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rm(list = ls())

#loading data
d <-read.csv(file.choose(), header = T)
head(d)

#lets look at the structure
str(d)
#summary
summary(d)

#Problem statment states respondents used a 5 point likert scale
#there are few variables which has values as 6
#We will convert them as 5 as 5 being the highest factor

d[d==6] <- 5  
d[,c(12,25)] <- 6 - d[,c(12,25)]
dim(d)

library(psych)
library(corrplot)
library(nFactors)
library(MASS)
library(GPArotation)
#calling libraries


corfac <- cor(d[-1])
corrplot(corfac)

#To do PCA or Factor; first lets do the KMO and Bartlett test

#preforming KMO test
KMO(d[,-1])

#overall MSA is 0.85 which is good enough for the model
#FACTOR analysis can be carried out for this data

#performing barllet test

print(cortest.bartlett(corfac, nrow(d)))
#P value is significantly low and hence we can assume
#there is some significiance b/w the variables


#lets do a PCA to identify no of factors to be used


pca1 <- princomp(d[,-1], scores = T, cor = T)
pca1
summary(pca1)
#from the summary, it looks like there are 4 components
#SD of upto comp 5 is greater than 1 (eigen values)
#It explains upto 62% of the model

screeplot(pca1, type = "b", main = "Scree Plot of PCA")

pca2 <- principal(d[,-1], nfactors = length(d[,-1]), rotate = "none")
pca2
cat("\n\n Eigen values \n")
print(pca2$values)
#Even in this principal function 5 components are significant
plot(pca2$values, type = "b",xlab = "Factors", ylab = "Eigen values", main = "SCREE PLOT") 

#alternative
no <- fa.parallel(d[,-1])


#We will use 5 factors for our factor analysis

sol1 <- fa(r=d[,-1], nfactors = 5, rotate = "oblimin", fm="pa")
print(sol1)
sol1$uniquenesses

#factor 5 explains only 0.1 variance
#lets try using 4 factors
#using oblimin rotation as there is some correlation within the factors as shown in corrplot
#varimax & promax also can be used
sol2 <- fa(d[,-1], nfactors = 4, rotate = "oblimin", fm="ml")
print(sol2)

#the loadings are distributed
#using a cutoff value of 0.3, lets see the factors


print(sol2$loadings, cutoff = 0.3)
#filling, natural, fiber & health are contributing to factor 1
#sugar, salt & sweet are in factor 2
#kids, family & economical are in factor 3
#plain has a negative correlation in factor 4


#Factor loading can be classified based on their magnitude.
#Value  Interpretation
#> 30   Minimum consideration level
#> 40   More important
#> 50   Practically significant

fa.diagram(sol2)
#This diagram tell us the pictures

fl <- round(unclass(sol2$loadings),2)
fl
write.csv(fl, "Factors for ds.csv")


library(lavaan)
#4 factors adding them to one unique variable 
factor1 <- c(2,3,4,8,9,14,19,23,26)
factor2 <- c(5,7,16,20,22)
factor3 <- c(11,13,15)
factor4 <- c(10,12,17,18,21,24,25)

models <- list()
fits <- list()


models$m3 <- 
  ' Health =~ Filling + Natural + Fibre + Satisfying +Energy +Regular +Quality +Nutritious
    Taste =~ Sweet + Salt + Calories + Sugar +Process 
    Famaly =~ Kids + Economical + Family 
    Result =~ Fun + Soggy + Plain + Crisp + Fruit + Treat + Boring 
  '


fits$m3 <- lavaan::cfa(models$m3, data = d)
fits$m3
standardizedSolution(fits$m3)

summary(fits$m3)





#Crombach's alpha is a measure of internal consistency, 
#that is, how closely related a set of items are as a group.


factor1alpha <- psych::alpha(d[,factor1], check.keys = TRUE)
factor2alpha <- psych::alpha(d[,factor2], check.keys = TRUE)
factor3alpha <- psych::alpha(d[,factor3], check.keys = TRUE)
factor4alpha <- psych::alpha(d[,factor4], check.keys = TRUE)


factor1alpha$total$raw_alpha
factor2alpha$total$raw_alpha
factor3alpha$total$raw_alpha
factor4alpha$total$raw_alpha

#alpha values are 0.7

d[,factor1]
#Just looking at factor 1 if it is alinged

#better to take the average of the factors and assign them to factors

?apply
#tried with table function; but mean is better 

#lets add all the factors to the original data set

d$factor1Score <- apply(d[,factor1],1,mean)
d$factor2Score <- apply(d[,factor2],1,mean)
d$factor3Score <- apply(d[,factor3],1,mean)
d$factor4Score <- apply(d[,factor4],1,mean)
colnames(d)[27:30] <-c("Health", "Taste", "Family", "Result")
?aggregate


#lets take our the delimited factors
d_full<-aggregate(d[,27:30],  list(d[,1]), mean)



#final factors
format(d_full, digits = 2)
?tapply
tapply(d[,1],d[,27:30],mean)

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