LDA Learning

Loading required R packages

# Install the two packages as follow
#install.packages(c("tidyverse", "caret"))
library(tidyverse)
library(caret)
theme_set(theme_classic())

We will use Credit Card Default data for this

Default <- read.csv("MCICreditCardDefault.csv")[,-1]
head(Default)

##   CreditLimit Male Education MaritalStatus Age BillOutstanding LastPayment
## 1       20000    0         2             1  24            3913           0
## 2      120000    0         2             2  26            2682           0
## 3       90000    0         2             2  34           29239        1518
## 4       50000    0         2             1  37           46990        2000
## 5       50000    1         2             1  57            8617        2000
## 6       50000    1         1             2  37           64400        2500
##   Default
## 1       1
## 2       1
## 3       0
## 4       0
## 5       0
## 6       0

Making Factor variable

names <- c(2,3,4,8)
Default[,names] <- lapply(Default[,names] , factor)
str(Default)

## 'data.frame':    29601 obs. of  8 variables:
##  $ CreditLimit    : int  20000 120000 90000 50000 50000 50000 500000 100000 140000 20000 ...
##  $ Male           : Factor w/ 2 levels "0","1": 1 1 1 1 2 2 2 1 1 2 ...
##  $ Education      : Factor w/ 4 levels "1","2","3","4": 2 2 2 2 2 1 1 2 3 3 ...
##  $ MaritalStatus  : Factor w/ 3 levels "1","2","3": 1 2 2 1 1 2 2 2 1 2 ...
##  $ Age            : int  24 26 34 37 57 37 29 23 28 35 ...
##  $ BillOutstanding: int  3913 2682 29239 46990 8617 64400 367965 11876 11285 0 ...
##  $ LastPayment    : int  0 0 1518 2000 2000 2500 55000 380 3329 0 ...
##  $ Default        : Factor w/ 2 levels "0","1": 2 2 1 1 1 1 1 1 1 1 ...

Split the data into training (80%) and test set (20%)

set.seed(123)
training.samples <- Default$Default %>%
  createDataPartition(p = 0.8, list = FALSE)
train.data <- Default[training.samples, ]
test.data <- Default[-training.samples, ]
dim(train.data)

## [1] 23681     8

dim(test.data)

## [1] 5920    8

Normalize the data. (Categorical variables are automatically ignored)

# Estimate preprocessing parameters
preproc.param <- train.data %>% 
  preProcess(method = c("center", "scale"))
# Transform the data using the estimated parameters
train.transformed <- preproc.param %>% predict(train.data)
test.transformed <- preproc.param %>% predict(test.data)

Linear discriminant analysis - LDA

library(MASS)

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:dplyr':
## 
##     select

# Fit the model
model <- lda(Default~., data = train.transformed)
model

## Call:
## lda(Default ~ ., data = train.transformed)
## 
## Prior probabilities of groups:
##         0         1 
## 0.7768675 0.2231325 
## 
## Group means:
##   CreditLimit     Male1 Education2 Education3   Education4 MaritalStatus2
## 0  0.08341306 0.3838126  0.4612165  0.1600804 0.0048921020      0.5432951
## 1 -0.29041446 0.4358441  0.5054883  0.1877366 0.0007570023      0.5081378
##   MaritalStatus3          Age BillOutstanding LastPayment
## 0     0.01049084 -0.008648351      0.01247380  0.04023246
## 1     0.01249054  0.030110469     -0.04342933 -0.14007505
## 
## Coefficients of linear discriminants:
##                         LD1
## CreditLimit     -0.88790102
## Male1            0.45614403
## Education2       0.14316883
## Education3       0.07489287
## Education4      -1.95414753
## MaritalStatus2  -0.39376662
## MaritalStatus3  -0.35799274
## Age              0.10485197
## BillOutstanding  0.13783843
## LastPayment     -0.27548470

plot(model)

Make predictions

predictions <- model %>% predict(test.transformed)
names(predictions)

## [1] "class"     "posterior" "x"

Understanding Outputs

# Predicted classes
head(predictions$class, 6)

## [1] 0 0 0 0 0 0
## Levels: 0 1

# Predicted probabilities of class memebership.
head(predictions$posterior, 6) 

##            0         1
## 10 0.6947669 0.3052331
## 15 0.8215088 0.1784912
## 23 0.7618830 0.2381170
## 32 0.7067022 0.2932978
## 33 0.7412506 0.2587494
## 44 0.7572820 0.2427180

# Linear discriminants
head(predictions$x, 3) 

##           LD1
## 10  1.1048056
## 15 -0.5276914
## 23  0.3152693

Model accuracy

mean(predictions$class==test.transformed$Default)

## [1] 0.7768581

It can be seen that, our model correctly classified 77.6% of observations, which is excellent.

Confusion Matrix

Pred <- predictions$class
Actual <- test.transformed$Default

confusionMatrix(table(Pred,Actual),positive = "1")

## Confusion Matrix and Statistics
## 
##     Actual
## Pred    0    1
##    0 4599 1321
##    1    0    0
##                                          
##                Accuracy : 0.7769         
##                  95% CI : (0.766, 0.7874)
##     No Information Rate : 0.7769         
##     P-Value [Acc > NIR] : 0.5074         
##                                          
##                   Kappa : 0              
##                                          
##  Mcnemar's Test P-Value : <2e-16         
##                                          
##             Sensitivity : 0.0000         
##             Specificity : 1.0000         
##          Pos Pred Value :    NaN         
##          Neg Pred Value : 0.7769         
##              Prevalence : 0.2231         
##          Detection Rate : 0.0000         
##    Detection Prevalence : 0.0000         
##       Balanced Accuracy : 0.5000         
##                                          
##        'Positive' Class : 1              
##