I am trying to reproduce the accounts of example 5 of this pdf on discriminant analysis. When doing the accounts without using any packages, I get the same results of the file, as per the code below. However, when using the MASS package of the R software and the lda() function, the accounts do not match. What error am I making when using the function of this package?
rm(list = ls())
cat("4")
RacaA <- data.frame(x1=c(6.36, 5.92, 5.92,6.44,6.40,6.56,6.64,6.68,6.72,6.76,6.72),
x2=c(5.24,5.12,5.36,5.64,5.16,5.56,5.36,4.96,5.48,5.60,5.08))
n1 <- length(RacaA$x1)
RacaB <- data.frame(x1=c(6.00,5.60,5.64,5.76,5.96,5.72,5.64,5.44,5.04,4.56,5.48,5.76),
x2=c(4.88,4.64,4.96,4.80,5.08,5.04,4.96,4.88,4.44,4.04,4.20,4.80))
n2 <- length(RacaB$x1)
barx1A <- mean(RacaA$x1)
barx2A <- mean(RacaA$x2)
v1 <- rbind(barx1A,barx2A)
CovRA <- cov(RacaA)
barx1B <- mean(RacaB$x1)
barx2B <- mean(RacaB$x2)
v2 <- rbind(barx1B,barx2B)
CovRB <- cov(RacaB)
Sc <- ((n1-1)/((n1-1)+(n2-1)))*CovRA+((n2-1)/((n1-1)+(n2-1)))*CovRB
Scinv <- solve(Sc)
x1_x2 <- cbind(v1-v2)
Dx <- t(x1_x2)%*%Scinv
DxA <- Dx%*%v1
DxB <- Dx%*%v2
m <- (1/2)*(DxA+DxB)
m
library(MASS)
m.X <- rbind(RacaA,RacaB)
RA = rep("RacaA", 11)
RB = rep("RacaB", 12)
Raca <- c(RA,RB)
m.Raca <- data.frame(m.X,Raca)
result.ad <- lda(Raca~., m.Raca)
pred<-predict(result.ad)$class
data.pred <- Raca
table(data.pred,pred)
plot(result.ad)
result.ad