PCA
Lucas Villalba
3/30/2022
Principal Component Analysis
Reading the data
# install psych package
# install.packages("psych")
# load psych package
library(psych)## Warning: package 'psych' was built under R version 4.1.3#
# install nFactors package
# install.packages("nFactors")
#load nFactors package
library(nFactors)## Warning: package 'nFactors' was built under R version 4.1.3## Loading required package: lattice##
## Attaching package: 'nFactors'## The following object is masked from 'package:lattice':
##
## parallel#
# install GPArotation package
# install.packages("GPArotation")
#load GPArotation package
library(GPArotation)
#Read in data file0
ss<-read.csv("C:/Users/Administrador/Documents/R/ABDA/PCA/StudentSurveyFA.csv", sep=",", header=T)
summary(ss)## BIO GEO CHEM ALG CALC
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:1.000 1st Qu.:2.00 1st Qu.:2.000
## Median :2.000 Median :2.00 Median :2.000 Median :3.00 Median :3.000
## Mean :2.353 Mean :2.17 Mean :2.237 Mean :3.05 Mean :3.063
## 3rd Qu.:3.000 3rd Qu.:3.00 3rd Qu.:3.000 3rd Qu.:4.00 3rd Qu.:4.000
## Max. :5.000 Max. :5.00 Max. :5.000 Max. :5.00 Max. :5.000
## STAT
## Min. :1.000
## 1st Qu.:2.000
## Median :3.000
## Mean :2.937
## 3rd Qu.:4.000
## Max. :5.000# generate the correlation matrix
corMat <- cor(ss)
#
# display the correlation matrix
corMat## BIO GEO CHEM ALG CALC STAT
## BIO 1.0000000 0.6822208 0.7470278 0.1153204 0.2134271 0.2028315
## GEO 0.6822208 1.0000000 0.6814857 0.1353557 0.2045215 0.2316288
## CHEM 0.7470278 0.6814857 1.0000000 0.0838225 0.1364251 0.1659747
## ALG 0.1153204 0.1353557 0.0838225 1.0000000 0.7709303 0.4094324
## CALC 0.2134271 0.2045215 0.1364251 0.7709303 1.0000000 0.5073147
## STAT 0.2028315 0.2316288 0.1659747 0.4094324 0.5073147 1.0000000Use Factor Analysis
as PCA is a subcategory of FA
# use fa() to conduct factor analysis
# save the solution to an R variable
solution <- fa(r = corMat, nfactors = 2, rotate ="oblimin", fm ="pa")
#display the solution output
solution## Factor Analysis using method = pa
## Call: fa(r = corMat, nfactors = 2, rotate = "oblimin", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## BIO 0.86 0.02 0.75 0.255 1.0
## GEO 0.78 0.05 0.63 0.369 1.0
## CHEM 0.87 -0.05 0.75 0.253 1.0
## ALG -0.04 0.81 0.65 0.354 1.0
## CALC 0.01 0.96 0.92 0.081 1.0
## STAT 0.13 0.50 0.29 0.709 1.1
##
## PA1 PA2
## SS loadings 2.14 1.84
## Proportion Var 0.36 0.31
## Cumulative Var 0.36 0.66
## Proportion Explained 0.54 0.46
## Cumulative Proportion 0.54 1.00
##
## With factor correlations of
## PA1 PA2
## PA1 1.00 0.21
## PA2 0.21 1.00
##
## Mean item complexity = 1
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 15 and the objective function was 2.87
## The degrees of freedom for the model are 4 and the objective function was 0.01
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.94 0.96
## Multiple R square of scores with factors 0.88 0.93
## Minimum correlation of possible factor scores 0.77 0.86Using prcomp()
PCA <- prcomp(ss, scale=TRUE)
plot(PCA$x[,1],PCA$x[,2])
pca.var=PCA$sdev^2
pca.var.per<-round(pca.var/sum(pca.var)*100,2)
barplot(pca.var.per,main="Scree plot",xlab="principal component",ylab="percentage variation")
barplot(pca.var.per,main="Scree plot",xlab="principal component",ylab="percentage variation")
loadingscores<-PCA$rotation[,1]