#Running Exploratory Factor Analysis in R Studio (3.5.3)
options(repos = c(CRAN = "https://cloud.r-project.org"))#Packages to install
install.packages("psych")
## Installing package into 'C:/Users/mnava/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'psych' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Users\mnava\AppData\Local\Temp\RtmpGmiAje\downloaded_packages
install.packages("GPArotation")
## Installing package into 'C:/Users/mnava/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'GPArotation' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Users\mnava\AppData\Local\Temp\RtmpGmiAje\downloaded_packages
library("psych")
## Warning: package 'psych' was built under R version 4.5.2
library("GPArotation")
## Warning: package 'GPArotation' was built under R version 4.5.2
##
## Attaching package: 'GPArotation'
## The following objects are masked from 'package:psych':
##
## equamax, varimin
#Getting the data into R
Data <- read.csv(file.choose(),header=T)
attach(Data)
names(Data)
## [1] "Obs" "Form.of.letter.of.application"
## [3] "Appearance" "Academic.ability"
## [5] "Likeability" "Self.confidence"
## [7] "Lucidity" "Honesty"
## [9] "Salesmanship" "Experience"
## [11] "Drive" "Ambition"
## [13] "Grasp" "Potential"
## [15] "Keeness.to.join" "Suitability"
options(scipen = 999)
#Overall Raw Score – determine top 3
Data$OverallRaw <- Form.of.letter.of.application + Appearance + Academic.ability +
Likeability + Self.confidence + Lucidity + Honesty + Salesmanship + Experience + Drive +
Ambition + Grasp + Potential + Keeness.to.join + Suitability
#Create data frame with variables
DataFrame <- Data[, c("Form.of.letter.of.application", "Appearance", "Academic.ability", "Likeability",
"Self.confidence", "Lucidity", "Honesty", "Salesmanship", "Experience", "Drive", "Ambition", "Grasp", "Potential",
"Keeness.to.join", "Suitability")]
#Scree Plot
ScreePlot <- scree(DataFrame, factors = TRUE, main = "Scree plot", hline = NULL, add = FALSE)
#Eigen Values Total Variance Explained
ev <- eigen(cor(DataFrame))
summary(ev)
## Length Class Mode
## values 15 -none- numeric
## vectors 225 -none- numeric
ev$values
## [1] 7.51379418 2.05630117 1.45581948 1.19789771 0.73915262 0.49457907
## [7] 0.35126183 0.30990202 0.25696154 0.18491037 0.15268036 0.09756308
## [13] 0.08881880 0.06463323 0.03572455
cumsum(ev$values)/15
## [1] 0.5009196 0.6380064 0.7350610 0.8149208 0.8641977 0.8971696 0.9205871
## [8] 0.9412472 0.9583780 0.9707053 0.9808840 0.9873882 0.9933095 0.9976184
## [15] 1.0000000
#Running the Orthogonal EFA
#Running Ortho FA
ORTHOFA <- factanal(DataFrame, factors = 4, rotation = "varimax", fm="pa")
print(ORTHOFA, digits=3, cutoff=.1, sort=TRUE)
##
## Call:
## factanal(x = DataFrame, factors = 4, rotation = "varimax", fm = "pa")
##
## Uniquenesses:
## Form.of.letter.of.application Appearance
## 0.443 0.685
## Academic.ability Likeability
## 0.521 0.185
## Self.confidence Lucidity
## 0.119 0.198
## Honesty Salesmanship
## 0.339 0.138
## Experience Drive
## 0.357 0.226
## Ambition Grasp
## 0.137 0.153
## Potential Keeness.to.join
## 0.090 0.005
## Suitability
## 0.252
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4
## Self.confidence 0.918 0.142
## Lucidity 0.838 0.111 0.291
## Salesmanship 0.885 0.258
## Drive 0.767 0.389 0.172
## Ambition 0.904 0.181
## Grasp 0.792 0.275 0.351 0.148
## Potential 0.735 0.349 0.432 0.247
## Form.of.letter.of.application 0.129 0.717 0.113 -0.117
## Experience 0.778 0.165
## Suitability 0.364 0.770 0.142
## Likeability 0.231 0.239 0.838
## Honesty 0.252 -0.216 0.742
## Academic.ability 0.126 0.677
## Keeness.to.join 0.424 0.389 0.554 -0.598
## Appearance 0.458 0.142 0.243 0.164
##
## Factor1 Factor2 Factor3 Factor4
## SS loadings 5.570 2.473 2.099 1.013
## Proportion Var 0.371 0.165 0.140 0.068
## Cumulative Var 0.371 0.536 0.676 0.744
##
## Test of the hypothesis that 4 factors are sufficient.
## The chi square statistic is 84 on 51 degrees of freedom.
## The p-value is 0.00247
#Create Ortho Factor Average Variables
Data$OrthoFA1 <- (Self.confidence + Appearance + Lucidity + Salesmanship + Drive + Ambition + Grasp + Potential )/8
Data$OrthoFA2 <- (Form.of.letter.of.application + Experience + Suitability)/3
Data$OrthoFA3 <- (Likeability + Honesty )/2
Data$OrthoFA4 <- (Academic.ability+ Keeness.to.join)/2
#Create Ortho Factor Data Frames (to be used for reliability analysis)
Ortho1_DataFrame <- Data[, c("Self.confidence", "Appearance", "Lucidity","Salesmanship","Drive","Ambition","Grasp","Potential")]
Ortho2_DataFrame <- Data[, c("Form.of.letter.of.application", "Experience", "Suitability")]
Ortho3_DataFrame <- Data[, c("Likeability", "Honesty")]
Ortho4_DataFrame <- Data[, c("Academic.ability","Keeness.to.join")]
#Factor Reliability Analysis – only need to interpret the “Raw Alpha” value
alpha(Ortho1_DataFrame)
## Number of categories should be increased in order to count frequencies.
##
## Reliability analysis
## Call: alpha(x = Ortho1_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.95 0.95 0.96 0.7 19 0.0095 6.1 2.5 0.76
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.93 0.95 0.97
## Duhachek 0.93 0.95 0.97
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Self.confidence 0.94 0.94 0.96 0.70 16 0.0109 0.0270 0.77
## Appearance 0.96 0.96 0.97 0.78 25 0.0086 0.0034 0.78
## Lucidity 0.94 0.94 0.95 0.69 16 0.0113 0.0239 0.75
## Salesmanship 0.94 0.94 0.95 0.68 15 0.0120 0.0266 0.72
## Drive 0.94 0.94 0.96 0.70 17 0.0107 0.0250 0.77
## Ambition 0.94 0.94 0.95 0.68 15 0.0117 0.0279 0.72
## Grasp 0.94 0.94 0.95 0.68 15 0.0116 0.0267 0.76
## Potential 0.94 0.94 0.95 0.69 15 0.0113 0.0282 0.76
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Self.confidence 48 0.87 0.87 0.86 0.83 6.9 2.4
## Appearance 48 0.58 0.61 0.54 0.51 7.1 2.0
## Lucidity 48 0.90 0.89 0.89 0.86 6.3 3.2
## Salesmanship 48 0.92 0.92 0.91 0.89 4.9 3.4
## Drive 48 0.86 0.85 0.83 0.81 5.3 2.9
## Ambition 48 0.92 0.92 0.92 0.89 6.0 2.9
## Grasp 48 0.92 0.91 0.91 0.89 6.2 3.0
## Potential 48 0.90 0.89 0.89 0.86 5.7 3.2
alpha(Ortho2_DataFrame)
## Number of categories should be increased in order to count frequencies.
##
## Reliability analysis
## Call: alpha(x = Ortho2_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.82 0.76 0.61 4.7 0.043 5.4 2.7 0.59
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.71 0.82 0.89
## Duhachek 0.74 0.82 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N
## Form.of.letter.of.application 0.82 0.82 0.69 0.69 4.5
## Experience 0.73 0.74 0.59 0.59 2.8
## Suitability 0.70 0.71 0.55 0.55 2.4
## alpha se var.r med.r
## Form.of.letter.of.application 0.052 NA 0.69
## Experience 0.076 NA 0.59
## Suitability 0.084 NA 0.55
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Form.of.letter.of.application 48 0.80 0.83 0.67 0.62 6.0 2.7
## Experience 48 0.88 0.87 0.78 0.70 4.2 3.3
## Suitability 48 0.89 0.88 0.81 0.73 6.0 3.3
alpha(Ortho3_DataFrame)
## Number of categories should be increased in order to count frequencies.
##
## Reliability analysis
## Call: alpha(x = Ortho3_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.78 0.78 0.65 0.65 3.6 0.062 7.1 2.4 0.65
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.61 0.78 0.88
## Duhachek 0.66 0.78 0.90
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Likeability 0.71 0.65 0.42 0.65 1.8 NA 0 0.65
## Honesty 0.58 0.65 0.42 0.65 1.8 NA 0 0.65
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Likeability 48 0.92 0.91 0.73 0.65 6.1 2.8
## Honesty 48 0.90 0.91 0.73 0.65 8.0 2.5
alpha(Ortho4_DataFrame)
## Warning in alpha(Ortho4_DataFrame): Some items were negatively correlated with the first principal component and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option
## Some items ( Academic.ability ) were negatively correlated with the first principal component and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option
## Warning in sqrt(Vtc): NaNs produced
##
## Reliability analysis
## Call: alpha(x = Ortho4_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## -0.9 -0.96 -0.32 -0.32 -0.49 0.52 6.3 1.4 -0.32
##
## 95% confidence boundaries
## lower alpha upper
## Feldt -2.39 -0.9 -0.06
## Duhachek -1.93 -0.9 0.13
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## Academic.ability -0.24 -0.32 0.1 -0.32 -0.24 NA 0
## Keeness.to.join -0.43 -0.32 0.1 -0.32 -0.24 NA 0
## med.r
## Academic.ability -0.32
## Keeness.to.join -0.32
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Academic.ability 48 0.41 0.58 NaN -0.32 7.1 2.0
## Keeness.to.join 48 0.73 0.58 NaN -0.32 5.6 2.7
##
## Non missing response frequency for each item
## 0 2 3 4 5 6 7 8 9 10 miss
## Academic.ability 0.00 0.02 0.02 0.06 0.12 0.10 0.23 0.21 0.08 0.15 0
## Keeness.to.join 0.08 0.02 0.08 0.08 0.25 0.15 0.08 0.12 0.02 0.10 0
#Ortho Overall Score
Data$Ortho_Overall <- Data$OrthoFA1 + Data$OrthoFA2 + Data$OrthoFA3 + Data$OrthoFA4
OBLIQFA <- factanal(DataFrame, factors = 4, rotation = "oblimin", fm="pa")
print(OBLIQFA, digits=3, cutoff=.1, sort=TRUE)
##
## Call:
## factanal(x = DataFrame, factors = 4, rotation = "oblimin", fm = "pa")
##
## Uniquenesses:
## Form.of.letter.of.application Appearance
## 0.443 0.685
## Academic.ability Likeability
## 0.521 0.185
## Self.confidence Lucidity
## 0.119 0.198
## Honesty Salesmanship
## 0.339 0.138
## Experience Drive
## 0.357 0.226
## Ambition Grasp
## 0.137 0.153
## Potential Keeness.to.join
## 0.090 0.005
## Suitability
## 0.252
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4
## Self.confidence 1.004 -0.260
## Lucidity 0.824 0.161
## Salesmanship 0.907 0.127
## Drive 0.725 0.272
## Ambition 0.944
## Grasp 0.718 0.158 0.250 0.129
## Potential 0.614 0.248 0.369 0.215
## Form.of.letter.of.application 0.704 -0.210
## Experience 0.824
## Suitability 0.231 0.764
## Likeability 0.129 0.870
## Honesty -0.336 0.774
## Academic.ability 0.203 0.104 0.668
## Keeness.to.join 0.226 0.218 0.412 -0.654
## Appearance 0.406 0.204 0.155
##
## Factor1 Factor2 Factor3 Factor4
## SS loadings 5.107 2.23 1.83 1.046
##
## Factor Correlations:
## Factor1 Factor2 Factor3 Factor4
## Factor1 1.000 0.3385 0.469 -0.1241
## Factor2 0.338 1.0000 0.213 -0.0384
## Factor3 0.469 0.2135 1.000 -0.1710
## Factor4 -0.124 -0.0384 -0.171 1.0000
##
## Test of the hypothesis that 4 factors are sufficient.
## The chi square statistic is 84 on 51 degrees of freedom.
## The p-value is 0.00247
#Create Oblique Factor Average Variables –
Data$ObliqFA1 <- (Self.confidence + Lucidity + Salesmanship + Drive + Ambition + Grasp + Potential + Appearance)/8
Data$ObliqFA2 <- (Form.of.letter.of.application + Experience + Suitability)/3
Data$ObliqFA3 <- (Likeability + Honesty)/2
Data$ObliqFA4 <- (Academic.ability + Keeness.to.join)/2
#Create Ortho Factor Data Frames (to be used for reliability analysis)
Obliq1_DataFrame <- Data[, c("Self.confidence", "Lucidity", "Salesmanship" ,"Drive" ,"Ambition", "Grasp","Potential","Appearance")]
Obliq2_DataFrame <- Data[, c("Form.of.letter.of.application", "Experience", "Suitability")]
Obliq3_DataFrame <- Data[, c("Likeability", "Honesty")]
Obliq4_DataFrame <- Data[, c("Academic.ability", "Keeness.to.join")]
#Factor Reliability Analysis – only need to interpret the “Raw Alpha” value
alpha(Obliq1_DataFrame)
## Number of categories should be increased in order to count frequencies.
##
## Reliability analysis
## Call: alpha(x = Obliq1_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.95 0.95 0.96 0.7 19 0.0095 6.1 2.5 0.76
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.93 0.95 0.97
## Duhachek 0.93 0.95 0.97
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Self.confidence 0.94 0.94 0.96 0.70 16 0.0109 0.0270 0.77
## Lucidity 0.94 0.94 0.95 0.69 16 0.0113 0.0239 0.75
## Salesmanship 0.94 0.94 0.95 0.68 15 0.0120 0.0266 0.72
## Drive 0.94 0.94 0.96 0.70 17 0.0107 0.0250 0.77
## Ambition 0.94 0.94 0.95 0.68 15 0.0117 0.0279 0.72
## Grasp 0.94 0.94 0.95 0.68 15 0.0116 0.0267 0.76
## Potential 0.94 0.94 0.95 0.69 15 0.0113 0.0282 0.76
## Appearance 0.96 0.96 0.97 0.78 25 0.0086 0.0034 0.78
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Self.confidence 48 0.87 0.87 0.86 0.83 6.9 2.4
## Lucidity 48 0.90 0.89 0.89 0.86 6.3 3.2
## Salesmanship 48 0.92 0.92 0.91 0.89 4.9 3.4
## Drive 48 0.86 0.85 0.83 0.81 5.3 2.9
## Ambition 48 0.92 0.92 0.92 0.89 6.0 2.9
## Grasp 48 0.92 0.91 0.91 0.89 6.2 3.0
## Potential 48 0.90 0.89 0.89 0.86 5.7 3.2
## Appearance 48 0.58 0.61 0.54 0.51 7.1 2.0
alpha(Obliq2_DataFrame)
## Number of categories should be increased in order to count frequencies.
##
## Reliability analysis
## Call: alpha(x = Obliq2_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.82 0.76 0.61 4.7 0.043 5.4 2.7 0.59
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.71 0.82 0.89
## Duhachek 0.74 0.82 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N
## Form.of.letter.of.application 0.82 0.82 0.69 0.69 4.5
## Experience 0.73 0.74 0.59 0.59 2.8
## Suitability 0.70 0.71 0.55 0.55 2.4
## alpha se var.r med.r
## Form.of.letter.of.application 0.052 NA 0.69
## Experience 0.076 NA 0.59
## Suitability 0.084 NA 0.55
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Form.of.letter.of.application 48 0.80 0.83 0.67 0.62 6.0 2.7
## Experience 48 0.88 0.87 0.78 0.70 4.2 3.3
## Suitability 48 0.89 0.88 0.81 0.73 6.0 3.3
alpha(Obliq3_DataFrame)
## Number of categories should be increased in order to count frequencies.
##
## Reliability analysis
## Call: alpha(x = Obliq3_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.78 0.78 0.65 0.65 3.6 0.062 7.1 2.4 0.65
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.61 0.78 0.88
## Duhachek 0.66 0.78 0.90
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Likeability 0.71 0.65 0.42 0.65 1.8 NA 0 0.65
## Honesty 0.58 0.65 0.42 0.65 1.8 NA 0 0.65
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Likeability 48 0.92 0.91 0.73 0.65 6.1 2.8
## Honesty 48 0.90 0.91 0.73 0.65 8.0 2.5
alpha(Obliq4_DataFrame)
## Warning in alpha(Obliq4_DataFrame): Some items were negatively correlated with the first principal component and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option
## Some items ( Academic.ability ) were negatively correlated with the first principal component and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option
## Warning in sqrt(Vtc): NaNs produced
##
## Reliability analysis
## Call: alpha(x = Obliq4_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## -0.9 -0.96 -0.32 -0.32 -0.49 0.52 6.3 1.4 -0.32
##
## 95% confidence boundaries
## lower alpha upper
## Feldt -2.39 -0.9 -0.06
## Duhachek -1.93 -0.9 0.13
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## Academic.ability -0.24 -0.32 0.1 -0.32 -0.24 NA 0
## Keeness.to.join -0.43 -0.32 0.1 -0.32 -0.24 NA 0
## med.r
## Academic.ability -0.32
## Keeness.to.join -0.32
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Academic.ability 48 0.41 0.58 NaN -0.32 7.1 2.0
## Keeness.to.join 48 0.73 0.58 NaN -0.32 5.6 2.7
##
## Non missing response frequency for each item
## 0 2 3 4 5 6 7 8 9 10 miss
## Academic.ability 0.00 0.02 0.02 0.06 0.12 0.10 0.23 0.21 0.08 0.15 0
## Keeness.to.join 0.08 0.02 0.08 0.08 0.25 0.15 0.08 0.12 0.02 0.10 0
#Oblique Overall Score
Data$Obliq_Overall_Score <- Data$ObliqFA1 + Data$ObliqFA2 + Data$ObliqFA3 + Data$ObliqFA4