Linear Discriminant Analysis (LDA)

Setup

library (ISLR)
library (MASS)
library (descr)

Load data

attach(Smarket)

Linear Discriminant Analysis

freq(Direction)

## Direction 
##       Frequency Percent
## Down        602   48.16
## Up          648   51.84
## Total      1250  100.00

train = Year<2005
lda.fit=lda(Direction~Lag1+Lag2,data=Smarket, subset=Year<2005)
lda.fit

## Call:
## lda(Direction ~ Lag1 + Lag2, data = Smarket, subset = Year < 
##     2005)
## 
## Prior probabilities of groups:
##     Down       Up 
## 0.491984 0.508016 
## 
## Group means:
##             Lag1        Lag2
## Down  0.04279022  0.03389409
## Up   -0.03954635 -0.03132544
## 
## Coefficients of linear discriminants:
##             LD1
## Lag1 -0.6420190
## Lag2 -0.5135293

plot(lda.fit, col="dodgerblue")

Smarket.2005=subset(Smarket,Year==2005) # Creating subset with 2005 data
lda.pred=predict(lda.fit,Smarket.2005)
names(lda.pred)

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

lda.class=lda.pred$class
Direction.2005=Smarket$Direction[!train]
table(lda.class,Direction.2005) 

##          Direction.2005
## lda.class Down  Up
##      Down   35  35
##      Up     76 106

data.frame(lda.pred)[1:5,]

##      class posterior.Down posterior.Up         LD1
## 999     Up      0.4901792    0.5098208  0.08293096
## 1000    Up      0.4792185    0.5207815  0.59114102
## 1001    Up      0.4668185    0.5331815  1.16723063
## 1002    Up      0.4740011    0.5259989  0.83335022
## 1003    Up      0.4927877    0.5072123 -0.03792892

table(lda.pred$class,Smarket.2005$Direction)

##       
##        Down  Up
##   Down   35  35
##   Up     76 106

mean(lda.pred$class==Smarket.2005$Direction)

## [1] 0.5595238