Exploratory Factor Analysis - EFA
Mikhilesh Dehane
7/25/2020
Exploratory Factor Analysis - EFA
library(readxl)## Warning: package 'readxl' was built under R version 3.6.3setwd("E:\\mikhilesh\\HU Sem VI ANLY 510 and 506\\ANLY 510 Kao Principals and Applications\\Lecture and other materials")
data <- read_xlsx("lecture 14 EFAexample.xlsx")
summary(data)## Q1 Q2 Q3 Q4 Q5
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.00
## Median :2.000 Median :2.000 Median :3.000 Median :3.000 Median :3.00
## Mean :2.164 Mean :2.359 Mean :2.728 Mean :2.719 Mean :2.87
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.00
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.00
## Q6 Q7 Q8 Q9 Q10
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:1.00
## Median :3.000 Median :3.000 Median :2.000 Median :3.000 Median :2.00
## Mean :2.958 Mean :2.562 Mean :2.283 Mean :2.578 Mean :2.01
## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.00
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.00
## Q11 Q12 Q13 Q14
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
## Median :2.000 Median :2.000 Median :2.000 Median :3.000
## Mean :2.229 Mean :2.466 Mean :2.328 Mean :2.612
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Q15 Q16
## Min. :1.000 Min. :1.00
## 1st Qu.:2.000 1st Qu.:2.00
## Median :2.000 Median :3.00
## Mean :2.324 Mean :2.93
## 3rd Qu.:3.000 3rd Qu.:3.00
## Max. :4.000 Max. :4.00apply(data, 2, shapiro.test)## $Q1
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.86276, p-value < 2.2e-16
##
##
## $Q2
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.87124, p-value < 2.2e-16
##
##
## $Q3
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.85818, p-value < 2.2e-16
##
##
## $Q4
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.87094, p-value < 2.2e-16
##
##
## $Q5
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.84137, p-value < 2.2e-16
##
##
## $Q6
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.84949, p-value < 2.2e-16
##
##
## $Q7
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.87347, p-value < 2.2e-16
##
##
## $Q8
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.85409, p-value < 2.2e-16
##
##
## $Q9
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.874, p-value < 2.2e-16
##
##
## $Q10
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.83384, p-value < 2.2e-16
##
##
## $Q11
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.85747, p-value < 2.2e-16
##
##
## $Q12
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.85988, p-value < 2.2e-16
##
##
## $Q13
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.87578, p-value < 2.2e-16
##
##
## $Q14
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.86893, p-value < 2.2e-16
##
##
## $Q15
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.84613, p-value < 2.2e-16
##
##
## $Q16
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.84426, p-value < 2.2e-16#REVERSE CODE data when you have -ve correlation
#Checking R-Matrix to know if the variables are highly corelated with each others or have similarities
corMat <- cor(data)
corMat## Q1 Q2 Q3 Q4 Q5 Q6
## Q1 1.0000000 0.5409363 -0.3656214 -0.2774137 -0.4046785 -0.6021803
## Q2 0.5409363 1.0000000 -0.3848507 -0.3815433 -0.4328253 -0.4540008
## Q3 -0.3656214 -0.3848507 1.0000000 0.4691103 0.5605341 0.4451519
## Q4 -0.2774137 -0.3815433 0.4691103 1.0000000 0.4424801 0.4154419
## Q5 -0.4046785 -0.4328253 0.5605341 0.4424801 1.0000000 0.5332802
## Q6 -0.6021803 -0.4540008 0.4451519 0.4154419 0.5332802 1.0000000
## Q7 -0.4251323 -0.4110314 0.3014960 0.3427030 0.3769419 0.4617225
## Q8 0.3544211 0.3485103 -0.4425779 -0.2177116 -0.4989637 -0.3698887
## Q9 -0.4152407 -0.3698851 0.2567018 0.2555184 0.3411775 0.4767936
## Q10 0.2890325 0.4579999 -0.3233705 -0.2385475 -0.3895095 -0.3331047
## Q11 0.6076953 0.4818159 -0.4047212 -0.3634059 -0.4188613 -0.5973084
## Q12 0.3687996 0.5385576 -0.2808081 -0.3658643 -0.3584818 -0.4154319
## Q13 0.2460532 0.2117046 -0.2760835 -0.1009017 -0.2964166 -0.1672920
## Q14 -0.5043518 -0.3803194 0.3300813 0.2530192 0.3928885 0.5364183
## Q15 0.4355843 0.5499629 -0.4248865 -0.3238739 -0.5186160 -0.4356544
## Q16 -0.6538815 -0.4763842 0.4484483 0.4147263 0.5045460 0.7084155
## Q7 Q8 Q9 Q10 Q11 Q12
## Q1 -0.4251323 0.3544211 -0.4152407 0.2890325 0.6076953 0.3687996
## Q2 -0.4110314 0.3485103 -0.3698851 0.4579999 0.4818159 0.5385576
## Q3 0.3014960 -0.4425779 0.2567018 -0.3233705 -0.4047212 -0.2808081
## Q4 0.3427030 -0.2177116 0.2555184 -0.2385475 -0.3634059 -0.3658643
## Q5 0.3769419 -0.4989637 0.3411775 -0.3895095 -0.4188613 -0.3584818
## Q6 0.4617225 -0.3698887 0.4767936 -0.3331047 -0.5973084 -0.4154319
## Q7 1.0000000 -0.3342145 0.3052033 -0.2992893 -0.4582815 -0.4691233
## Q8 -0.3342145 1.0000000 -0.2290853 0.3663103 0.3841354 0.3308320
## Q9 0.3052033 -0.2290853 1.0000000 -0.1738292 -0.4169176 -0.3056779
## Q10 -0.2992893 0.3663103 -0.1738292 1.0000000 0.4026391 0.4105560
## Q11 -0.4582815 0.3841354 -0.4169176 0.4026391 1.0000000 0.4715192
## Q12 -0.4691233 0.3308320 -0.3056779 0.4105560 0.4715192 1.0000000
## Q13 -0.2127298 0.2975758 -0.1063857 0.2094700 0.2256271 0.2124407
## Q14 0.3549708 -0.2713426 0.6617897 -0.2329149 -0.4924756 -0.3145705
## Q15 -0.3715010 0.4614843 -0.3169341 0.4136292 0.4931320 0.4692704
## Q16 0.4805563 -0.3869749 0.4523550 -0.3691348 -0.6490574 -0.4246754
## Q13 Q14 Q15 Q16
## Q1 0.2460532 -0.5043518 0.4355843 -0.6538815
## Q2 0.2117046 -0.3803194 0.5499629 -0.4763842
## Q3 -0.2760835 0.3300813 -0.4248865 0.4484483
## Q4 -0.1009017 0.2530192 -0.3238739 0.4147263
## Q5 -0.2964166 0.3928885 -0.5186160 0.5045460
## Q6 -0.1672920 0.5364183 -0.4356544 0.7084155
## Q7 -0.2127298 0.3549708 -0.3715010 0.4805563
## Q8 0.2975758 -0.2713426 0.4614843 -0.3869749
## Q9 -0.1063857 0.6617897 -0.3169341 0.4523550
## Q10 0.2094700 -0.2329149 0.4136292 -0.3691348
## Q11 0.2256271 -0.4924756 0.4931320 -0.6490574
## Q12 0.2124407 -0.3145705 0.4692704 -0.4246754
## Q13 1.0000000 -0.1777712 0.3218061 -0.2099937
## Q14 -0.1777712 1.0000000 -0.4147098 0.5599550
## Q15 0.3218061 -0.4147098 1.0000000 -0.4692582
## Q16 -0.2099937 0.5599550 -0.4692582 1.0000000#Looking at the correlation table, we can identify some good/strong ideas about the variables. #So now we can move to next step. And We will use KMO Test to verify if the data is good to go.
#The statistic is a measure of the proportion of variance among variables that might be common variance. General speaking over 0.5 is good.
library(psych)## Warning: package 'psych' was built under R version 3.6.3KMO(corMat)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = corMat)
## Overall MSA = 0.93
## MSA for each item =
## Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16
## 0.92 0.92 0.92 0.90 0.93 0.94 0.96 0.93 0.87 0.93 0.95 0.93 0.91 0.89 0.94 0.94# When we want to decide how many factors do we need in this study, The best way to do is to use the eigenvalue and the scree plot.
library(nFactors)## Warning: package 'nFactors' was built under R version 3.6.3## Loading required package: lattice##
## Attaching package: 'nFactors'## The following object is masked from 'package:lattice':
##
## parallel#Scree of eigen values
scree <- scree(data)
scree## Scree of eigen values
## Call: NULL
## Eigen values of factors [1] 6.42 0.71 0.37 0.25 0.18 0.05 0.00 -0.03 -0.09 -0.10 -0.14 -0.17
## [13] -0.18 -0.24 -0.28 -0.34
## Eigen values of Principal Components [1] 6.98 1.34 0.99 0.97 0.76 0.73 0.65 0.58 0.48 0.47 0.44 0.41 0.34 0.32 0.28
## [16] 0.27#We usually select the factors =or> 1EFA <- fa(r = corMat, fm = "pa")
EFA## Factor Analysis using method = pa
## Call: fa(r = corMat, fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 h2 u2 com
## Q1 -0.71 0.50 0.50 1
## Q2 -0.69 0.47 0.53 1
## Q3 0.60 0.36 0.64 1
## Q4 0.52 0.27 0.73 1
## Q5 0.69 0.47 0.53 1
## Q6 0.76 0.58 0.42 1
## Q7 0.60 0.36 0.64 1
## Q8 -0.55 0.31 0.69 1
## Q9 0.55 0.30 0.70 1
## Q10 -0.52 0.27 0.73 1
## Q11 -0.75 0.56 0.44 1
## Q12 -0.61 0.37 0.63 1
## Q13 -0.34 0.11 0.89 1
## Q14 0.63 0.40 0.60 1
## Q15 -0.68 0.46 0.54 1
## Q16 0.79 0.63 0.37 1
##
## PA1
## SS loadings 6.42
## Proportion Var 0.40
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 120 and the objective function was 7.39
## The degrees of freedom for the model are 104 and the objective function was 1.35
##
## The root mean square of the residuals (RMSR) is 0.07
## The df corrected root mean square of the residuals is 0.07
##
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.96
## Multiple R square of scores with factors 0.92
## Minimum correlation of possible factor scores 0.85#OR - we can use data or R-matrix for factor analysis
EFA <- fa(data, fm = "pa")
EFA## Factor Analysis using method = pa
## Call: fa(r = data, fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 h2 u2 com
## Q1 -0.71 0.50 0.50 1
## Q2 -0.69 0.47 0.53 1
## Q3 0.60 0.36 0.64 1
## Q4 0.52 0.27 0.73 1
## Q5 0.69 0.47 0.53 1
## Q6 0.76 0.58 0.42 1
## Q7 0.60 0.36 0.64 1
## Q8 -0.55 0.31 0.69 1
## Q9 0.55 0.30 0.70 1
## Q10 -0.52 0.27 0.73 1
## Q11 -0.75 0.56 0.44 1
## Q12 -0.61 0.37 0.63 1
## Q13 -0.34 0.11 0.89 1
## Q14 0.63 0.40 0.60 1
## Q15 -0.68 0.46 0.54 1
## Q16 0.79 0.63 0.37 1
##
## PA1
## SS loadings 6.42
## Proportion Var 0.40
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 120 and the objective function was 7.39 with Chi Square of 5860.21
## The degrees of freedom for the model are 104 and the objective function was 1.35
##
## The root mean square of the residuals (RMSR) is 0.07
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 800 with the empirical chi square 872 with prob < 1.3e-121
## The total number of observations was 800 with Likelihood Chi Square = 1066.11 with prob < 2.6e-159
##
## Tucker Lewis Index of factoring reliability = 0.806
## RMSEA index = 0.108 and the 90 % confidence intervals are 0.102 0.114
## BIC = 370.91
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.96
## Multiple R square of scores with factors 0.92
## Minimum correlation of possible factor scores 0.85#perform the rotation (varimax and oblimin) to improve the factor loadings
EFA2 <- fa(r = corMat, nfactors = 2, rotate = "varimax", fm = "pa") #using 2 factor
EFA2## Factor Analysis using method = pa
## Call: fa(r = corMat, nfactors = 2, rotate = "varimax", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## Q1 0.38 -0.63 0.54 0.46 1.7
## Q2 0.57 -0.40 0.48 0.52 1.8
## Q3 -0.58 0.26 0.41 0.59 1.4
## Q4 -0.44 0.29 0.28 0.72 1.7
## Q5 -0.64 0.32 0.52 0.48 1.5
## Q6 -0.41 0.67 0.62 0.38 1.7
## Q7 -0.44 0.40 0.35 0.65 2.0
## Q8 0.59 -0.19 0.39 0.61 1.2
## Q9 -0.13 0.67 0.47 0.53 1.1
## Q10 0.56 -0.17 0.34 0.66 1.2
## Q11 0.47 -0.59 0.57 0.43 1.9
## Q12 0.53 -0.33 0.38 0.62 1.7
## Q13 0.39 -0.08 0.16 0.84 1.1
## Q14 -0.19 0.74 0.59 0.41 1.1
## Q15 0.64 -0.32 0.51 0.49 1.5
## Q16 -0.44 0.69 0.67 0.33 1.7
##
## PA1 PA2
## SS loadings 3.75 3.52
## Proportion Var 0.23 0.22
## Cumulative Var 0.23 0.45
## Proportion Explained 0.52 0.48
## Cumulative Proportion 0.52 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 120 and the objective function was 7.39
## The degrees of freedom for the model are 89 and the objective function was 0.84
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.05
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.87 0.89
## Multiple R square of scores with factors 0.76 0.78
## Minimum correlation of possible factor scores 0.52 0.57EFA3 <- fa(r = corMat, nfactors = 3, rotate = "oblimin", fm = "pa") #using 3 factor and oblimin - oblique rotation## Loading required namespace: GPArotationEFA3## Factor Analysis using method = pa
## Call: fa(r = corMat, nfactors = 3, rotate = "oblimin", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 h2 u2 com
## Q1 -0.55 0.25 -0.02 0.54 0.46 1.4
## Q2 -0.13 0.62 -0.05 0.55 0.45 1.1
## Q3 0.03 0.07 0.77 0.56 0.44 1.0
## Q4 0.13 -0.13 0.35 0.28 0.72 1.5
## Q5 0.08 -0.01 0.74 0.63 0.37 1.0
## Q6 0.61 -0.07 0.20 0.63 0.37 1.2
## Q7 0.24 -0.39 0.06 0.37 0.63 1.7
## Q8 0.06 0.21 -0.51 0.39 0.61 1.4
## Q9 0.75 0.05 -0.06 0.47 0.53 1.0
## Q10 0.11 0.52 -0.21 0.36 0.64 1.4
## Q11 -0.45 0.36 -0.05 0.58 0.42 1.9
## Q12 -0.04 0.74 0.06 0.53 0.47 1.0
## Q13 0.09 0.17 -0.32 0.16 0.84 1.7
## Q14 0.82 0.07 0.00 0.60 0.40 1.0
## Q15 -0.05 0.44 -0.32 0.51 0.49 1.9
## Q16 0.61 -0.15 0.16 0.67 0.33 1.3
##
## PA1 PA2 PA3
## SS loadings 3.06 2.46 2.32
## Proportion Var 0.19 0.15 0.15
## Cumulative Var 0.19 0.35 0.49
## Proportion Explained 0.39 0.31 0.30
## Cumulative Proportion 0.39 0.70 1.00
##
## With factor correlations of
## PA1 PA2 PA3
## PA1 1.00 -0.60 0.59
## PA2 -0.60 1.00 -0.62
## PA3 0.59 -0.62 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 120 and the objective function was 7.39
## The degrees of freedom for the model are 75 and the objective function was 0.59
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.05
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2 PA3
## Correlation of (regression) scores with factors 0.94 0.91 0.91
## Multiple R square of scores with factors 0.87 0.82 0.83
## Minimum correlation of possible factor scores 0.75 0.64 0.67print(EFA3, cut = 0.4, digits = 2)## Factor Analysis using method = pa
## Call: fa(r = corMat, nfactors = 3, rotate = "oblimin", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 h2 u2 com
## Q1 -0.55 0.54 0.46 1.4
## Q2 0.62 0.55 0.45 1.1
## Q3 0.77 0.56 0.44 1.0
## Q4 0.28 0.72 1.5
## Q5 0.74 0.63 0.37 1.0
## Q6 0.61 0.63 0.37 1.2
## Q7 0.37 0.63 1.7
## Q8 -0.51 0.39 0.61 1.4
## Q9 0.75 0.47 0.53 1.0
## Q10 0.52 0.36 0.64 1.4
## Q11 -0.45 0.58 0.42 1.9
## Q12 0.74 0.53 0.47 1.0
## Q13 0.16 0.84 1.7
## Q14 0.82 0.60 0.40 1.0
## Q15 0.44 0.51 0.49 1.9
## Q16 0.61 0.67 0.33 1.3
##
## PA1 PA2 PA3
## SS loadings 3.06 2.46 2.32
## Proportion Var 0.19 0.15 0.15
## Cumulative Var 0.19 0.35 0.49
## Proportion Explained 0.39 0.31 0.30
## Cumulative Proportion 0.39 0.70 1.00
##
## With factor correlations of
## PA1 PA2 PA3
## PA1 1.00 -0.60 0.59
## PA2 -0.60 1.00 -0.62
## PA3 0.59 -0.62 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 120 and the objective function was 7.39
## The degrees of freedom for the model are 75 and the objective function was 0.59
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.05
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2 PA3
## Correlation of (regression) scores with factors 0.94 0.91 0.91
## Multiple R square of scores with factors 0.87 0.82 0.83
## Minimum correlation of possible factor scores 0.75 0.64 0.67library(GPArotation)
EFA4 <- fa(data, nfactors = 2, rotate = "varimax", fm = "pa", scores = TRUE)
EFA4## Factor Analysis using method = pa
## Call: fa(r = data, nfactors = 2, rotate = "varimax", scores = TRUE,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## Q1 0.38 -0.63 0.54 0.46 1.7
## Q2 0.57 -0.40 0.48 0.52 1.8
## Q3 -0.58 0.26 0.41 0.59 1.4
## Q4 -0.44 0.29 0.28 0.72 1.7
## Q5 -0.64 0.32 0.52 0.48 1.5
## Q6 -0.41 0.67 0.62 0.38 1.7
## Q7 -0.44 0.40 0.35 0.65 2.0
## Q8 0.59 -0.19 0.39 0.61 1.2
## Q9 -0.13 0.67 0.47 0.53 1.1
## Q10 0.56 -0.17 0.34 0.66 1.2
## Q11 0.47 -0.59 0.57 0.43 1.9
## Q12 0.53 -0.33 0.38 0.62 1.7
## Q13 0.39 -0.08 0.16 0.84 1.1
## Q14 -0.19 0.74 0.59 0.41 1.1
## Q15 0.64 -0.32 0.51 0.49 1.5
## Q16 -0.44 0.69 0.67 0.33 1.7
##
## PA1 PA2
## SS loadings 3.75 3.52
## Proportion Var 0.23 0.22
## Cumulative Var 0.23 0.45
## Proportion Explained 0.52 0.48
## Cumulative Proportion 0.52 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 120 and the objective function was 7.39 with Chi Square of 5860.21
## The degrees of freedom for the model are 89 and the objective function was 0.84
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 800 with the empirical chi square 417.24 with prob < 6.1e-44
## The total number of observations was 800 with Likelihood Chi Square = 667.72 with prob < 1.7e-89
##
## Tucker Lewis Index of factoring reliability = 0.864
## RMSEA index = 0.09 and the 90 % confidence intervals are 0.084 0.097
## BIC = 72.79
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1 PA2
## Correlation of (regression) scores with factors 0.87 0.89
## Multiple R square of scores with factors 0.76 0.78
## Minimum correlation of possible factor scores 0.52 0.57head(EFA4$scores, 10)## PA1 PA2
## [1,] 1.2710614 -1.1323495
## [2,] -0.6012196 0.4323597
## [3,] 2.4938431 -1.7911749
## [4,] 1.6146596 -2.0485713
## [5,] -0.7770873 1.6301372
## [6,] 0.8029936 0.2256166
## [7,] -0.6243222 -0.7722059
## [8,] 0.8823098 -0.6847066
## [9,] 1.4684812 -0.9006286
## [10,] 1.2094306 -1.1024223data <- cbind(data, EFA4$scores)
data## Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 PA1
## 1 2 4 2 2 2 2 1 3 1 4 3 3 4 1 3 2 1.2710613779
## 2 1 1 3 3 3 3 1 2 3 1 1 2 2 3 2 3 -0.6012195833
## 3 4 4 1 1 1 1 1 4 1 4 4 4 4 1 4 1 2.4938430809
## 4 4 4 4 4 1 1 1 4 1 4 4 4 4 1 4 1 1.6146596052
## 5 1 1 4 4 4 4 4 3 4 1 1 3 3 4 1 4 -0.7770873329
## 6 2 2 3 2 2 3 1 2 3 3 2 3 4 2 3 3 0.8029935665
## 7 3 2 3 3 3 2 2 2 3 2 1 2 2 2 2 2 -0.6243222136
## 8 2 3 2 1 2 2 1 2 1 3 3 3 3 2 3 3 0.8823098164
## 9 3 3 1 2 2 2 1 3 1 3 3 4 4 2 3 2 1.4684811896
## 10 4 4 2 3 2 2 2 3 2 3 4 3 3 2 3 2 1.2094306250
## 11 2 1 3 2 2 2 1 3 4 1 2 3 4 3 2 3 0.5108977328
## 12 4 4 2 2 2 1 1 3 1 2 4 4 4 1 4 1 1.2697269547
## 13 2 2 3 3 2 3 1 3 2 2 2 2 2 2 3 3 0.2466260188
## 14 4 3 1 1 3 2 1 3 2 3 3 3 4 2 4 2 1.5016168883
## 15 1 2 2 1 4 4 1 3 4 2 4 4 4 3 1 4 0.6746233487
## 16 3 3 1 1 1 2 1 1 1 4 4 4 4 1 4 1 1.7070411414
## 17 4 3 2 2 2 2 2 4 1 3 2 3 2 1 4 2 1.0332243026
## 18 4 3 2 2 2 3 2 3 3 2 3 3 3 2 4 2 1.3310118897
## 19 3 3 2 2 2 2 1 3 2 3 3 3 3 2 3 2 1.1480684737
## 20 1 1 3 4 3 4 1 3 2 1 2 3 3 3 2 3 -0.2458018050
## 21 3 3 2 2 2 2 2 3 3 3 3 3 4 2 3 2 1.3354806167
## 22 2 3 2 2 4 2 2 3 3 2 3 3 4 3 3 3 0.7920002447
## 23 3 3 3 3 3 3 2 2 2 1 3 3 3 2 3 3 -0.0925297124
## 24 2 3 3 3 2 3 2 2 2 2 2 3 2 3 2 3 0.2048706358
## 25 3 3 2 2 2 2 1 2 2 1 4 4 3 2 3 2 0.7350454167
## 26 2 2 4 3 3 3 2 2 3 1 2 2 1 3 1 3 -1.0720355424
## 27 3 4 2 2 2 2 2 3 2 3 3 3 4 2 3 2 1.3495334297
## 28 2 2 4 4 3 2 1 2 3 1 2 3 3 3 3 4 -0.1730797380
## 29 4 3 2 2 2 2 1 3 1 3 3 2 3 1 4 2 0.8823775100
## 30 3 3 2 2 3 2 2 3 3 2 3 3 3 2 3 2 0.7320068747
## 31 3 3 3 2 2 3 2 3 2 3 3 3 3 2 3 2 0.9004123477
## 32 4 4 2 3 2 2 2 3 2 3 3 3 2 2 2 2 0.7574903526
## 33 2 3 2 2 2 2 2 3 1 1 2 2 4 2 3 2 0.4390288652
## 34 4 4 1 1 2 2 1 3 4 4 3 3 4 3 4 2 2.6958271385
## 35 3 3 2 3 2 2 3 3 3 3 3 3 3 2 3 2 1.0928703898
## 36 3 3 3 2 3 2 2 2 2 2 3 2 3 2 2 3 -0.2950188580
## 37 4 3 3 3 2 2 3 3 2 2 3 3 3 2 3 2 0.4942839306
## 38 2 2 4 3 3 4 1 2 1 2 2 3 1 2 2 3 -0.8519319388
## 39 3 3 2 2 2 2 2 3 2 3 3 3 2 2 3 2 0.9803451667
## 40 2 2 2 2 3 3 1 2 3 2 2 4 2 3 2 3 0.4025138782
## 41 3 3 2 2 2 2 2 3 2 2 3 3 2 2 3 3 0.7925390889
## 42 1 1 3 2 3 3 1 2 4 2 3 4 4 2 3 2 0.5173614574
## 43 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 3 -0.5637019796
## 44 3 3 2 2 3 2 2 2 2 3 3 2 2 2 2 2 0.0096966250
## 45 2 2 3 3 3 3 2 2 2 2 2 3 3 2 3 3 -0.0944313518
## 46 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 3 0.8628633961
## 47 2 2 3 4 3 3 1 2 2 1 2 3 2 2 2 4 -0.6795566675
## 48 2 2 2 2 2 2 1 2 2 1 2 2 1 2 2 3 -0.3150262595
## 49 3 3 2 2 2 3 2 3 2 2 3 3 3 2 3 3 0.9307805086
## 50 3 2 3 3 4 2 1 2 3 1 2 3 2 2 2 3 -0.8304439137
## 51 1 1 4 4 4 4 2 2 2 2 3 3 3 2 3 4 -0.7155276827
## 52 3 2 2 3 2 3 1 4 2 4 2 2 2 2 3 2 1.0544518623
## 53 1 2 3 3 3 3 3 3 3 2 2 2 3 3 3 3 0.3133083973
## 54 3 3 2 3 2 2 2 3 2 2 3 3 4 2 3 2 0.9071820086
## 55 3 3 4 2 2 2 1 2 2 1 2 4 3 2 3 2 0.1725979775
## 56 2 2 2 2 3 3 1 3 4 1 2 2 2 4 2 3 0.4953262367
## 57 1 2 3 2 3 4 1 2 3 2 2 3 2 4 2 3 0.3148685113
## 58 3 3 3 2 2 3 2 2 3 2 3 3 3 3 3 3 0.8573030787
## 59 3 3 2 3 3 2 2 2 2 2 3 4 2 3 3 2 0.5489197909
## 60 1 4 2 1 4 2 1 1 3 1 2 4 2 1 2 2 -0.3827693135
## 61 3 2 2 2 2 2 1 3 2 1 3 3 3 2 3 2 0.5797980672
## 62 3 3 3 3 3 3 4 2 3 2 3 3 2 2 3 3 0.0267001952
## 63 3 3 3 3 3 1 1 1 4 1 3 3 2 2 4 2 0.1505082976
## 64 2 2 2 2 3 3 2 2 3 2 2 3 3 3 3 3 0.5713667697
## 65 4 4 3 3 3 2 1 3 1 2 3 3 2 1 3 1 0.0054548466
## 66 3 3 2 2 3 2 2 2 3 2 4 4 4 4 3 2 1.2621228216
## 67 4 4 1 1 1 1 1 4 1 4 4 4 4 1 4 1 2.4938430809
## 68 2 2 3 3 3 3 3 3 3 1 1 2 1 3 1 3 -0.7553291041
## 69 1 1 4 3 3 4 1 2 3 1 2 2 1 3 3 3 -0.5330066305
## 70 3 3 3 4 3 2 2 2 2 2 3 4 2 2 3 2 0.0357274524
## 71 1 2 2 2 2 2 3 2 3 3 2 2 3 3 3 3 0.8435617242
## 72 2 2 3 3 3 3 2 2 3 2 2 2 3 3 2 3 -0.1628997734
## 73 4 4 2 2 1 2 2 2 3 2 4 3 3 2 3 2 1.3094802717
## 74 3 4 1 1 2 2 1 3 2 2 4 3 3 2 3 2 1.4700318039
## 75 3 3 2 3 2 2 2 3 1 3 4 4 2 2 3 2 0.9694813714
## 76 3 3 2 3 2 2 2 3 2 3 3 3 2 2 3 2 0.9054582468
## 77 3 3 2 2 2 2 2 3 2 2 3 3 2 3 3 2 0.9996704414
## 78 2 2 2 2 3 3 3 3 2 2 2 2 2 2 2 3 -0.1822587307
## 79 3 2 2 3 2 2 3 3 1 2 3 2 3 1 3 2 0.0464837162
## 80 2 3 2 2 2 2 2 3 2 2 3 3 3 2 3 3 0.9208044547
## 81 3 3 3 3 3 4 2 3 2 2 3 3 4 2 3 3 0.4745577665
## 82 3 3 3 2 3 3 2 2 2 2 3 3 2 3 3 3 0.3020294591
## 83 2 3 3 2 2 3 2 3 2 1 2 2 2 2 3 3 0.2209071559
## 84 1 1 3 3 3 4 3 2 2 1 2 2 2 2 2 4 -0.9938475987
## 85 3 3 4 4 3 3 3 2 2 2 2 3 2 2 3 3 -0.4155577537
## 86 4 4 3 3 3 2 2 2 2 2 2 2 1 2 2 2 -0.5088266896
## 87 3 4 2 2 1 2 1 3 2 4 3 3 4 1 4 2 1.9856955897
## 88 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 -0.1785611311
## 89 3 2 2 3 3 3 3 3 3 2 3 2 3 2 3 3 0.3203998724
## 90 2 3 3 2 3 3 3 3 2 2 3 2 3 2 3 3 0.2181658989
## 91 3 3 2 3 2 2 1 3 2 2 3 4 4 2 3 2 1.1272199087
## 92 3 3 3 3 3 3 1 2 2 2 3 3 3 2 3 3 0.1747346663
## 93 2 3 3 3 2 3 1 3 2 3 2 2 2 2 3 3 0.6140905200
## 94 3 3 3 3 2 2 1 3 2 3 4 3 3 2 3 2 0.9180567961
## 95 2 1 4 2 2 3 2 2 3 1 3 3 2 3 3 3 0.0307414416
## 96 2 3 2 3 3 3 3 2 2 2 3 2 3 2 3 2 0.1204132364
## 97 3 3 2 2 3 2 2 2 2 2 2 3 2 2 2 3 -0.0875795072
## 98 3 3 2 2 3 2 2 3 3 2 3 2 3 2 3 2 0.5784274482
## 99 2 4 3 4 3 3 1 2 1 4 2 4 3 1 3 3 0.4129116680
## 100 2 3 2 2 2 3 1 3 2 2 3 3 3 2 3 2 1.0112396869
## 101 3 3 2 1 2 2 2 3 2 3 3 3 2 2 3 3 1.0682319140
## 102 2 2 3 2 3 3 2 2 2 2 2 3 2 3 2 3 -0.1883040435
## 103 1 2 3 3 3 4 4 2 4 2 1 2 3 3 3 4 0.1583424854
## 104 2 3 3 2 3 2 2 2 2 3 3 4 1 2 3 2 0.3120428962
## 105 3 2 4 2 3 2 1 3 2 1 3 3 2 2 3 2 -0.2592182469
## 106 3 3 3 1 2 1 2 3 1 3 4 4 3 2 3 2 0.9653692198
## 107 2 2 3 3 3 3 2 2 2 2 2 2 2 2 2 3 -0.6369015698
## 108 2 2 3 1 4 4 1 1 4 1 3 3 1 4 1 2 -0.5537295185
## 109 4 4 2 2 2 2 1 3 1 3 3 3 2 1 3 2 0.8137247410
## 110 4 4 3 1 2 2 1 2 2 3 4 4 2 1 3 1 0.7986321312
## 111 3 2 2 2 2 2 1 3 2 2 3 3 2 2 3 1 0.6663393116
## 112 3 3 2 3 3 3 2 1 2 2 3 2 2 3 3 3 0.0636971973
## 113 3 4 1 2 1 1 1 4 1 4 4 4 2 2 4 2 2.4765580336
## 114 3 3 2 2 2 2 2 3 2 3 3 3 3 2 3 2 1.0816100002
## 115 3 3 3 4 3 2 2 3 3 3 3 2 2 3 3 3 0.5431514488
## 116 2 3 2 2 1 2 2 3 2 4 2 3 4 3 2 3 1.5945398430
## 117 2 2 3 3 4 3 2 2 4 1 2 1 1 3 2 3 -0.8686119925
## 118 1 1 3 4 3 4 3 2 4 2 2 2 2 4 2 3 -0.1354545150
## 119 2 2 3 2 3 3 3 2 2 2 2 3 1 2 2 3 -0.5761585304
## 120 4 4 1 1 2 1 2 3 2 3 4 4 4 2 3 1 1.7822465499
## 121 1 1 4 4 4 3 2 1 3 1 1 1 1 4 1 4 -1.7995215832
## 122 3 3 2 1 3 3 2 2 2 2 3 3 1 2 3 3 0.2736946042
## 123 2 1 4 4 4 4 4 1 2 1 1 1 1 2 3 3 -1.9530785307
## 124 1 2 3 3 3 4 3 2 3 2 2 2 3 3 2 4 -0.1523813010
## 125 2 2 2 2 3 3 2 3 2 3 3 2 3 3 2 2 0.4564513150
## 126 4 3 2 2 2 2 2 3 2 2 3 3 2 2 3 2 0.7525387292
## 127 2 2 1 2 2 2 2 2 2 1 3 3 3 2 3 2 0.5304742108
## 128 2 4 2 1 3 3 4 4 1 1 2 3 2 2 3 3 0.4753207579
## 129 4 4 2 2 1 2 1 3 2 4 4 4 1 1 4 1 1.8585296368
## 130 2 3 3 1 3 2 3 2 2 2 3 4 1 2 2 2 -0.1679605207
## 131 2 3 2 1 4 4 2 1 2 1 1 3 3 4 1 4 -0.4381363632
## 132 2 2 4 2 4 3 2 2 3 2 2 3 3 3 2 3 -0.4540106689
## 133 3 3 3 3 3 4 4 3 2 3 3 3 2 2 3 3 0.3399170577
## 134 3 3 2 2 3 2 2 2 3 2 3 2 2 2 3 2 0.2491224607
## 135 3 3 3 2 3 2 2 3 4 3 4 3 2 4 2 2 0.9816653735
## 136 3 3 3 3 3 3 1 3 2 2 3 3 2 2 2 2 0.0008842014
## 137 2 3 3 2 3 3 2 2 3 2 2 3 2 3 2 3 0.1309603355
## 138 3 3 1 1 1 2 2 4 1 3 3 1 2 1 3 2 1.1229536665
## 139 2 2 3 3 3 3 2 2 2 2 3 2 1 3 2 3 -0.4549857425
## 140 2 2 3 2 3 3 3 2 3 2 2 3 1 3 2 3 -0.2034215675
## 141 3 3 2 2 2 3 2 3 2 2 2 3 2 3 3 3 0.9865973740
## 142 1 1 3 3 3 3 2 2 4 2 2 2 1 3 2 3 -0.3524817212
## 143 3 2 3 3 3 2 2 2 2 2 3 2 1 2 2 2 -0.7520938683
## 144 3 2 3 2 3 3 1 2 2 2 3 3 2 2 2 3 -0.3059278013
## 145 3 3 2 2 2 2 2 3 2 2 3 3 2 2 3 2 0.7795392615
## 146 3 2 2 3 3 3 3 3 4 2 3 2 2 4 3 3 0.8120031817
## 147 2 2 3 1 3 4 2 2 3 1 3 2 2 3 1 3 -0.5027965633
## 148 3 3 2 2 2 2 2 3 2 3 3 3 3 2 3 2 1.0816100002
## 149 3 2 2 1 3 3 2 2 3 2 3 3 2 2 2 2 0.0602808393
## 150 4 3 1 2 1 1 2 4 1 3 4 4 4 1 4 1 1.9850331863
## 151 3 3 3 2 3 2 1 2 2 3 2 3 1 2 3 3 0.1478717573
## 152 1 2 3 3 3 4 3 2 2 1 2 2 1 3 2 4 -0.7083226563
## 153 4 4 2 2 2 1 2 3 3 3 4 3 2 3 3 1 1.5058132606
## 154 1 3 3 2 3 3 3 3 3 2 2 3 1 3 3 3 0.5059036727
## 155 2 2 4 3 3 3 2 3 2 2 2 3 2 2 2 3 -0.4734562280
## 156 2 2 3 3 3 3 2 3 3 2 2 3 3 3 3 3 0.5063457651
## 157 3 3 3 2 3 2 2 2 3 2 3 3 2 2 2 2 -0.1030983094
## 158 2 3 2 2 3 3 3 1 1 2 2 3 1 1 4 3 -0.2168508967
## 159 1 3 2 3 2 3 3 3 3 2 1 2 3 3 2 4 0.6618686237
## 160 2 2 4 3 3 3 2 2 3 2 2 2 2 3 2 3 -0.4823388457
## 161 2 3 3 2 2 3 2 2 2 3 3 3 2 3 3 3 0.8312388998
## 162 2 1 2 2 2 3 3 3 3 1 1 1 2 3 2 4 -0.0792123460
## 163 3 3 2 2 2 2 2 2 2 2 3 3 2 2 3 3 0.5644989349
## 164 1 1 3 3 3 3 3 1 3 2 2 1 1 3 1 3 -1.2407915161
## 165 3 1 2 2 3 2 2 2 2 2 3 2 2 2 2 2 -0.5244264722
## 166 2 1 4 4 4 4 3 2 1 1 1 1 3 4 1 4 -1.7306457477
## 167 2 2 3 3 4 4 4 2 4 1 2 3 1 4 3 4 -0.1366365350
## 168 2 2 3 3 3 3 3 2 3 2 2 3 3 3 2 3 -0.0757788203
## 169 2 2 3 2 3 3 2 2 2 2 2 3 2 2 2 3 -0.4084352234
## 170 3 3 3 2 4 3 4 1 3 3 3 3 1 3 1 3 -0.6834357063
## 171 3 3 2 3 4 4 2 1 4 2 2 3 2 3 3 4 0.2080121193
## 172 2 2 2 3 2 3 2 3 3 2 2 3 2 3 3 3 0.9246581734
## 173 2 2 3 2 4 3 3 2 3 2 2 2 2 3 3 3 -0.2695132058
## 174 2 2 2 2 3 3 2 3 2 1 2 3 3 2 3 2 0.2128642281
## 175 1 3 3 2 3 4 2 3 3 2 1 3 2 4 2 3 0.5800593069
## 176 1 3 2 1 2 3 3 2 3 2 2 3 1 3 4 3 1.1599536384
## 177 3 3 2 3 3 2 2 3 2 2 3 2 2 2 2 2 -0.0379560461
## 178 2 2 2 3 3 3 3 2 3 2 3 2 3 3 2 3 0.0518654727
## 179 2 3 3 3 3 3 2 3 3 2 2 3 2 3 2 3 0.2841135696
## 180 1 3 3 2 4 3 2 2 3 3 2 4 2 3 3 3 0.4985691543
## 181 3 2 4 1 3 4 1 4 2 1 2 2 3 3 3 4 0.2484287601
## 182 1 2 4 4 3 4 3 1 2 1 2 1 1 3 2 4 -1.3830033954
## 183 2 3 2 3 3 4 2 3 2 2 3 3 4 1 2 3 0.2119753996
## 184 2 2 3 1 4 3 4 2 1 1 2 2 1 2 1 3 -1.6637501599
## 185 3 2 2 2 3 2 2 3 2 1 3 3 2 2 2 1 -0.1899540283
## 186 2 2 3 2 3 2 2 2 2 2 2 3 1 2 2 3 -0.5466766431
## 187 3 3 2 1 3 2 3 2 1 1 4 3 4 2 3 2 0.1706920105
## 188 3 3 2 2 3 3 2 3 1 2 3 3 3 2 3 3 0.4767717224
## 189 1 2 3 4 4 4 3 2 4 3 2 2 3 3 3 3 0.0993665946
## 190 4 4 2 1 2 1 3 2 1 2 4 3 1 1 4 1 0.5262828464
## 191 1 2 4 4 3 3 3 2 3 2 1 2 3 3 2 4 -0.5454685267
## 192 2 2 3 3 4 3 3 2 3 2 2 2 2 3 2 3 -0.6320260836
## 193 2 2 2 2 3 2 2 2 2 3 3 2 2 2 2 2 -0.1299614386
## 194 2 4 3 4 3 3 1 2 3 3 2 3 2 3 3 3 0.7027354284
## 195 3 3 3 2 3 3 3 2 2 2 2 3 2 3 3 3 0.1725215047
## 196 2 2 1 3 3 3 3 2 3 2 2 2 2 3 3 3 0.3933513549
## 197 4 3 2 2 1 1 2 3 2 3 4 3 3 2 3 1 1.3690855385
## 198 3 3 2 2 3 2 2 3 2 2 2 3 3 2 2 3 0.2417254804
## 199 2 2 3 2 3 3 3 2 3 1 2 3 1 3 2 3 -0.4042274728
## 200 2 2 3 2 3 3 2 2 3 2 2 3 1 3 2 3 -0.1369630941
## 201 2 2 2 2 2 3 3 2 2 2 2 2 3 2 3 3 0.2799949099
## 202 3 3 2 2 2 3 3 3 2 3 3 3 4 2 3 3 1.1663927739
## 203 2 2 4 4 3 4 4 2 2 2 3 2 4 2 4 3 -0.1850720253
## 204 3 3 3 2 3 2 3 3 2 2 2 3 2 2 2 3 -0.1441720654
## 205 2 2 3 3 3 3 3 2 2 2 2 3 3 2 2 3 -0.4485157832
## 206 1 1 2 2 3 4 4 1 4 3 1 1 3 4 1 4 -0.2511893632
## 207 2 2 2 2 2 2 2 3 3 3 2 2 3 2 3 3 0.8909286395
## 208 2 3 3 3 3 3 3 2 3 2 2 2 2 3 2 3 -0.1639644845
## 209 3 1 4 4 4 4 3 1 2 2 3 2 1 1 2 3 -1.9408934337
## 210 2 3 3 2 2 3 2 3 3 2 2 2 2 2 3 3 0.5743188441
## 211 1 3 4 1 2 4 4 3 4 2 1 3 3 3 4 4 1.2272492241
## 212 2 3 1 2 2 2 2 3 3 2 3 3 1 4 1 2 0.9410654258
## 213 1 1 4 4 4 4 4 1 4 1 1 1 3 4 1 4 -1.5403264940
## 214 1 1 4 4 4 4 3 1 1 2 1 2 1 1 1 4 -2.4402232444
## 215 2 2 3 3 3 3 3 2 3 2 2 2 2 3 2 3 -0.3306230804
## 216 1 2 1 3 3 3 3 3 2 3 3 3 3 2 3 3 0.7943547246
## 217 1 1 4 4 4 4 3 1 4 2 1 1 3 3 1 4 -1.4931932952
## 218 2 3 3 2 3 3 3 2 4 3 2 3 2 3 3 3 0.7055395081
## 219 1 1 3 3 4 3 4 2 3 3 2 2 2 3 2 3 -0.6373367155
## 220 2 3 3 2 3 4 2 2 3 3 2 3 2 3 2 3 0.3687428269
## 221 3 1 4 4 3 4 1 2 2 2 4 2 3 2 2 3 -0.7928230017
## 222 1 1 4 1 3 4 4 1 4 1 1 2 1 4 1 4 -1.0632129718
## 223 2 2 3 3 3 4 3 2 3 2 2 2 3 3 2 3 -0.1923816607
## 224 1 2 4 4 4 3 4 2 3 2 2 2 3 2 2 3 -1.0834115298
## 225 3 3 1 1 3 2 1 1 4 1 3 4 3 3 3 2 0.9609566830
## 226 2 2 2 2 3 3 3 2 2 1 1 2 3 2 3 3 -0.2852634794
## 227 2 2 4 3 3 4 3 2 2 3 3 2 2 2 3 3 -0.3330763517
## 228 2 3 3 4 4 2 3 2 1 2 2 2 1 1 2 3 -1.4239697529
## 229 2 2 3 3 4 3 4 2 3 2 2 2 2 3 3 4 -0.3978587717
## 230 2 2 3 3 3 3 3 2 2 2 2 2 2 3 2 2 -0.4962286908
## 231 3 3 3 3 3 3 2 3 3 2 3 2 3 3 3 3 0.5554738831
## 232 1 1 3 3 4 3 3 2 3 1 2 2 1 3 2 3 -1.0737548861
## 233 3 2 3 3 3 3 2 3 1 2 3 3 2 1 3 3 -0.3043440456
## 234 1 1 3 3 3 3 3 2 3 2 2 2 2 3 2 3 -0.4702811441
## 235 2 1 3 3 3 3 3 2 2 2 2 2 3 3 2 3 -0.5486226258
## 236 2 2 3 2 3 4 3 1 4 1 2 3 3 3 2 4 -0.2271557632
## 237 2 2 3 2 3 3 3 2 3 2 2 3 3 3 2 3 -0.0008919005
## 238 1 1 3 4 3 4 4 1 4 1 1 1 1 4 2 4 -0.9356529613
## 239 2 1 4 4 4 4 4 1 4 1 1 1 1 4 2 4 -1.4822307355
## 240 2 2 3 3 3 3 3 2 3 2 3 3 2 3 2 3 -0.1139941730
## 241 3 2 3 3 4 4 4 2 4 1 3 2 1 4 2 3 -0.5547927983
## 242 1 1 4 3 4 4 4 1 4 1 1 1 1 4 1 4 -1.6679692412
## 243 3 2 2 3 3 3 3 2 3 2 2 2 2 3 2 3 -0.1394493740
## 244 2 2 4 4 4 4 4 1 4 1 1 1 1 4 1 4 -1.6031980974
## 245 1 1 4 4 4 4 4 1 4 3 1 1 2 4 1 4 -1.2399795171
## 246 2 2 4 3 4 4 4 2 3 1 2 2 3 3 1 4 -1.2538494119
## 247 1 1 4 4 4 4 3 2 4 1 1 1 1 3 1 4 -1.6684887136
## 248 2 2 4 4 3 4 3 2 3 2 2 2 1 3 2 4 -0.6749726590
## 249 1 3 3 2 4 3 3 2 2 2 3 3 3 2 2 3 -0.4183232573
## 250 2 2 3 3 3 3 3 2 3 2 2 2 3 3 2 3 -0.2293582469
## 251 3 2 3 3 2 3 4 2 2 1 2 2 2 1 2 3 -0.9163531311
## 252 2 2 2 3 4 4 3 2 3 1 2 2 4 3 1 3 -0.6627774549
## 253 3 2 3 3 3 3 3 2 3 2 2 2 3 2 2 3 -0.4764899591
## 254 2 2 2 4 3 3 3 2 3 2 2 2 3 3 2 3 -0.0860709281
## 255 1 1 3 4 3 4 3 2 3 2 2 2 3 3 4 3 0.1683252716
## 256 2 3 3 2 3 3 4 1 2 2 2 3 1 2 2 4 -0.6909987345
## 257 3 3 3 3 2 2 3 3 2 1 3 3 2 2 3 2 0.2192137241
## 258 2 2 2 2 3 3 4 2 3 2 2 2 1 3 2 3 -0.2052852289
## 259 1 2 4 4 4 4 4 1 3 2 1 1 2 3 2 4 -1.3592378313
## 260 3 3 3 3 3 3 3 2 2 3 2 3 2 2 2 3 -0.2093166478
## 261 4 3 3 2 3 1 4 2 1 2 2 2 2 2 2 2 -0.8218328482
## 262 1 1 4 4 3 4 4 1 3 1 1 1 3 3 1 4 -1.6116604537
## 263 2 2 3 3 3 3 4 2 2 1 2 2 2 2 2 3 -0.9706244220
## 264 2 2 3 3 4 3 3 1 4 1 2 2 2 3 2 4 -0.8952665325
## 265 2 3 3 3 3 2 3 2 3 3 2 3 2 2 3 2 0.2079392118
## 266 2 3 3 3 3 3 3 3 2 2 2 3 2 2 2 3 -0.1550818668
## 267 3 3 3 3 3 3 3 2 2 3 3 3 3 2 3 3 0.2426236246
## 268 1 2 4 2 4 3 3 1 4 1 2 2 2 3 2 4 -1.0115533190
## 269 2 2 3 4 3 3 3 2 3 1 2 2 2 3 1 3 -0.8939418635
## 270 3 3 2 2 3 2 2 3 3 3 3 3 3 2 3 2 0.9328127800
## 271 1 1 4 4 4 4 4 1 4 1 1 1 1 4 1 4 -1.7428561611
## 272 2 1 1 2 2 1 1 1 2 3 3 2 3 2 2 3 0.1386636016
## 273 2 3 3 3 2 3 3 3 2 3 2 3 2 3 3 2 0.8418843521
## 274 2 2 3 2 3 3 4 2 3 2 3 2 3 3 3 3 0.1297456383
## 275 2 2 3 3 3 3 3 2 3 2 2 2 2 3 2 3 -0.3306230804
## 276 2 3 4 3 3 4 3 2 3 3 2 3 2 3 2 3 0.0092231948
## 277 2 3 2 2 2 2 3 3 3 3 3 3 2 3 3 3 1.3266240158
## 278 2 2 3 3 3 4 3 1 4 1 1 2 4 3 2 4 -0.4174067570
## 279 3 2 2 3 2 3 4 3 3 1 2 1 3 2 2 3 -0.1497163685
## 280 2 2 3 3 3 3 3 2 3 2 3 2 4 2 2 3 -0.2851751124
## 281 2 2 2 2 2 2 1 4 4 3 1 4 1 1 4 1 1.4211078782
## 282 2 1 3 4 3 3 4 1 4 1 1 1 1 4 1 4 -1.2872560377
## 283 2 2 3 2 3 3 3 2 3 2 3 2 3 2 2 3 -0.3115530260
## 284 1 2 3 3 4 3 4 1 3 3 1 2 4 1 1 3 -1.2871264052
## 285 1 2 4 3 3 4 4 1 3 1 1 1 1 4 1 4 -1.3525134250
## 286 2 2 3 3 2 2 2 2 3 2 3 2 2 2 2 3 -0.1568198889
## 287 3 2 3 3 3 2 4 2 2 2 3 2 3 2 2 2 -0.6824811482
## 288 2 3 3 3 3 3 2 2 2 3 2 3 3 2 3 3 0.2730331494
## 289 2 2 3 3 3 3 4 2 3 3 2 2 2 3 2 3 -0.1962756487
## 290 2 2 3 2 2 2 3 3 2 2 3 3 2 2 2 2 0.0676225277
## 291 4 4 2 3 2 1 2 4 1 3 4 4 3 1 2 1 0.8807108711
## 292 3 3 3 3 3 2 3 3 2 2 3 3 2 2 3 2 0.1186166262
## 293 2 3 3 3 3 3 3 2 3 1 2 1 2 2 3 3 -0.4508550383
## 294 4 3 2 3 2 2 3 2 1 2 3 2 3 1 3 2 -0.0418983741
## 295 3 2 3 3 3 3 4 3 3 1 2 2 4 3 2 3 -0.1943181704
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## 800 1.755053129#After we did the analysis, we need to separate variables to different factors
F1 <- c("Q1", "Q2", "Q4", "Q6", "Q9", "Q10")
F2 <- c("Q3", "Q5", "Q7", "Q8")
#Cronbach's Alpha to check if these variables are measuring the same aspects and we have good intgernal consistency
alpha.pa1 <- alpha(data[F1])## Warning in alpha(data[F1]): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( Q4 Q6 Q9 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' optionprint(alpha.pa1, digits = 3)##
## Reliability analysis
## Call: alpha(x = data[F1])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## -0.454 -0.444 0.114 -0.054 -0.307 0.0846 2.46 0.292 -0.239
##
## lower alpha upper 95% confidence boundaries
## -0.62 -0.454 -0.288
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Q1 -0.187 -0.200 0.1789 -0.0345 -0.167 0.0676 0.150 -0.206
## Q2 -0.365 -0.398 0.0663 -0.0604 -0.285 0.0752 0.147 -0.206
## Q4 -0.406 -0.381 0.1726 -0.0583 -0.276 0.0815 0.200 -0.253
## Q6 -0.229 -0.179 0.1743 -0.0313 -0.152 0.0702 0.140 -0.206
## Q9 -0.393 -0.380 0.1612 -0.0583 -0.276 0.0798 0.187 -0.258
## Q10 -0.589 -0.601 0.0521 -0.0812 -0.375 0.0924 0.199 -0.324
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Q1 800 0.246 0.256 -0.00294 -0.23780 2.16 0.847
## Q2 800 0.362 0.379 0.33163 -0.13165 2.36 0.852
## Q4 800 0.391 0.370 -0.00381 -0.10969 2.72 0.863
## Q6 800 0.254 0.240 -0.01370 -0.21493 2.96 0.818
## Q9 800 0.396 0.370 0.06265 -0.11738 2.58 0.885
## Q10 800 0.441 0.479 0.33241 0.00185 2.01 0.770
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## Q1 0.230 0.436 0.274 0.060 0
## Q2 0.152 0.431 0.321 0.095 0
## Q4 0.076 0.324 0.405 0.195 0
## Q6 0.036 0.248 0.439 0.278 0
## Q9 0.101 0.388 0.344 0.168 0
## Q10 0.254 0.520 0.189 0.038 0alpha.pa2 <- alpha(data[F2])## Warning in alpha(data[F2]): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( Q8 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' optionprint(alpha.pa2, digits = 3)##
## Reliability analysis
## Call: alpha(x = data[F2])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.0423 -0.025 0.3 -0.00613 -0.0244 0.0478 2.61 0.431 -0.0164
##
## lower alpha upper 95% confidence boundaries
## -0.051 0.042 0.136
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Q3 -0.464 -0.656 -0.0811 -0.152 -0.396 0.0799 0.2167 -0.334
## Q5 -0.512 -0.696 -0.1693 -0.158 -0.410 0.0837 0.1616 -0.334
## Q7 -0.507 -0.511 0.1196 -0.127 -0.338 0.0892 0.3553 -0.443
## Q8 0.655 0.679 0.6056 0.413 2.111 0.0214 0.0177 0.377
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Q3 800 0.689 0.716 0.712 0.301 2.73 0.793
## Q5 800 0.700 0.726 0.788 0.342 2.87 0.759
## Q7 800 0.755 0.678 0.479 0.229 2.56 1.034
## Q8 800 -0.174 -0.139 -0.893 -0.535 2.28 0.775
##
## Non missing response frequency for each item
## 1 2 3 4 miss
## Q3 0.050 0.338 0.448 0.165 0
## Q5 0.040 0.241 0.528 0.191 0
## Q7 0.186 0.290 0.299 0.225 0
## Q8 0.146 0.478 0.324 0.052 0#alpha.pa1 <- aplha(data[F1], check.keys = TRUE)Summary Write Up -
Initially, the factorability of the 10 items was examined. Several well-recognized criteria for the factorability of a correlation were used. Firstly, it was observed that 6 of the 10 items correlated at least 0.3 with at least one other item, suggesting reasonable factorability. Secondly, the Kaiser-Meyer-Olkin measure of sampling adequacy was .93 (overall MSA), above the commonly recommended value of .84. Given these overall indicators, factor analysis was deemed to be suitable with all 16 items. An exploratory factor analysis with oblique rotation was conducted since the factors are correlated. In total, 45% of the variance is explained by the two factors. Factor one includes 6 items, explains 23% of the variance and, factor two includes 4 items, explains 22% of the variance. The test of Cronbach’s alpha was also performed in terms of studying the internal consistency.The Cronbach’s alpha for the first factor was .454 and .042 for factor 2.