RIDIT Analysis and PCA on Auto Accident Personal Injury Claims
Ramesh Babu Paramkusham, Ph.D
2025-09-06
Notes:
-RIDIT Transformation converts categorical responses into numerical scores between -1 and 1.
-PCA helps reduce dimensionality and detect patterns in RIDIT scores or other numeric indicators.
-The plotellipses function visualizes the contribution of qualitative variables in PCA.
-This R Markdown file produces interactive visualizations and reports results in an organized document.
-PCA reduces dimensionality; first few components explain majority of variance.
-Using ‘quali.sup’ in PCA allows visualization of categorical outcomes without including them in variance computation.
-Scree plots help determine the number of principal components to retain.
1. Load Required Libraries
library(psych)
library(corrplot)
library(Hmisc)
library(tidyverse)
library(GGally)
library(factoextra)
library(FactoMineR)
library(emuR) 2. Load Dataset
filename <- "/Users/rameshbabuparamkusham/Documents/DAT 610/DAT 610 Auto Accident Personal Injury Claims.csv"
data <- read.csv(filename, header = TRUE)
head(data)## Claim_Number Policy_ID CLAIM_AMOUNT PAID_AMOUNT CLAIM_SUSPICION_SCORE IND_01
## 1 NA NA NA NA
## 2 5001463 364697 $13,463 $3,646 3 1
## 3 NA NA NA NA
## 4 5004844 426960 $1,246 $594 3 1
## 5 NA NA NA NA
## 6 5005493 426313 $19,883 $15,138 3 1
## IND_02 IND_03 IND_04 IND_05 IND_06 IND_07 IND_08 IND_09 IND_10 IND_11 IND_12
## 1 NA NA NA NA NA NA NA NA NA NA NA
## 2 1 1 4 5 3 3 1 2 2 1 3
## 3 NA NA NA NA NA NA NA NA NA NA NA
## 4 2 1 4 1 1 5 1 2 1 1 5
## 5 NA NA NA NA NA NA NA NA NA NA NA
## 6 1 4 1 1 1 1 2 3 5 4 5
## IND_13 IND_14 IND_15 IND_16 IND_17 IND_18 IND_19 IND_20 RIDIT_01 RIDIT_02
## 1 NA NA NA NA NA NA NA NA NA NA
## 2 5 2 1 2 4 1 2 3 -0.5039841 -0.5059761
## 3 NA NA NA NA NA NA NA NA NA NA
## 4 1 2 2 1 1 5 1 2 -0.5039841 0.2290837
## 5 NA NA NA NA NA NA NA NA NA NA
## 6 1 1 4 1 1 1 3 1 -0.5039841 -0.5059761
## RIDIT_03 RIDIT_04 RIDIT_05 RIDIT_06 RIDIT_07 RIDIT_08 RIDIT_09
## 1 NA NA NA NA NA NA NA
## 2 -0.4701195 0.7888446 0.8964143 0.6513944 0.5916335 -0.5039841 0.2310757
## 3 NA NA NA NA NA NA NA
## 4 -0.4701195 0.7888446 -0.4980080 -0.4920319 0.9143426 -0.5039841 0.2310757
## 5 NA NA NA NA NA NA NA
## 6 0.7988048 -0.4920319 -0.4980080 -0.4920319 -0.5278884 0.2649402 0.6055777
## RIDIT_10 RIDIT_11 RIDIT_12 RIDIT_13 RIDIT_14 RIDIT_15 RIDIT_16
## 1 NA NA NA NA NA NA NA
## 2 0.3147410 -0.5139442 0.6354582 0.9302789 0.2370518 -0.4920319 0.2629482
## 3 NA NA NA NA NA NA NA
## 4 -0.4561753 -0.5139442 0.9203187 -0.4960159 0.2370518 0.2569721 -0.5000000
## 5 NA NA NA NA NA NA NA
## 6 0.9163347 0.7430279 0.9203187 -0.4960159 -0.5139442 0.7968127 -0.5000000
## RIDIT_17 RIDIT_18 RIDIT_19 RIDIT_20
## 1 NA NA NA NA
## 2 0.7549801 -0.4980080 0.3007968 0.6235060
## 3 NA NA NA NA
## 4 -0.5079681 0.8984064 -0.4780876 0.2450199
## 5 NA NA NA NA
## 6 -0.5079681 -0.4980080 0.6533865 -0.5079681head(data$PAID_AMOUNT)## [1] "" "$3,646 " "" "$594 " "" "$15,138 "auto <- data
myData <- auto[1:502, 6:25]3. RIDIT Transformation
-RIDIT (Relative to an Identified Distribution) converts ordered categorical variables into numerical scores, enabling comparison across categories.
# Compute RIDIT values for selected indicators
rid <- data.frame(
"RIDIT" = cbind(
"_01" = 2 * (0 + 0.5 * table(myData$IND_01)[1] / 502) - 1,
"i2" = 2 * (table(myData$IND_01)[1] / 502 + 0.5 * table(myData$IND_01)[2] / 502) - 1,
"i5" = 2 * (
table(myData$IND_02)[1] / 502 +
table(myData$IND_02)[2] / 502 +
table(myData$IND_02)[3] / 502 +
table(myData$IND_02)[4] / 502 +
0.5 * table(myData$IND_02)[5] / 502
) - 1
)
)
# Display RIDIT values
rid## RIDIT._01 RIDIT.i2 RIDIT.i5
## 1 -0.7669323 -0.376494 -0.045816734. Scatterplot of IND_01 vs RIDIT
attach(auto)
plot(auto[,7], auto[,27],
main = "Scatterplot of IND_01 vs RIDIT",
xlab = "IND_01",
ylab = "RIDIT_01",
pch = 19)
5. PCA on RIDIT-Transformed Variables
# Select RIDIT columns
myRidit <- auto[1:502, 26:45]
# Perform PCA using correlation matrix
myRiditPCA <- princomp(~ ., data = myRidit, cor = TRUE)
# Summary of PCA
summary(myRiditPCA)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.23981626 1.21132271 1.17313228 1.1170640 1.10801855
## Proportion of Variance 0.07685722 0.07336514 0.06881197 0.0623916 0.06138526
## Cumulative Proportion 0.07685722 0.15022235 0.21903432 0.2814259 0.34281117
## Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## Standard deviation 1.0652540 1.05981080 1.02337336 1.01406730 1.00265478
## Proportion of Variance 0.0567383 0.05615995 0.05236465 0.05141662 0.05026583
## Cumulative Proportion 0.3995495 0.45570942 0.50807408 0.55949070 0.60975653
## Comp.11 Comp.12 Comp.13 Comp.14 Comp.15
## Standard deviation 0.99272057 0.98810750 0.93065384 0.90732164 0.89409002
## Proportion of Variance 0.04927471 0.04881782 0.04330583 0.04116163 0.03996985
## Cumulative Proportion 0.65903124 0.70784906 0.75115489 0.79231651 0.83228636
## Comp.16 Comp.17 Comp.18 Comp.19 Comp.20
## Standard deviation 0.87224347 0.84693418 0.80929865 0.80064886 0.76168476
## Proportion of Variance 0.03804043 0.03586488 0.03274821 0.03205193 0.02900818
## Cumulative Proportion 0.87032680 0.90619167 0.93893989 0.97099182 1.00000000# Scree plot to determine number of components
screeplot(myRiditPCA, type = "line")
6. PCA using FactoMineR
# PCA on original data columns
res.pca <- PCA(auto[,6:25], scale.unit = TRUE, ncp = 5, graph = TRUE)
7. PCA with Qualitative Supplementary Variable
-We transform CLAIM_SUSPICION_SCORE into a factor and include it as a qualitative supplementary variable.
# Transform claim suspicion score to factor
auto$CS2 <- as.factor(auto$CLAIM_SUSPICION_SCORE)
# Combine variables for PCA
myData2 <- auto[c(6:25, 46)]
# PCA including qualitative variable
res.pca3 <- PCA(myData2[1:21], scale.unit = TRUE, ncp = 5, quali.sup = 21, graph = TRUE)
# Scatterplots with ellipses
plotellipses(res.pca3, 21)