectures/bias_data")
# Read in the data:
d0 = read_csv("./car_insurance_claim_data.csv")
# Read in the functions:
source("ethics_functions.R")
# List the functions defined in this file:
tmt.env <- new.env()
sys.source("ethics_functions.R", envir = tmt.env)
utils::lsf.str(envir=tmt.env)## dollars_to_numeric : function (input)
## expand_factor2bin : function (data, col)
## fAUC : function (model, data, ...)
## get_best_cutoff : function (fpr, tpr, cutoff, cost.fp = 1)
## make_dependency_hist_plot : function (data, x, y, title, method = "loess", q_ymax = 1, q_xmax = 1)
## make_dependency_plot : function (data, x, y, title, method = "loess", q_ymax = 1, q_xmax = 1)
## make_WOE_table : function (df, y)
## opt_cut_off : function (perf, pred, cost.fp = 1)
## pct_table : function (x, y, round_digits = 2)
## space_to_underscore : function (input)
## str_clean : function (x)The data is imported from kaggle, the licence is unknown and it is believed to be “public domain.”
3.1 Data Dictionary
The data contains 10302 rows with 27 columns.
Each record (row) represents a set of attributes of an insurance
company individual customer that are related to their socio-demographic
profile and the insured vehicle. The binary response variable
TARGET_FLAG is 1 if the customer’s car was in a crash, and
0 if not. The continuous response variable TARGET_AMT
defines the cost related to the car crash.
The variables of the data are: ID, KIDSDRIV, BIRTH, AGE, HOMEKIDS, YOJ, INCOME, PARENT1, HOME_VAL, MSTATUS, GENDER, EDUCATION, OCCUPATION, TRAVTIME, CAR_USE, BLUEBOOK, TIF, CAR_TYPE, RED_CAR, OLDCLAIM, CLM_FREQ, REVOKED, MVR_PTS, CLM_AMT, CAR_AGE, CLAIM_FLAG, URBANICITY.
For the purpose of this exercise we added RACE, that is supposed to be representing some proxy for a small privileged class, large underprivileged class and a reference “race.” The labels of this feature are chosen in this order: A, B, and C.
The data dictionary enriched with some additional variables is as follows:
| variable name | definition | prejudice or expectation |
|---|---|---|
| ID | unique identifier | none |
| KIDSDRIV | number of teenager drivers | teenagers cause more accidents |
| BIRTH | birth date | used to derive age |
| AGE | age in years | young people cause more accidents, and older people too |
| HOMEKIDS | nbr kids at home | more kids might be more distraction in the car |
| YOJ | years on job | people that job-hop might be more prone to risk taking and accidents |
| INCOME | annual income in USD | income correlates to reliability and responsibility |
| PARENT1 | yes or no single parent | not clear |
| HOME_VAL | home value in USD if owner | similar to INCOME |
| MSTATUS | marital status “yes” if married | marriage might be a sign of stability and risk aversion(?) |
| GENDER | sex | men cause more and more expensive accidents |
| EDUCATION | level of the diploma | higher education correlates to safer driving |
| OCCUPATION | categories of employment | white color workers might drive safer |
| TRAVTIME | distance to work (probably in minutes) | longer distance translates in more probability to be involved in an accident |
| CAR_USE | commercial or private use | commercial use might be more risky |
| BLUEBOOK | resale value of the car | not clear |
| TIF | time in force = the time with the same insurer (numeric, probably in years, minimum is “1”) | longer should be better |
| CAR_TYPE | categorical | sports cars are more prone to accidents than minivans |
| RED_CAR | “yes” if the car is red | urban legend says that red cars are more prone to accidents |
| OLDCLAIM | total amount in USD of claims in the last 5 years | your past performance might be indicative, but note how this should interact with TIF |
| CLM_FREQ | not claim frequency, but the number of claims in the last 5 years | past performance might be indicative |
| REVOKED | “yes” if main driver’s licence was revoked during the last 7 years | licence being revoked should be indicative for driving style |
| MVR_PTS | motor vehicle record points (number) | traffic tickets should be indicative for the driving style and hence propensity to be involved in an accident |
| CLM_AMT | if last year in a car accident, the dollar amount of the claim paid by insurer | target variable |
| CAR_AGE | age of car in years | one might assume that drivers of older cars are less prudent |
| CLAIM_FLAG | 0 = NO, 1 = YES | target variable |
| URBANICITY | categorical, 2 options | cities should be more dangerous |
3.2 Data quality
We were not able to contact the data provider, and close observation
made us assume that some variables have been manipulated to eliminate
missing values. The missing values have then been assigned to some
“assumption” for example in the variable EDUCATION we have
“<High School” (lower than highs school) and
“z_High School”. The latter seems to be the collection of
missing values.
| factor(d0\(CLAIM_FLAG) | 0 | 1 | Total | | factor(d0\)EDUCATION) | ||||
| <High School | 1023 (67.5%) | 492 (32.5%) | 1515 (100.0%) | |
| Bachelors | 2150 (76.2%) | 673 (23.8%) | 2823 (100.0%) | |
| Masters | 1674 (80.6%) | 404 (19.4%) | 2078 (100.0%) | |
| PhD | 780 (83.5%) | 154 (16.5%) | 934 (100.0%) | |
| z_High School | 1929 (65.3%) | 1023 (34.7%) | 2952 (100.0%) | |
| Total | 7556 (73.3%) | 2746 (26.7%) | 10302 (100.0%) |
The table above of the EDUCATION variable shows that
somehow the probability of being involved in an accident increases with
education. Therefore we must conclude that z_High_School
and <High_School are not really logical here. The people
with lower than high school are for 32.4% involved in accidents and the
z_High_School have a higher probability to be in accidents
(34.6%).
For this particular variable we might take the two classes with
highest probability to be involved in an accident together as
<=High_School. This is logically consistent, and leaves
us with similar buckets sizes.
Therefore we assume that this unfortunate data manipulation is also
done in other variables. For example the variable GENDER
seems to have mixed the missing values with females. Conclusions based
on small differences hence will not be reliable.
| factor(d0\(CLAIM_FLAG) | 0 | 1 | Total | | factor(d0\)GENDER) | ||||
| M | 3539 (74.4%) | 1218 (25.6%) | 4757 (100.0%) | |
| z_F | 4017 (72.4%) | 1528 (27.6%) | 5545 (100.0%) | |
| Total | 7556 (73.3%) | 2746 (26.7%) | 10302 (100.0%) |
These considerations place serious footnotes at the reliability of the data.
Issues to consider for data quality:
- the partial treatment of missing values (see above)
- the huge amount of accidents. This data set is probably a subset that has been designed to have more accidents (one would expect one in thousand and not 26% accidents)
- the relative large amount of red cars indicates the a similar issue
3.3 First Data Cleanup
# Preprocess the variables into numeric / factors as necessary
# dollar values are in the format "$20,540" (string) -> convert this:
df = as.tbl(d0) %>%
mutate_at(c("INCOME","HOME_VAL","BLUEBOOK","OLDCLAIM", "CLM_AMT"),
parse_number) %>%
mutate_at(c("EDUCATION","OCCUPATION","CAR_TYPE","URBANICITY"),
space_to_underscore) %>%
mutate_at(c("PARENT1", "MSTATUS", "GENDER", "EDUCATION","OCCUPATION", "CAR_USE", "CAR_TYPE", "RED_CAR", "REVOKED", "URBANICITY"),
as.factor) %>%
mutate(CLAIM_FLAG = as.factor(CLAIM_FLAG))We also notice that
- the
IDcolumn will never yield useful information - the
BIRTHdata is the same asAGEbut in a less usable format.
Therefore, we will remove those columns before moving forward.
4 Exploring the Data (Univariate Analysis)
The univariate summaries for the individual variables (after some cleaning) are provided below.
summarytools::dfSummary(df,
plain.ascii = FALSE,
style = 'grid',
graph.magnif = 0.85,
varnumbers = FALSE,
valid.col = FALSE,
tmp.img.dir = "/tmp")| Variable | Stats / Values | Freqs (% of Valid) | Graph | Missing |
|---|---|---|---|---|
| KIDSDRIV [numeric] |
Mean (sd) : 0.2 (0.5) min < med < max: 0 < 0 < 4 IQR (CV) : 0 (3) |
0 : 9069 (88.0%) 1 : 804 ( 7.8%) 2 : 351 ( 3.4%) 3 : 74 ( 0.7%) 4 : 4 ( 0.0%) |
 |
0 (0.0%) |
| AGE [numeric] |
Mean (sd) : 44.8 (8.6) min < med < max: 16 < 45 < 81 IQR (CV) : 12 (0.2) |
61 distinct values |  |
7 (0.1%) |
| HOMEKIDS [numeric] |
Mean (sd) : 0.7 (1.1) min < med < max: 0 < 0 < 5 IQR (CV) : 1 (1.5) |
0 : 6694 (65.0%) 1 : 1106 (10.7%) 2 : 1427 (13.9%) 3 : 856 ( 8.3%) 4 : 201 ( 2.0%) 5 : 18 ( 0.2%) |
 |
0 (0.0%) |
| YOJ [numeric] |
Mean (sd) : 10.5 (4.1) min < med < max: 0 < 11 < 23 IQR (CV) : 4 (0.4) |
21 distinct values |  |
548 (5.3%) |
| INCOME [numeric] |
Mean (sd) : 61572.1 (47457.2) min < med < max: 0 < 53529 < 367030 IQR (CV) : 58582 (0.8) |
8151 distinct values |  |
570 (5.5%) |
| PARENT1 [factor] |
1. No 2. Yes |
8959 (87.0%) 1343 (13.0%) |
 |
0 (0.0%) |
| HOME_VAL [numeric] |
Mean (sd) : 154523 (129188.4) min < med < max: 0 < 160661 < 885282 IQR (CV) : 238256 (0.8) |
6334 distinct values |  |
575 (5.6%) |
| MSTATUS [factor] |
1. Yes 2. z_No |
6188 (60.1%) 4114 (39.9%) |
 |
0 (0.0%) |
| GENDER [factor] |
1. M 2. z_F |
4757 (46.2%) 5545 (53.8%) |
 |
0 (0.0%) |
| EDUCATION [factor] |
1. <High_School 2. Bachelors 3. Masters 4. PhD 5. z_High_School |
1515 (14.7%) 2823 (27.4%) 2078 (20.2%) 934 ( 9.1%) 2952 (28.7%) |
 |
0 (0.0%) |
| OCCUPATION [factor] |
1. Clerical 2. Doctor 3. Home_Maker 4. Lawyer 5. Manager 6. Professional 7. Student 8. z_Blue_Collar |
1590 (16.5%) 321 ( 3.3%) 843 ( 8.7%) 1031 (10.7%) 1257 (13.0%) 1408 (14.6%) 899 ( 9.3%) 2288 (23.7%) |
 |
665 (6.5%) |
| TRAVTIME [numeric] |
Mean (sd) : 33.4 (15.9) min < med < max: 5 < 33 < 142 IQR (CV) : 22 (0.5) |
100 distinct values |  |
0 (0.0%) |
| CAR_USE [factor] |
1. Commercial 2. Private |
3789 (36.8%) 6513 (63.2%) |
 |
0 (0.0%) |
| BLUEBOOK [numeric] |
Mean (sd) : 15659.9 (8428.8) min < med < max: 1500 < 14400 < 69740 IQR (CV) : 11690 (0.5) |
2985 distinct values |  |
0 (0.0%) |
| TIF [numeric] |
Mean (sd) : 5.3 (4.1) min < med < max: 1 < 4 < 25 IQR (CV) : 6 (0.8) |
23 distinct values |  |
0 (0.0%) |
| CAR_TYPE [factor] |
1. Minivan 2. Panel_Truck 3. Pickup 4. Sports_Car 5. Van 6. z_SUV |
2694 (26.2%) 853 ( 8.3%) 1772 (17.2%) 1179 (11.4%) 921 ( 8.9%) 2883 (28.0%) |
 |
0 (0.0%) |
| RED_CAR [factor] |
1. no 2. yes |
7326 (71.1%) 2976 (28.9%) |
 |
0 (0.0%) |
| OLDCLAIM [numeric] |
Mean (sd) : 4034 (8733.1) min < med < max: 0 < 0 < 57037 IQR (CV) : 4647.5 (2.2) |
3545 distinct values |  |
0 (0.0%) |
| CLM_FREQ [numeric] |
Mean (sd) : 0.8 (1.2) min < med < max: 0 < 0 < 5 IQR (CV) : 2 (1.4) |
0 : 6292 (61.1%) 1 : 1279 (12.4%) 2 : 1492 (14.5%) 3 : 992 ( 9.6%) 4 : 225 ( 2.2%) 5 : 22 ( 0.2%) |
 |
0 (0.0%) |
| REVOKED [factor] |
1. No 2. Yes |
9041 (87.8%) 1261 (12.2%) |
 |
0 (0.0%) |
| MVR_PTS [numeric] |
Mean (sd) : 1.7 (2.2) min < med < max: 0 < 1 < 13 IQR (CV) : 3 (1.3) |
14 distinct values |  |
0 (0.0%) |
| CLM_AMT [numeric] |
Mean (sd) : 1511.3 (4725.2) min < med < max: 0 < 0 < 123247 IQR (CV) : 1144.8 (3.1) |
2346 distinct values |  |
0 (0.0%) |
| CAR_AGE [numeric] |
Mean (sd) : 8.3 (5.7) min < med < max: -3 < 8 < 28 IQR (CV) : 11 (0.7) |
30 distinct values |  |
639 (6.2%) |
| CLAIM_FLAG [factor] |
1. 0 2. 1 |
7556 (73.3%) 2746 (26.7%) |
 |
0 (0.0%) |
| URBANICITY [factor] |
1. Highly_Urban/ Urban 2. z_Highly_Rural/ Rural |
8230 (79.9%) 2072 (20.1%) |
 |
0 (0.0%) |