Principal Component Analysis (PCA)

#install.packages("magrittr")  # for piping %>%

#install.packages("ade4")      # PCA computation

#install.packages("factoextra")# PCA visualization

library(psych)

#library(fmsb)

#PCA - principal component analysis

#Covid19 data analysis

mydata<- read.csv(file.choose())

summary(mydata)

#Define_mydataiables

#mydata<- cbind(CO1,CO2,CO3,CO4,CO5,CO6,CO7,CO8,PMO1,PMO2,PMO3,

            #AT1,AT2,AT3,AT4,AT5,AT6,AT7,SN1,SN2,SN3,SN4,

            #PBC1,PBC2,PBC3,PBC4)

#Calculating_Cronbach's Alpha

covid_concern<- alpha(data.frame(mydata[c("CO2", "CO3", "CO5", "CO7")]))

attitude<- alpha(data.frame(mydata[c("SN3", "PBC1", "PBC2")]))

social_norm<- alpha(data.frame(mydata[c("CO4", "AT7", "SN1", "SN2", "PMO1")]))

perc_beh_control<- alpha(data.frame(mydata[c("AT2", "AT4", "AT5", "AT6")]))

perc_mor_obligation<-alpha(data.frame(mydata[c("CO8", "AT1")]))

#KMO

covid_concern<- KMO(data.frame(mydata[c("CO2", "CO3", "CO5", "CO7")]))

attitude<- KMO(data.frame(mydata[c("SN3", "PBC1", "PBC2")]))

social_norm<- KMO(data.frame(mydata[c("CO4", "AT7", "SN1", "SN2", "PMO1")]))

perc_beh_control<- KMO(data.frame(mydata[c("AT2", "AT4", "AT5", "AT6")]))

perc_mor_obligation<-KMO(data.frame(mydata[c("CO8", "AT1")]))

#Bartlett's Test of Sphericity

#$pvalue is the sphericity(sig.) value

covid_concern<-cortest.bartlett(cor(data.frame(mydata[, 1:8])))

attitude<- cortest.bartlett(cor(data.frame(mydata[, 9:15])))

social_norm<- cortest.bartlett(cor(data.frame(mydata[, 16:19])))

perc_beh_control<- cortest.bartlett(cor(data.frame(mydata[, 20:23])))

perc_mor_obligation<-cortest.bartlett(cor(data.frame(mydata[c("CO8", "AT1")])))

#Descriptive statistics

summary(mydata)

cor(mydata)

#Principal Component Analysis

pca1<-princomp(mydata, scores=TRUE, cor=TRUE)

summary(pca1)

#Loading of principal components

loadings(pca1)

#pca1$loadings

#Scree plot of eigenvalues

plot(pca1)

#barplot(pca1)

screeplot(pca1, type="line", main="Scree Plot")

#Biplot of score mydataiables

biplot(pca1)

#Scores of the components

pca1$scores[1:26, ]

#Rotation

#mydataimax(pca1$roatation)

#Promax(pca1$rotation)

#Factor analysis - different results from other softwares and no roation

fa1<- factanal(mydata, factor = 5)

fa1

fa2<- factanal(mydata, factor=5, rotation="varimax",  scores = "regression")

fa2

fa3<- factanal(mydata, factors=5, rotation = "cluster", scores = "regression")

fa3

library(ade4)

library(factoextra)

library(magrittr)

#Visualize eigenvalues (scree plot). Show the percentage of variances explained by each principal component.

fviz_eig(pca1)

#Graph of individuals. Individuals with a similar profile are grouped together.

fviz_pca_ind(pca1,

             col.ind = "cos2", # Color by the quality of representation

             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),

             repel = TRUE)     # Avoid text overlapping 

#Graph of variables. Positive correlated variables point to the same side of the plot. Negative correlated variables point to opposite sides of the graph.

fviz_pca_var(pca1,

             col.var = "contrib", # Color by contributions to the PC

             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),

             repel = TRUE     # Avoid text overlapping

)

#Biplot of individuals and variables

fviz_pca_biplot(pca1, repel = TRUE,

                col.var = "#2E9FDF", # Variables color

                col.ind = "#696969"  # Individuals color

)

#The ade4 package creates R base plots.

# Scree plot

screeplot(pca1, main = "Screeplot - Eigenvalues", xlab="Component")

# Correlation circle of variables

s.corcircle(pca1$co)