Read dataset
t = "C:\\Users\\Thuan Nguyen\\Documents\\myData.csv"
data = read.csv(t)
myData = data[,2:21]
Attaching data and fix it
attach(myData)
fix(myData)
Load the requirement libraries
library(devtools)
## Loading required package: usethis
library(psych)
library(GPArotation)
library(corpcor)
library(corrplot)
## corrplot 0.84 loaded
library(factoextra)
## Loading required package: ggplot2
##
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
##
## %+%, alpha
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(likert)
## Loading required package: xtable
#library(jbryer)
library(ggplot2)
library(grid)
Correlation Analysis
corMatrix=cor(myData)
round(corMatrix,5)
## V1 V2 V4 V5 V7 V8 V9 V10
## V1 1.00000 0.44146 0.40224 0.40576 -0.05227 -0.05321 -0.02591 0.00489
## V2 0.44146 1.00000 0.32520 0.34585 -0.11228 -0.06484 -0.05851 -0.01247
## V4 0.40224 0.32520 1.00000 0.57540 0.01186 0.03317 0.05933 0.05464
## V5 0.40576 0.34585 0.57540 1.00000 0.06406 0.05556 0.06737 0.06994
## V7 -0.05227 -0.11228 0.01186 0.06406 1.00000 0.61864 0.27116 0.29047
## V8 -0.05321 -0.06484 0.03317 0.05556 0.61864 1.00000 0.31220 0.27300
## V9 -0.02591 -0.05851 0.05933 0.06737 0.27116 0.31220 1.00000 0.38393
## V10 0.00489 -0.01247 0.05464 0.06994 0.29047 0.27300 0.38393 1.00000
## V11 -0.00911 -0.01060 0.08077 0.07293 0.33682 0.35439 0.31957 0.63952
## V13 -0.04210 -0.05011 -0.13486 -0.17060 -0.02406 -0.02393 0.04622 -0.01932
## V14 -0.08278 -0.07092 -0.16808 -0.16568 -0.11871 -0.08121 0.02069 -0.06217
## V15 -0.09367 -0.12194 -0.24665 -0.24976 -0.29354 -0.29061 -0.21291 -0.21784
## V16 -0.04828 -0.03497 -0.11099 -0.12293 -0.06115 -0.09219 -0.06125 -0.06853
## V17 -0.06189 -0.05366 -0.14644 -0.17484 -0.18992 -0.18399 -0.13648 -0.17652
## V18 -0.01436 -0.06824 -0.05312 -0.15556 -0.21949 -0.21548 -0.11141 -0.13411
## V23 -0.06328 -0.09279 0.00097 -0.09355 -0.07683 -0.08496 -0.09861 -0.14821
## V24 -0.03076 -0.07402 0.02159 -0.05177 -0.10446 -0.12009 -0.12763 -0.18196
## V25 -0.04725 -0.08300 -0.05650 -0.08654 -0.08681 -0.07528 -0.05148 -0.13702
## V26 -0.07307 -0.08400 -0.10178 -0.15538 -0.12702 -0.08521 -0.08705 -0.14524
## V27 0.03268 0.01428 -0.02613 -0.03676 -0.11739 -0.10740 -0.10421 -0.14805
## V11 V13 V14 V15 V16 V17 V18 V23
## V1 -0.00911 -0.04210 -0.08278 -0.09367 -0.04828 -0.06189 -0.01436 -0.06328
## V2 -0.01060 -0.05011 -0.07092 -0.12194 -0.03497 -0.05366 -0.06824 -0.09279
## V4 0.08077 -0.13486 -0.16808 -0.24665 -0.11099 -0.14644 -0.05312 0.00097
## V5 0.07293 -0.17060 -0.16568 -0.24976 -0.12293 -0.17484 -0.15556 -0.09355
## V7 0.33682 -0.02406 -0.11871 -0.29354 -0.06115 -0.18992 -0.21949 -0.07683
## V8 0.35439 -0.02393 -0.08121 -0.29061 -0.09219 -0.18399 -0.21548 -0.08496
## V9 0.31957 0.04622 0.02069 -0.21291 -0.06125 -0.13648 -0.11141 -0.09861
## V10 0.63952 -0.01932 -0.06217 -0.21784 -0.06853 -0.17652 -0.13411 -0.14821
## V11 1.00000 -0.06672 -0.09397 -0.31675 -0.16541 -0.25912 -0.26523 -0.14392
## V13 -0.06672 1.00000 0.52034 0.27850 0.25149 0.13116 0.24729 0.03158
## V14 -0.09397 0.52034 1.00000 0.32058 0.27422 0.16124 0.27786 0.05906
## V15 -0.31675 0.27850 0.32058 1.00000 0.31078 0.47950 0.44699 0.22403
## V16 -0.16541 0.25149 0.27422 0.31078 1.00000 0.28520 0.26146 0.14622
## V17 -0.25912 0.13116 0.16124 0.47950 0.28520 1.00000 0.26382 0.18278
## V18 -0.26523 0.24729 0.27786 0.44699 0.26146 0.26382 1.00000 0.30498
## V23 -0.14392 0.03158 0.05906 0.22403 0.14622 0.18278 0.30498 1.00000
## V24 -0.16592 0.05850 0.07149 0.18794 0.09710 0.13701 0.20667 0.59482
## V25 -0.17817 0.07389 0.09565 0.28002 0.13652 0.23200 0.31874 0.50802
## V26 -0.15583 0.09786 0.11314 0.29704 0.12636 0.25062 0.29856 0.50287
## V27 -0.17980 0.11873 0.11307 0.25548 0.09982 0.17250 0.25912 0.33535
## V24 V25 V26 V27
## V1 -0.03076 -0.04725 -0.07307 0.03268
## V2 -0.07402 -0.08300 -0.08400 0.01428
## V4 0.02159 -0.05650 -0.10178 -0.02613
## V5 -0.05177 -0.08654 -0.15538 -0.03676
## V7 -0.10446 -0.08681 -0.12702 -0.11739
## V8 -0.12009 -0.07528 -0.08521 -0.10740
## V9 -0.12763 -0.05148 -0.08705 -0.10421
## V10 -0.18196 -0.13702 -0.14524 -0.14805
## V11 -0.16592 -0.17817 -0.15583 -0.17980
## V13 0.05850 0.07389 0.09786 0.11873
## V14 0.07149 0.09565 0.11314 0.11307
## V15 0.18794 0.28002 0.29704 0.25548
## V16 0.09710 0.13652 0.12636 0.09982
## V17 0.13701 0.23200 0.25062 0.17250
## V18 0.20667 0.31874 0.29856 0.25912
## V23 0.59482 0.50802 0.50287 0.33535
## V24 1.00000 0.53704 0.42091 0.33701
## V25 0.53704 1.00000 0.56590 0.36322
## V26 0.42091 0.56590 1.00000 0.46981
## V27 0.33701 0.36322 0.46981 1.00000
corrplot(corMatrix, method = "color")
KMO and Bartlett Test
#KMO Test
KMO(myData)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = myData)
## Overall MSA = 0.8
## MSA for each item =
## V1 V2 V4 V5 V7 V8 V9 V10 V11 V13 V14 V15 V16 V17 V18 V23
## 0.77 0.77 0.73 0.76 0.74 0.74 0.84 0.71 0.76 0.71 0.74 0.87 0.87 0.86 0.88 0.83
## V24 V25 V26 V27
## 0.80 0.85 0.85 0.88
#Bartlett Test
cortest.bartlett(myData)
## R was not square, finding R from data
## $chisq
## [1] 3408.639
##
## $p.value
## [1] 0
##
## $df
## [1] 190
EFA analysis
pca1 <- prcomp(myData, scale = TRUE)
get_eig(pca1)
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 4.4154995 22.077498 22.07750
## Dim.2 2.3719553 11.859777 33.93727
## Dim.3 2.1020392 10.510196 44.44747
## Dim.4 1.6417939 8.208969 52.65644
## Dim.5 1.0206835 5.103418 57.75986
## Dim.6 0.9635107 4.817553 62.57741
## Dim.7 0.8373678 4.186839 66.76425
## Dim.8 0.7646453 3.823226 70.58748
## Dim.9 0.7001072 3.500536 74.08801
## Dim.10 0.6697637 3.348818 77.43683
## Dim.11 0.6535989 3.267994 80.70482
## Dim.12 0.5497797 2.748898 83.45372
## Dim.13 0.5193246 2.596623 86.05035
## Dim.14 0.4833616 2.416808 88.46715
## Dim.15 0.4718451 2.359225 90.82638
## Dim.16 0.4276291 2.138145 92.96452
## Dim.17 0.3986494 1.993247 94.95777
## Dim.18 0.3554408 1.777204 96.73497
## Dim.19 0.3325270 1.662635 98.39761
## Dim.20 0.3204780 1.602390 100.00000
fviz_screeplot(pca1, addlabels = TRUE, n = 12)
pc2 <- principal(myData, nfactors = 4, rotate = "varimax") #Choice n = 4 factors
print.psych(pc2, cut = 0.4, sort = TRUE)
## Principal Components Analysis
## Call: principal(r = myData, nfactors = 4, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item RC3 RC1 RC4 RC2 h2 u2 com
## V23 16 0.79 0.63 0.37 1.0
## V25 18 0.79 0.64 0.36 1.1
## V24 17 0.76 0.59 0.41 1.0
## V26 19 0.75 0.61 0.39 1.1
## V27 20 0.59 0.40 0.60 1.3
## V11 9 0.72 0.56 0.44 1.1
## V8 6 0.71 0.53 0.47 1.1
## V10 8 0.70 0.52 0.48 1.1
## V7 5 0.69 0.51 0.49 1.1
## V9 7 0.64 0.42 0.58 1.1
## V14 11 0.76 0.58 0.42 1.0
## V13 10 0.75 0.57 0.43 1.0
## V16 13 0.57 0.34 0.66 1.1
## V15 12 0.57 0.57 0.43 2.5
## V18 15 0.52 0.44 0.56 2.2
## V17 14 0.40 0.32 0.68 2.7
## V4 3 0.76 0.61 0.39 1.1
## V1 1 0.76 0.58 0.42 1.0
## V5 4 0.75 0.62 0.38 1.2
## V2 2 0.69 0.50 0.50 1.1
##
## RC3 RC1 RC4 RC2
## SS loadings 3.05 2.77 2.40 2.30
## Proportion Var 0.15 0.14 0.12 0.12
## Cumulative Var 0.15 0.29 0.41 0.53
## Proportion Explained 0.29 0.26 0.23 0.22
## Cumulative Proportion 0.29 0.55 0.78 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 4 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.07
## with the empirical chi square 992.62 with prob < 3.6e-139
##
## Fit based upon off diagonal values = 0.91
Cronbackâs alpha
#psych::alpha(myData[, c(06, 18, 13, 07, 14, 10, 15)])
Structural Equation Modelling
library(lavaan)
## This is lavaan 0.6-5
## lavaan is BETA software! Please report any bugs.
##
## Attaching package: 'lavaan'
## The following object is masked from 'package:psych':
##
## cor2cov
model <- '
# measurement model
n1 =~ V1 + V2 + V4 +V5
n2 =~ V7 + V8 + V9 + V10 + V11
n3 =~ V13 + V14 + V15 + V16 + V17 + V18
n4 =~ V23 + V24 + V25 +V26 + V27
# regressions
n4 ~ n1
n4 ~ n2
n4 ~ n3
n1 ~ n2
n1 ~ n3
n2 ~ n3
'
fit <- sem(model, data=myData)
summary(fit, standardized=TRUE)
## lavaan 0.6-5 ended normally after 67 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 46
##
## Number of observations 593
##
## Model Test User Model:
##
## Test statistic 674.762
## Degrees of freedom 164
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Structured
## Standard errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## n1 =~
## V1 1.000 0.637 0.573
## V2 0.832 0.090 9.235 0.000 0.530 0.501
## V4 1.265 0.110 11.520 0.000 0.806 0.731
## V5 1.463 0.126 11.587 0.000 0.932 0.758
## n2 =~
## V7 1.000 0.553 0.543
## V8 1.032 0.106 9.738 0.000 0.571 0.551
## V9 1.025 0.116 8.867 0.000 0.567 0.481
## V10 1.454 0.129 11.233 0.000 0.804 0.710
## V11 1.560 0.135 11.529 0.000 0.863 0.768
## n3 =~
## V13 1.000 0.248 0.405
## V14 1.048 0.147 7.152 0.000 0.260 0.456
## V15 2.311 0.266 8.680 0.000 0.573 0.779
## V16 1.149 0.163 7.040 0.000 0.285 0.443
## V17 1.742 0.222 7.834 0.000 0.432 0.553
## V18 1.714 0.214 7.997 0.000 0.425 0.582
## n4 =~
## V23 1.000 1.095 0.721
## V24 0.983 0.066 14.914 0.000 1.077 0.695
## V25 1.083 0.068 15.825 0.000 1.186 0.747
## V26 1.100 0.072 15.358 0.000 1.204 0.719
## V27 0.946 0.082 11.598 0.000 1.036 0.531
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## n4 ~
## n1 0.057 0.093 0.620 0.536 0.033 0.033
## n2 -0.161 0.116 -1.381 0.167 -0.081 -0.081
## n3 1.968 0.360 5.466 0.000 0.445 0.445
## n1 ~
## n2 -0.136 0.073 -1.864 0.062 -0.118 -0.118
## n3 -1.054 0.207 -5.096 0.000 -0.410 -0.410
## n2 ~
## n3 -1.051 0.172 -6.119 0.000 -0.471 -0.471
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .V1 0.830 0.057 14.658 0.000 0.830 0.672
## .V2 0.840 0.054 15.492 0.000 0.840 0.749
## .V4 0.568 0.052 10.823 0.000 0.568 0.466
## .V5 0.643 0.066 9.805 0.000 0.643 0.425
## .V7 0.730 0.048 15.289 0.000 0.730 0.705
## .V8 0.747 0.049 15.209 0.000 0.747 0.697
## .V9 1.070 0.068 15.846 0.000 1.070 0.769
## .V10 0.636 0.052 12.342 0.000 0.636 0.496
## .V11 0.518 0.050 10.454 0.000 0.518 0.411
## .V13 0.313 0.019 16.306 0.000 0.313 0.836
## .V14 0.257 0.016 15.992 0.000 0.257 0.792
## .V15 0.212 0.021 9.921 0.000 0.212 0.393
## .V16 0.333 0.021 16.082 0.000 0.333 0.804
## .V17 0.422 0.028 15.128 0.000 0.422 0.694
## .V18 0.352 0.024 14.777 0.000 0.352 0.661
## .V23 1.107 0.083 13.349 0.000 1.107 0.480
## .V24 1.240 0.089 13.889 0.000 1.240 0.517
## .V25 1.115 0.088 12.705 0.000 1.115 0.442
## .V26 1.351 0.101 13.387 0.000 1.351 0.482
## .V27 2.740 0.173 15.846 0.000 2.740 0.718
## .n1 0.351 0.054 6.517 0.000 0.864 0.864
## .n2 0.238 0.038 6.182 0.000 0.778 0.778
## n3 0.061 0.013 4.574 0.000 1.000 1.000
## .n4 0.925 0.105 8.835 0.000 0.771 0.771
Bootstraping
model <- '
# measurement model
n1 =~ V1 + V2 + V4 +V5
n2 =~ V7 + V8 + V9 + V10 + V11
n3 =~ V13 + V14 + V15 + V16 + V17 + V18
n4 =~ V23 + V24 + V25 +V26 + V27
# regressions
n4 ~ n1
n4 ~ n2
n4 ~ n3
n1 ~ n2
n1 ~ n3
n2 ~ n3
'
fit2 <- sem(model, data=myData, se="bootstrap")
summary(fit2, standardized=TRUE)
## lavaan 0.6-5 ended normally after 67 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 46
##
## Number of observations 593
##
## Model Test User Model:
##
## Test statistic 674.762
## Degrees of freedom 164
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 1000
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## n1 =~
## V1 1.000 0.637 0.573
## V2 0.832 0.074 11.316 0.000 0.530 0.501
## V4 1.265 0.123 10.264 0.000 0.806 0.731
## V5 1.463 0.163 8.990 0.000 0.932 0.758
## n2 =~
## V7 1.000 0.553 0.543
## V8 1.032 0.070 14.662 0.000 0.571 0.551
## V9 1.025 0.185 5.534 0.000 0.567 0.481
## V10 1.454 0.361 4.024 0.000 0.804 0.710
## V11 1.560 0.364 4.287 0.000 0.863 0.768
## n3 =~
## V13 1.000 0.248 0.405
## V14 1.048 0.112 9.343 0.000 0.260 0.456
## V15 2.311 0.402 5.755 0.000 0.573 0.779
## V16 1.149 0.193 5.965 0.000 0.285 0.443
## V17 1.742 0.347 5.019 0.000 0.432 0.553
## V18 1.714 0.268 6.391 0.000 0.425 0.582
## n4 =~
## V23 1.000 1.095 0.721
## V24 0.983 0.055 17.735 0.000 1.077 0.695
## V25 1.083 0.070 15.366 0.000 1.186 0.747
## V26 1.100 0.079 14.006 0.000 1.204 0.719
## V27 0.946 0.087 10.841 0.000 1.036 0.531
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## n4 ~
## n1 0.057 0.100 0.575 0.565 0.033 0.033
## n2 -0.161 0.152 -1.059 0.290 -0.081 -0.081
## n3 1.968 0.517 3.807 0.000 0.445 0.445
## n1 ~
## n2 -0.136 0.077 -1.763 0.078 -0.118 -0.118
## n3 -1.054 0.267 -3.951 0.000 -0.410 -0.410
## n2 ~
## n3 -1.051 0.350 -3.008 0.003 -0.471 -0.471
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .V1 0.830 0.064 12.942 0.000 0.830 0.672
## .V2 0.840 0.057 14.777 0.000 0.840 0.749
## .V4 0.568 0.054 10.454 0.000 0.568 0.466
## .V5 0.643 0.085 7.603 0.000 0.643 0.425
## .V7 0.730 0.104 7.016 0.000 0.730 0.705
## .V8 0.747 0.118 6.319 0.000 0.747 0.697
## .V9 1.070 0.062 17.375 0.000 1.070 0.769
## .V10 0.636 0.124 5.146 0.000 0.636 0.496
## .V11 0.518 0.127 4.069 0.000 0.518 0.411
## .V13 0.313 0.024 12.900 0.000 0.313 0.836
## .V14 0.257 0.020 12.589 0.000 0.257 0.792
## .V15 0.212 0.026 8.057 0.000 0.212 0.393
## .V16 0.333 0.025 13.479 0.000 0.333 0.804
## .V17 0.422 0.038 11.219 0.000 0.422 0.694
## .V18 0.352 0.029 12.238 0.000 0.352 0.661
## .V23 1.107 0.100 11.067 0.000 1.107 0.480
## .V24 1.240 0.112 11.066 0.000 1.240 0.517
## .V25 1.115 0.110 10.159 0.000 1.115 0.442
## .V26 1.351 0.123 10.975 0.000 1.351 0.482
## .V27 2.740 0.168 16.273 0.000 2.740 0.718
## .n1 0.351 0.064 5.497 0.000 0.864 0.864
## .n2 0.238 0.087 2.747 0.006 0.778 0.778
## n3 0.061 0.018 3.356 0.001 1.000 1.000
## .n4 0.925 0.108 8.533 0.000 0.771 0.771