deal_with_continuos_variables.R

# Deal with continuous variables
data <- data.frame(state.x77)
str(data)

library(ggplot2)
#plot Frost variable and check the data points are all over
qplot(y = Frost, data = data, colour = 'red')


# method 1 - create bins and add labels
bins <- cut(data$Frost, 3, include.lowest = TRUE)
bins
bins <- cut(data$Frost, 3, include.lowest = TRUE, labels = c('Low', 'Medium', 'High'))
bins



# method 2 - normalization, Z-score
## I like this z-score tutorial: http://stats.seandolinar.com/calculating-z-scores-with-r/
income <- matrix(data$Income)
hist(income)
income_sd <- sd(income)*sqrt((length(income)-1)/length(income))
income_mean <- mean(income)
get_z <- function(v, my_mean, my_sd) (v-my_mean)/my_sd
apply(income, 1, get_z, income_mean, income_sd)



# method 3 - convert highly skewed variables
## check skewness 
library(e1071)
## in this case, the value indiaates its skewed towards right
skewness(data$Income)
skewness(data$Illiteracy)  
## or simply check histogram
hist(data$Income)
hist(data$Illiteracy)
## data$Illiteracy is highly skewed, change to log values, much better!
hist(log(data$Illiteracy))
skewness(log(data$Illiteracy))


# method 4 - outliers
## here, we will see Area has more obvious outliers
boxplot(data)
## method 1 - squish
boxplot(quantiles <- quantile(data$Area, c(.05, .90 )))
data$Area <- squish(data$Area, quantile(data$Area, c(.05, .90)))
boxplot(data)
boxplot(data$Area)

## method 2 - binning
summary(data$Area)
bins1 <- cut(data$Area, 3, include.lowest = FALSE, labels = c('Low', 'Medium', 'High'))
bins1

## log is always a better way
bins2 <- cut(log(data$Area), 3, include.lowest = FALSE, labels = c('Low', 'Medium', 'High'))
bins2
hist(log(data$Area))
## Note: as you can see, after squishing the outliers in Area, other data like Population
## starts to have outliers.... 
## When dealing with outliers, need to do deeper research to understand the data and see how to deal with them


# method 5 - PCA and Factor Analysis
## PCA - Finding out few 'principal' variables which explain significant amount of variation in dependent variable
## Factor Analysis - factor reduction
data(Boston, package = 'MASS')
my_data <- Boston
str(my_data)
# check correlation table
cor(my_data)
pcaData <- princomp(my_data, scores = TRUE, cor = TRUE)
summary(pcaData)
# represent the contribution of each factor, higher the value, higher contributions
loadings(pcaData)
# the top 3 compnents contribute most
screeplot(pcaData, type = 'line', main = 'Screeplot')
biplot(pcaData)
pcaData$scores[1:10,]

#Exploratory Factor Analysis
#Using PCA we've determined 3 factors - Comp 1, Comp 2 and Comp 3
pcaFac <- factanal(my_data, factors = 3, rotation = 'varimax')
pcaFac

#To find the scores of factors
pcaFac.scores <- factanal(my_data, factors = 3, rotation = 'varimax', scores = 'regression')
pcaFac.scores$scores[1:10,]