Exploratory Factor Analysis (EFA)

Tutorial

Author

Orlando Sabogal-Cardona

Published

May 15, 2024

Libraries and data

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.3     ✔ readr     2.1.4
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ ggplot2   3.4.4     ✔ tibble    3.2.1
✔ lubridate 1.9.3     ✔ tidyr     1.3.0
✔ purrr     1.0.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(magrittr)


Attaching package: 'magrittr'

The following object is masked from 'package:purrr':

    set_names

The following object is masked from 'package:tidyr':

    extract

library(psych)

Warning: package 'psych' was built under R version 4.3.3


Attaching package: 'psych'

The following objects are masked from 'package:ggplot2':

    %+%, alpha

library(EFA.dimensions)

Warning: package 'EFA.dimensions' was built under R version 4.3.3

**************************************************************************************************
EFA.dimensions 0.1.8.1

Please contact Brian O'Connor at brian.oconnor@ubc.ca if you have questions or suggestions.
**************************************************************************************************

library(psychTools)

Warning: package 'psychTools' was built under R version 4.3.3


Attaching package: 'psychTools'

The following object is masked from 'package:dplyr':

    recode

Toy data: bfi

Test_Data <- bfi
Test_Data[1:10,]

      A1 A2 A3 A4 A5 C1 C2 C3 C4 C5 E1 E2 E3 E4 E5 N1 N2 N3 N4 N5 O1 O2 O3 O4
61617  2  4  3  4  4  2  3  3  4  4  3  3  3  4  4  3  4  2  2  3  3  6  3  4
61618  2  4  5  2  5  5  4  4  3  4  1  1  6  4  3  3  3  3  5  5  4  2  4  3
61620  5  4  5  4  4  4  5  4  2  5  2  4  4  4  5  4  5  4  2  3  4  2  5  5
61621  4  4  6  5  5  4  4  3  5  5  5  3  4  4  4  2  5  2  4  1  3  3  4  3
61622  2  3  3  4  5  4  4  5  3  2  2  2  5  4  5  2  3  4  4  3  3  3  4  3
61623  6  6  5  6  5  6  6  6  1  3  2  1  6  5  6  3  5  2  2  3  4  3  5  6
61624  2  5  5  3  5  5  4  4  2  3  4  3  4  5  5  1  2  2  1  1  5  2  5  6
61629  4  3  1  5  1  3  2  4  2  4  3  6  4  2  1  6  3  2  6  4  3  2  4  5
61630  4  3  6  3  3  6  6  3  4  5  5  3 NA  4  3  5  5  2  3  3  6  6  6  6
61633  2  5  6  6  5  6  5  6  2  1  2  2  4  5  5  5  5  5  2  4  5  1  5  5
      O5 gender education age
61617  3      1        NA  16
61618  3      2        NA  18
61620  2      2        NA  17
61621  5      2        NA  17
61622  3      1        NA  17
61623  1      2         3  21
61624  1      1        NA  18
61629  3      1         2  19
61630  1      1         1  19
61633  2      2        NA  17

dim(Test_Data)

[1] 2800   28

glimpse(Test_Data)

Rows: 2,800
Columns: 28
$ A1        <int> 2, 2, 5, 4, 2, 6, 2, 4, 4, 2, 4, 2, 5, 5, 4, 4, 4, 5, 4, 4, …
$ A2        <int> 4, 4, 4, 4, 3, 6, 5, 3, 3, 5, 4, 5, 5, 5, 5, 3, 6, 5, 4, 4, …
$ A3        <int> 3, 5, 5, 6, 3, 5, 5, 1, 6, 6, 5, 5, 5, 5, 2, 6, 6, 5, 5, 6, …
$ A4        <int> 4, 2, 4, 5, 4, 6, 3, 5, 3, 6, 6, 5, 6, 6, 2, 6, 2, 4, 4, 5, …
$ A5        <int> 4, 5, 4, 5, 5, 5, 5, 1, 3, 5, 5, 5, 4, 6, 1, 3, 5, 5, 3, 5, …
$ C1        <int> 2, 5, 4, 4, 4, 6, 5, 3, 6, 6, 4, 5, 5, 4, 5, 5, 4, 5, 5, 1, …
$ C2        <int> 3, 4, 5, 4, 4, 6, 4, 2, 6, 5, 3, 4, 4, 4, 5, 5, 4, 5, 4, 1, …
$ C3        <int> 3, 4, 4, 3, 5, 6, 4, 4, 3, 6, 5, 5, 3, 4, 5, 5, 4, 5, 5, 1, …
$ C4        <int> 4, 3, 2, 5, 3, 1, 2, 2, 4, 2, 3, 4, 2, 2, 2, 3, 4, 4, 4, 5, …
$ C5        <int> 4, 4, 5, 5, 2, 3, 3, 4, 5, 1, 2, 5, 2, 1, 2, 5, 4, 3, 6, 6, …
$ E1        <int> 3, 1, 2, 5, 2, 2, 4, 3, 5, 2, 1, 3, 3, 2, 3, 1, 1, 2, 1, 1, …
$ E2        <int> 3, 1, 4, 3, 2, 1, 3, 6, 3, 2, 3, 3, 3, 2, 4, 1, 2, 2, 2, 1, …
$ E3        <int> 3, 6, 4, 4, 5, 6, 4, 4, NA, 4, 2, 4, 3, 4, 3, 6, 5, 4, 4, 4,…
$ E4        <int> 4, 4, 4, 4, 4, 5, 5, 2, 4, 5, 5, 5, 2, 6, 6, 6, 5, 6, 5, 5, …
$ E5        <int> 4, 3, 5, 4, 5, 6, 5, 1, 3, 5, 4, 4, 4, 5, 5, 4, 5, 6, 5, 6, …
$ N1        <int> 3, 3, 4, 2, 2, 3, 1, 6, 5, 5, 3, 4, 1, 1, 2, 4, 4, 6, 5, 5, …
$ N2        <int> 4, 3, 5, 5, 3, 5, 2, 3, 5, 5, 3, 5, 2, 1, 4, 5, 4, 5, 6, 5, …
$ N3        <int> 2, 3, 4, 2, 4, 2, 2, 2, 2, 5, 4, 3, 2, 1, 2, 4, 4, 5, 5, 5, …
$ N4        <int> 2, 5, 2, 4, 4, 2, 1, 6, 3, 2, 2, 2, 2, 2, 2, 5, 4, 4, 5, 1, …
$ N5        <int> 3, 5, 3, 1, 3, 3, 1, 4, 3, 4, 3, NA, 2, 1, 3, 5, 5, 4, 2, 1,…
$ O1        <int> 3, 4, 4, 3, 3, 4, 5, 3, 6, 5, 5, 4, 4, 5, 5, 6, 5, 5, 4, 4, …
$ O2        <int> 6, 2, 2, 3, 3, 3, 2, 2, 6, 1, 3, 6, 2, 3, 2, 6, 1, 1, 2, 1, …
$ O3        <int> 3, 4, 5, 4, 4, 5, 5, 4, 6, 5, 5, 4, 4, 4, 5, 6, 5, 4, 2, 5, …
$ O4        <int> 4, 3, 5, 3, 3, 6, 6, 5, 6, 5, 6, 5, 5, 4, 5, 3, 6, 5, 4, 3, …
$ O5        <int> 3, 3, 2, 5, 3, 1, 1, 3, 1, 2, 3, 4, 2, 4, 5, 2, 3, 4, 2, 2, …
$ gender    <int> 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, …
$ education <int> NA, NA, NA, NA, NA, 3, NA, 2, 1, NA, 1, NA, NA, NA, 1, NA, N…
$ age       <int> 16, 18, 17, 17, 17, 21, 18, 19, 19, 17, 21, 16, 16, 16, 17, …

Test_Data <- drop_na(Test_Data)
# Test_Data <- Test_Data[complete.cases(Test_Data),]
dim(Test_Data)

[1] 2236   28

Content

summary(Test_Data$A1)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   1.000   2.000   2.365   3.000   6.000

Test_Data %>% group_by(A1) %>% summarise(Total = n())

# A tibble: 6 × 2
     A1 Total
  <int> <int>
1     1   767
2     2   666
3     3   315
4     4   260
5     5   163
6     6    65

Test_Data %>% group_by(A2) %>% summarise(Total = n())

# A tibble: 6 × 2
     A2 Total
  <int> <int>
1     1    34
2     2    99
3     3   115
4     4   433
5     5   830
6     6   725

Scale and distribution

Test_Data %>% select(-gender, -education, - age) %>% 
  mutate(Temp_Id = seq(1, dim(Test_Data)[1])) %>% 
  pivot_longer(cols = -Temp_Id, names_to = "Variable", values_to = "Score") %>% 
  group_by(Variable, Score) %>% summarise(Total = n()) %>% 
  pivot_wider(id_cols = Variable, names_from = Score, values_from = Total, values_fill = 0)

`summarise()` has grouped output by 'Variable'. You can override using the
`.groups` argument.

# A tibble: 25 × 7
# Groups:   Variable [25]
   Variable   `1`   `2`   `3`   `4`   `5`   `6`
   <chr>    <int> <int> <int> <int> <int> <int>
 1 A1         767   666   315   260   163    65
 2 A2          34    99   115   433   830   725
 3 A3          71   133   154   456   804   618
 4 A4          96   159   141   356   545   939
 5 A5          48   145   193   490   785   575
 6 C1          49   121   207   505   838   516
 7 C2          67   189   228   504   792   456
 8 C3          66   195   227   610   739   399
 9 C4         650   650   368   348   174    46
10 C5         420   473   266   485   377   215
# ℹ 15 more rows

Variance-covariance matrix

cov(Test_Data %>% select(-gender, -education, - age))

             A1          A2          A3           A4           A5          C1
A1  1.937575288 -0.54784891 -0.47207882 -0.289210119 -0.325245225  0.03378076
A2 -0.547848907  1.33845333  0.72324441  0.573191982  0.555268476  0.12903075
A3 -0.472078816  0.72324441  1.66248194  0.703525391  0.814292060  0.15854014
A4 -0.289210119  0.57319198  0.70352539  2.096532238  0.572968668  0.14544509
A5 -0.325245225  0.55526848  0.81429206  0.572968668  1.577116375  0.18869986
C1  0.033780761  0.12903075  0.15854014  0.145445086  0.188699860  1.48014151
C2  0.024720358  0.19052859  0.24499506  0.414161594  0.179990635  0.68094792
C3 -0.016916193  0.27641842  0.22043958  0.246005771  0.211476230  0.49960980
C4  0.189605920 -0.21931461 -0.20526107 -0.317001837 -0.200970893 -0.57992820
C5  0.054749613 -0.20906440 -0.30796465 -0.564203415 -0.333342138 -0.49679517
E1  0.268834968 -0.44263206 -0.45199601 -0.323503540 -0.498085828 -0.05649030
E2  0.187016004 -0.44923281 -0.59889324 -0.469856287 -0.663323368 -0.19883981
E3 -0.082791258  0.38597327  0.66449957  0.387700152  0.694018161  0.21900005
E4 -0.138642230  0.50907481  0.74184946  0.689566300  0.888443329  0.25562146
E5 -0.033109620  0.45740596  0.44877998  0.306227564  0.445398262  0.42223610
N1  0.346265703 -0.14407779 -0.13825683 -0.213128269 -0.377217226 -0.11239270
N2  0.281965238 -0.06837113 -0.16526355 -0.322601482 -0.364778908 -0.05135009
N3  0.196317329 -0.03773197 -0.05878586 -0.154273571 -0.259833595 -0.02280839
N4  0.096093616 -0.15568629 -0.26696442 -0.361442813 -0.413113862 -0.17107331
N5  0.017940114  0.04530041 -0.08441628 -0.005726109 -0.155887191 -0.09844961
O1  0.003932198  0.13995410  0.20361083  0.068935819  0.205550019  0.24131419
O2  0.142703493  0.05802448  0.06144421  0.114066746  0.002933490 -0.24966963
O3 -0.103631045  0.20232438  0.33083286  0.071804477  0.332540931  0.27232714
O4 -0.146584065  0.07326762  0.03668584 -0.106958335  0.005305095  0.11682014
O5  0.200912063 -0.12218887 -0.06379201  0.067541511 -0.071365854 -0.21209094
             C2            C3         C4          C5          E1         E2
A1  0.024720358 -0.0169161934  0.1896059  0.05474961  0.26883497  0.1870160
A2  0.190528589  0.2764184206 -0.2193146 -0.20906440 -0.44263206 -0.4492328
A3  0.244995057  0.2204395833 -0.2052611 -0.30796465 -0.45199601 -0.5988932
A4  0.414161594  0.2460057709 -0.3170018 -0.56420342 -0.32350354 -0.4698563
A5  0.179990635  0.2114762299 -0.2009709 -0.33334214 -0.49808583 -0.6633234
C1  0.680947922  0.4996098018 -0.5799282 -0.49679517 -0.05649030 -0.1988398
C2  1.719533323  0.6001612819 -0.6851465 -0.63895479  0.04978929 -0.1439441
C3  0.600161282  1.6567640361 -0.6217655 -0.73931757 -0.03984024 -0.1791970
C4 -0.685146454 -0.6217654569  1.8572699  1.07516298  0.21881916  0.4578334
C5 -0.638954789 -0.7393175733  1.0751630  2.65556403  0.17600221  0.6777609
E1  0.049789293 -0.0398402388  0.2188192  0.17600221  2.61831410  1.2099515
E2 -0.143944124 -0.1791970321  0.4578334  0.67776090  1.20995146  2.5781455
E3  0.272113834  0.1780296391 -0.1570558 -0.37029891 -0.72319058 -0.8629380
E4  0.231176838  0.1933106018 -0.2323764 -0.49034369 -0.98018513 -1.2262703
E5  0.430206545  0.3717080277 -0.4258779 -0.52305291 -0.65840487 -0.8324125
N1 -0.033450393 -0.1605395541  0.4486279  0.52364661  0.02271394  0.4205126
N2 -0.002533687 -0.1251307664  0.3176862  0.59179943  0.01746167  0.4811536
N3  0.018292493 -0.1509470811  0.4293525  0.60519784  0.12863655  0.4855427
N4 -0.075729671 -0.2597655609  0.5940266  0.89212360  0.58967395  0.8829934
N5  0.105111597 -0.0740268056  0.4691703  0.48515626  0.11711229  0.6657576
O1  0.227769107  0.1305755324 -0.1499522 -0.15978017 -0.18440008 -0.2870880
O2 -0.102994121 -0.0646916634  0.4358486  0.29864871  0.13908906  0.1907083
O3  0.279080173  0.0878166108 -0.1136313 -0.12742553 -0.41349245 -0.4675143
O4  0.048114042 -0.0002433236  0.1150352  0.26828749  0.15770571  0.3266483
O5 -0.098605692  0.0077359299  0.3315836  0.10605668  0.19729703  0.1694049
            E3          E4          E5          N1           N2          N3
A1 -0.08279126 -0.13864223 -0.03310962  0.34626570  0.281965238  0.19631733
A2  0.38597327  0.50907481  0.45740596 -0.14407779 -0.068371133 -0.03773197
A3  0.66449957  0.74184946  0.44877998 -0.13825683 -0.165263554 -0.05878586
A4  0.38770015  0.68956630  0.30622756 -0.21312827 -0.322601482 -0.15427357
A5  0.69401816  0.88844333  0.44539826 -0.37721723 -0.364778908 -0.25983360
C1  0.21900005  0.25562146  0.42223610 -0.11239270 -0.051350086 -0.02280839
C2  0.27211383  0.23117684  0.43020654 -0.03345039 -0.002533687  0.01829249
C3  0.17802964  0.19331060  0.37170803 -0.16053955 -0.125130766 -0.15094708
C4 -0.15705578 -0.23237645 -0.42587795  0.44862790  0.317686185  0.42935251
C5 -0.37029891 -0.49034369 -0.52305291  0.52364661  0.591799434  0.60519784
E1 -0.72319058 -0.98018513 -0.65840487  0.02271394  0.017461671  0.12863655
E2 -0.86293797 -1.22627035 -0.83241247  0.42051262  0.481153626  0.48554266
E3  1.80214029  0.84497765  0.71444774 -0.09037271 -0.116190225 -0.02611567
E4  0.84497765  2.12897332  0.64379585 -0.33051930 -0.338576397 -0.29182185
E5  0.71444774  0.64379585  1.76921076  0.08179595  0.092794340 -0.12611206
N1 -0.09037271 -0.33051930  0.08179595  2.44751914  1.708530734  1.41329155
N2 -0.11619022 -0.33857640  0.09279434  1.70853073  2.355499794  1.34199293
N3 -0.02611567 -0.29182185 -0.12611206  1.41329155  1.341992932  2.54847222
N4 -0.31581964 -0.70641006 -0.43673066  0.99549851  0.929579426  1.29313691
N5 -0.18834328 -0.22322920 -0.30255450  0.97458169  0.878733196  1.11644155
O1  0.48945224  0.20350838  0.43893658 -0.09153510 -0.079288679 -0.08311902
O2 -0.15175029  0.11602794 -0.17900213  0.33882832  0.290180612  0.27382790
O3  0.65475341  0.36638292  0.47109932 -0.05994805 -0.043196344 -0.04942031
O4  0.06180820 -0.17719962 -0.03062276  0.16750109  0.240420534  0.32082058
O5 -0.23043226  0.08616017 -0.20185214  0.21580843  0.037838422  0.11581964
            N4           N5           O1          O2          O3            O4
A1  0.09609362  0.017940114  0.003932198  0.14270349 -0.10363104 -0.1465840647
A2 -0.15568629  0.045300413  0.139954097  0.05802448  0.20232438  0.0732676200
A3 -0.26696442 -0.084416283  0.203610834  0.06144421  0.33083286  0.0366858364
A4 -0.36144281 -0.005726109  0.068935819  0.11406675  0.07180448 -0.1069583348
A5 -0.41311386 -0.155887191  0.205550019  0.00293349  0.33254093  0.0053050950
C1 -0.17107331 -0.098449612  0.241314188 -0.24966963  0.27232714  0.1168201446
C2 -0.07572967  0.105111597  0.227769107 -0.10299412  0.27908017  0.0481140419
C3 -0.25976556 -0.074026806  0.130575532 -0.06469166  0.08781661 -0.0002433236
C4  0.59402657  0.469170339 -0.149952176  0.43584861 -0.11363132  0.1150352379
C5  0.89212360  0.485156259 -0.159780168  0.29864871 -0.12742553  0.2682874900
E1  0.58967395  0.117112293 -0.184400075  0.13908906 -0.41349245  0.1577057145
E2  0.88299336  0.665757605 -0.287088041  0.19070828 -0.46751430  0.3266483374
E3 -0.31581964 -0.188343278  0.489452242 -0.15175029  0.65475341  0.0618081986
E4 -0.70641006 -0.223229200  0.203508382  0.11602794  0.36638292 -0.1771996174
E5 -0.43673066 -0.302554498  0.438936580 -0.17900213  0.47109932 -0.0306227564
N1  0.99549851  0.974581687 -0.091535100  0.33882832 -0.05994805  0.1675010906
N2  0.92957943  0.878733196 -0.079288679  0.29018061 -0.04319634  0.2404205336
N3  1.29313691  1.116441552 -0.083119024  0.27382790 -0.04942031  0.3208205769
N4  2.43547082  1.004813645 -0.100693552  0.20261413 -0.11021839  0.4247589776
N5  1.00481365  2.630818656 -0.268050770  0.49205456 -0.16166373  0.2028854658
O1 -0.10069355 -0.268050770  1.254497085 -0.40448248  0.52291684  0.2274275332
O2  0.20261413  0.492054564 -0.404482477  2.38969937 -0.53794688 -0.1481232466
O3 -0.11021839 -0.161663725  0.522916842 -0.53794688  1.42387213  0.2425183993
O4  0.42475898  0.202885466  0.227427533 -0.14812325  0.24251840  1.3816474769
O5  0.06958895  0.307254885 -0.375993004  0.68027638 -0.51172235 -0.2868849375
            O5
A1  0.20091206
A2 -0.12218887
A3 -0.06379201
A4  0.06754151
A5 -0.07136585
C1 -0.21209094
C2 -0.09860569
C3  0.00773593
C4  0.33158364
C5  0.10605668
E1  0.19729703
E2  0.16940486
E3 -0.23043226
E4  0.08616017
E5 -0.20185214
N1  0.21580843
N2  0.03783842
N3  0.11581964
N4  0.06958895
N5  0.30725489
O1 -0.37599300
O2  0.68027638
O3 -0.51172235
O4 -0.28688494
O5  1.76757393

Correlation matrix

cor(Test_Data %>% select(-gender, -education, - age))

             A1          A2          A3           A4           A5          C1
A1  1.000000000 -0.34019654 -0.26303089 -0.143493893 -0.186058607  0.01994750
A2 -0.340196538  1.00000000  0.48484732  0.342174560  0.382181386  0.09167269
A3 -0.263030888  0.48484732  1.00000000  0.376834395  0.502886366  0.10106695
A4 -0.143493893  0.34217456  0.37683439  1.000000000  0.315099875  0.08256513
A5 -0.186058607  0.38218139  0.50288637  0.315099875  1.000000000  0.12350601
C1  0.019947502  0.09167269  0.10106695  0.082565128  0.123506009  1.00000000
C2  0.013543165  0.12558947  0.14490173  0.218129173  0.109298132  0.42683201
C3 -0.009441544  0.18562439  0.13282529  0.131997040  0.130827596  0.31904284
C4  0.099950527 -0.13910042 -0.11681285 -0.160647324 -0.117425869 -0.34977205
C5  0.024136449 -0.11089197 -0.14656963 -0.239114851 -0.162884574 -0.25058055
E1  0.119356367 -0.23644513 -0.21664330 -0.138075744 -0.245110232 -0.02869534
E2  0.083675009 -0.24183332 -0.28927921 -0.202097322 -0.328957442 -0.10178833
E3 -0.044305831  0.24851999  0.38390338  0.199457743  0.411665685  0.13409059
E4 -0.068262334  0.30157468  0.39432309  0.326392482  0.484855974  0.14399936
E5 -0.017882783  0.29724217  0.26167680  0.159002415  0.266640959  0.26092395
N1  0.159007327 -0.07960354 -0.06854016 -0.094086484 -0.191997953 -0.05905048
N2  0.131985050 -0.03850611 -0.08351358 -0.145169055 -0.189258901 -0.02750097
N3  0.088346509 -0.02042998 -0.02855976 -0.066742244 -0.129605514 -0.01174365
N4  0.044235789 -0.08622978 -0.13267327 -0.159954829 -0.210788266 -0.09010298
N5  0.007946034  0.02414099 -0.04036475 -0.002438167 -0.076530245 -0.04989039
O1  0.002522152  0.10800632  0.14098977  0.042506891  0.146133849  0.17709097
O2  0.066318345  0.03244427  0.03082697  0.050960848  0.001511058 -0.13275243
O3 -0.062391451  0.14655853  0.21502783  0.041559016  0.221910444  0.18758747
O4 -0.089589857  0.05387805  0.02420591 -0.062844205  0.003593873  0.08168974
O5  0.108564523 -0.07944037 -0.03721337  0.035085786 -0.042743473 -0.13112385
             C2            C3          C4          C5           E1          E2
A1  0.013543165 -0.0094415440  0.09995053  0.02413645  0.119356367  0.08367501
A2  0.125589472  0.1856243880 -0.13910042 -0.11089197 -0.236445131 -0.24183332
A3  0.144901725  0.1328252934 -0.11681285 -0.14656963 -0.216643301 -0.28927921
A4  0.218129173  0.1319970403 -0.16064732 -0.23911485 -0.138075744 -0.20209732
A5  0.109298132  0.1308275955 -0.11742587 -0.16288457 -0.245110232 -0.32895744
C1  0.426832009  0.3190428391 -0.34977205 -0.25058055 -0.028695339 -0.10178833
C2  1.000000000  0.3555759237 -0.38338985 -0.29901050  0.023464958 -0.06836518
C3  0.355575924  1.0000000000 -0.35445308 -0.35247012 -0.019128492 -0.08670552
C4 -0.383389846 -0.3544530778  1.00000000  0.48412600  0.099228623  0.20922628
C5 -0.299010503 -0.3524701242  0.48412600  1.00000000  0.066746555  0.25902663
E1  0.023464958 -0.0191284919  0.09922862  0.06674656  1.000000000  0.46569692
E2 -0.068365175 -0.0867055249  0.20922628  0.25902663  0.465696916  1.00000000
E3  0.154579189  0.1030309453 -0.08584641 -0.16926990 -0.332925906 -0.40034238
E4  0.120824195  0.1029295879 -0.11686097 -0.20622300 -0.415156775 -0.52341650
E5  0.246650460  0.2171109988 -0.23494048 -0.24131118 -0.305909086 -0.38975804
N1 -0.016305453 -0.0797239255  0.21041937  0.20539831  0.008972605  0.16740263
N2 -0.001258943 -0.0633420683  0.15188654  0.23662173  0.007031264  0.19524886
N3  0.008738314 -0.0734605944  0.19734973  0.23263713  0.049798189  0.18942344
N4 -0.037005758 -0.1293182379  0.27930383  0.35079644  0.233512217  0.35238082
N5  0.049419674 -0.0354579174  0.21224994  0.18355144  0.044621704  0.25563303
O1  0.155079607  0.0905725610 -0.09823821 -0.08754063 -0.101745543 -0.15963443
O2 -0.050808398 -0.0325121997  0.20688382  0.11855248  0.055604566  0.07683237
O3  0.178356192  0.0571756155 -0.06987552 -0.06553036 -0.214151550 -0.24400891
O4  0.031215329 -0.0001608256  0.07181163  0.14006300  0.082915922  0.17307252
O5 -0.056559804  0.0045205721  0.18300662  0.04895204  0.091710883  0.07935666
            E3          E4          E5           N1           N2           N3
A1 -0.04430583 -0.06826233 -0.01788278  0.159007327  0.131985050  0.088346509
A2  0.24851999  0.30157468  0.29724217 -0.079603539 -0.038506108 -0.020429977
A3  0.38390338  0.39432309  0.26167680 -0.068540157 -0.083513577 -0.028559755
A4  0.19945774  0.32639248  0.15900242 -0.094086484 -0.145169055 -0.066742244
A5  0.41166568  0.48485597  0.26664096 -0.191997953 -0.189258901 -0.129605514
C1  0.13409059  0.14399936  0.26092395 -0.059050478 -0.027500970 -0.011743647
C2  0.15457919  0.12082420  0.24665046 -0.016305453 -0.001258943  0.008738314
C3  0.10303095  0.10292959  0.21711100 -0.079723926 -0.063342068 -0.073460594
C4 -0.08584641 -0.11686097 -0.23494048  0.210419374  0.151886538  0.197349734
C5 -0.16926990 -0.20622300 -0.24131118  0.205398308  0.236621728  0.232637129
E1 -0.33292591 -0.41515678 -0.30590909  0.008972605  0.007031264  0.049798189
E2 -0.40034238 -0.52341650 -0.38975804  0.167402629  0.195248864  0.189423443
E3  1.00000000  0.43138577  0.40011643 -0.043030853 -0.056394111 -0.012186160
E4  0.43138577  1.00000000  0.33172124 -0.144793368 -0.151192425 -0.125283171
E5  0.40011643  0.33172124  1.00000000  0.039307822  0.045455890 -0.059391856
N1 -0.04303085 -0.14479337  0.03930782  1.000000000  0.711570954  0.565885756
N2 -0.05639411 -0.15119243  0.04545589  0.711570954  1.000000000  0.547732790
N3 -0.01218616 -0.12528317 -0.05939186  0.565885756  0.547732790  1.000000000
N4 -0.15074863 -0.31022750 -0.21039355  0.407742613  0.388108811  0.519054657
N5 -0.08649886 -0.09432362 -0.14023886  0.384069431  0.352996209  0.431172033
O1  0.32552264  0.12452667  0.29463013 -0.052238390 -0.046124834 -0.046486372
O2 -0.07312462  0.05144058 -0.08705561  0.140102223  0.122308101  0.110959915
O3  0.40874079  0.21043337  0.29681592 -0.032112679 -0.023586851 -0.025943584
O4  0.03916996 -0.10331873 -0.01958646  0.091086909  0.133269693  0.170971467
O5 -0.12911009  0.04441530 -0.11414444  0.103756799  0.018543969  0.054569937
            N4           N5           O1           O2          O3            O4
A1  0.04423579  0.007946034  0.002522152  0.066318345 -0.06239145 -0.0895898569
A2 -0.08622978  0.024140990  0.108006320  0.032444268  0.14655853  0.0538780468
A3 -0.13267327 -0.040364753  0.140989765  0.030826973  0.21502783  0.0242059055
A4 -0.15995483 -0.002438167  0.042506891  0.050960848  0.04155902 -0.0628442050
A5 -0.21078827 -0.076530245  0.146133849  0.001511058  0.22191044  0.0035938725
C1 -0.09010298 -0.049890394  0.177090967 -0.132752426  0.18758747  0.0816897366
C2 -0.03700576  0.049419674  0.155079607 -0.050808398  0.17835619  0.0312153292
C3 -0.12931824 -0.035457917  0.090572561 -0.032512200  0.05717562 -0.0001608256
C4  0.27930383  0.212249943 -0.098238208  0.206883818 -0.06987552  0.0718116262
C5  0.35079644  0.183551439 -0.087540628  0.118552475 -0.06553036  0.1400629954
E1  0.23351222  0.044621704 -0.101745543  0.055604566 -0.21415155  0.0829159219
E2  0.35238082  0.255633030 -0.159634428  0.076832365 -0.24400891  0.1730725196
E3 -0.15074863 -0.086498858  0.325522638 -0.073124615  0.40874079  0.0391699633
E4 -0.31022750 -0.094323615  0.124526667  0.051440579  0.21043337 -0.1033187270
E5 -0.21039355 -0.140238859  0.294630133 -0.087055615  0.29681592 -0.0195864563
N1  0.40774261  0.384069431 -0.052238390  0.140102223 -0.03211268  0.0910869094
N2  0.38810881  0.352996209 -0.046124834  0.122308101 -0.02358685  0.1332696930
N3  0.51905466  0.431172033 -0.046486372  0.110959915 -0.02594358  0.1709714673
N4  1.00000000  0.396961696 -0.057607015  0.083985947 -0.05918711  0.2315541012
N5  0.39696170  1.000000000 -0.147549171  0.196243903 -0.08352791  0.1064159817
O1 -0.05760701 -0.147549171  1.000000000 -0.233610979  0.39125717  0.1727466319
O2  0.08398595  0.196243903 -0.233610979  1.000000000 -0.29163004 -0.0815178964
O3 -0.05918711 -0.083527913  0.391257168 -0.291630043  1.00000000  0.1729062034
O4  0.23155410  0.106415982  0.172746632 -0.081517896  0.17290620  1.0000000000
O5  0.03353977  0.142483491 -0.252496954  0.330997691 -0.32255970 -0.1835778712
             O5
A1  0.108564523
A2 -0.079440368
A3 -0.037213370
A4  0.035085786
A5 -0.042743473
C1 -0.131123855
C2 -0.056559804
C3  0.004520572
C4  0.183006619
C5  0.048952044
E1  0.091710883
E2  0.079356655
E3 -0.129110091
E4  0.044415304
E5 -0.114144445
N1  0.103756799
N2  0.018543969
N3  0.054569937
N4  0.033539766
N5  0.142483491
O1 -0.252496954
O2  0.330997691
O3 -0.322559697
O4 -0.183577871
O5  1.000000000

Visual: correlation matrix

corrplot::corrplot(cor(Test_Data %>% select(-gender, -education, - age)), 
                   method = "color")

corrplot::corrplot(cor(Test_Data %>% select(-gender, -education, - age)), 
                   method = "circle")

corrplot::corrplot(cor(Test_Data %>% select(-gender, -education, - age)), 
                   method = "circle", type = "lower")

GGally::ggcorr(Test_Data %>% select(-gender, -education, - age))

Registered S3 method overwritten by 'GGally':
  method from   
  +.gg   ggplot2

One final nuance

Test_Data %<>% mutate(Temp_Id = seq(1, dim(Test_Data)[1])) 

Data_Factorial <- Test_Data %>% select(-gender, -education, - age, -Temp_Id)

EFA

How many factors?

Eigenvalues_Correlation <- eigen(cor(Data_Factorial))
Eigenvalues_Correlation$values

 [1] 5.0685162 2.7624793 2.1526230 1.8923330 1.5175329 1.0788293 0.8309057
 [8] 0.8045002 0.7140883 0.7015381 0.6808421 0.6489735 0.6312563 0.5880320
[15] 0.5659652 0.5448396 0.5199335 0.4938686 0.4827362 0.4425003 0.4288706
[22] 0.4070974 0.3888753 0.3847626 0.2681008

EMPKC(Data_Factorial) # Empirical Kaiser Criterion (Braeken and van Assen, 2017)



EMPIRICAL KAISER CRITERION


Kind of correlations analyzed: Pearson

    Nfactors    Eigenvalue    Reference Values
           1         5.069               1.223
           2         2.762               1.211
           3         2.153               1.200
           4         1.892               1.187
           5         1.518               1.175
           6         1.079               1.162
           7         0.831               1.148
           8         0.805               1.134
           9         0.714               1.119
          10         0.702               1.104
          11         0.681               1.087
          12         0.649               1.070
          13         0.631               1.052
          14         0.588               1.032
          15         0.566               1.011
          16         0.545               1.000
          17         0.520               1.000
          18         0.494               1.000
          19         0.483               1.000
          20         0.443               1.000
          21         0.429               1.000
          22         0.407               1.000
          23         0.389               1.000
          24         0.385               1.000
          25         0.268               1.000


The number of factors according to the Empirical Kaiser Criterion = 5

SCREE_PLOT(Data_Factorial)


Scree Plot:


Specified kind of correlations for this analysis: Pearson



Total Variance Explained (Initial Eigenvalues):

             Eigenvalues    Proportion of Variance    Cumulative Prop. Variance
Factor 1            5.07                      0.20                         0.20
Factor 2            2.76                      0.11                         0.31
Factor 3            2.15                      0.09                         0.40
Factor 4            1.89                      0.08                         0.48
Factor 5            1.52                      0.06                         0.54
Factor 6            1.08                      0.04                         0.58
Factor 7            0.83                      0.03                         0.61
Factor 8            0.80                      0.03                         0.64
Factor 9            0.71                      0.03                         0.67
Factor 10           0.70                      0.03                         0.70
Factor 11           0.68                      0.03                         0.73
Factor 12           0.65                      0.03                         0.75
Factor 13           0.63                      0.03                         0.78
Factor 14           0.59                      0.02                         0.80
Factor 15           0.57                      0.02                         0.83
Factor 16           0.54                      0.02                         0.85
Factor 17           0.52                      0.02                         0.87
Factor 18           0.49                      0.02                         0.89
Factor 19           0.48                      0.02                         0.91
Factor 20           0.44                      0.02                         0.92
Factor 21           0.43                      0.02                         0.94
Factor 22           0.41                      0.02                         0.96
Factor 23           0.39                      0.02                         0.97
Factor 24           0.38                      0.02                         0.99
Factor 25           0.27                      0.01                         1.00

fa.parallel(Data_Factorial, fa = "fa") # n.iter =

Parallel analysis suggests that the number of factors =  6  and the number of components =  NA

RAWPAR(Data_Factorial, factormodel = "PAF", Ndatasets = 1000)



PARALLEL ANALYSIS


Randomization method: generated data


Type of correlations specified for the real data eigenvalues: Pearson


Type of correlations specified for the random data eigenvalues: pearson


Extraction Method: Common Factor Analysis


Variables = 25


Cases = 2236


Ndatasets = 1000


Percentile = 95


Compare the Real Data eigenvalues below to the corresponding

random data Mean and Percentile eigenvalues

   Root   Real Data     Mean   Percentile
      1       4.468    0.207        0.235
      2       2.214    0.179        0.199
      3       1.482    0.157        0.177
      4       1.194    0.137        0.155
      5       0.862    0.120        0.135
      6       0.415    0.104        0.120
      7       0.180    0.089        0.102
      8       0.124    0.074        0.087
      9       0.042    0.060        0.072
     10       0.023    0.046        0.059
     11       0.006    0.033        0.045
     12      -0.037    0.019        0.032
     13      -0.069    0.007        0.018
     14      -0.081   -0.006        0.005
     15      -0.104   -0.019       -0.007
     16      -0.112   -0.032       -0.021
     17      -0.121   -0.044       -0.034
     18      -0.141   -0.058       -0.046
     19      -0.149   -0.070       -0.060
     20      -0.171   -0.084       -0.072
     21      -0.176   -0.097       -0.085
     22      -0.193   -0.112       -0.100
     23      -0.205   -0.128       -0.114
     24      -0.209   -0.145       -0.131
     25      -0.232   -0.167       -0.149


The number of factors according to the parallel analysis = 8

Ful model

Full <- fa(Data_Factorial, nfactors = 25, rotate = "none")

Full

Factor Analysis using method =  minres
Call: fa(r = Data_Factorial, nfactors = 25, rotate = "none")
Standardized loadings (pattern matrix) based upon correlation matrix
     MR1   MR2   MR3   MR4   MR5   MR6   MR7   MR8   MR9  MR10  MR11  MR12
A1 -0.22 -0.03  0.15  0.03 -0.42  0.31  0.07 -0.05  0.02  0.01 -0.02  0.10
A2  0.47  0.31 -0.20  0.14  0.37 -0.23  0.14  0.15 -0.12  0.01 -0.05  0.07
A3  0.53  0.31 -0.25  0.10  0.28  0.02  0.13 -0.12  0.09  0.00 -0.02 -0.12
A4  0.41  0.13 -0.16  0.30  0.18  0.03 -0.01 -0.23 -0.06  0.23 -0.02  0.17
A5  0.57  0.19 -0.27  0.04  0.18  0.15  0.02 -0.05  0.19 -0.10  0.07 -0.07
C1  0.33  0.13  0.47  0.14  0.00  0.11 -0.09  0.19  0.17  0.03 -0.03  0.03
C2  0.33  0.19  0.49  0.32  0.06  0.19 -0.10  0.06 -0.05  0.23 -0.03 -0.11
C3  0.33  0.05  0.35  0.34  0.03  0.02  0.07  0.14 -0.07 -0.20  0.06  0.01
C4 -0.47  0.13 -0.45 -0.24  0.02  0.27  0.08  0.06 -0.11  0.04  0.05  0.04
C5 -0.50  0.16 -0.29 -0.31  0.12  0.08 -0.01  0.26  0.10  0.17 -0.08 -0.06
E1 -0.43 -0.21  0.27  0.14  0.27  0.25  0.23 -0.14  0.06 -0.01 -0.09 -0.03
E2 -0.63 -0.06  0.22  0.09  0.33  0.11  0.11 -0.01  0.03  0.03  0.20  0.02
E3  0.55  0.34 -0.09 -0.20 -0.10  0.21  0.03 -0.09 -0.07 -0.11  0.01 -0.07
E4  0.62  0.19 -0.34  0.08 -0.19  0.15 -0.16  0.03  0.15  0.01  0.02  0.12
E5  0.53  0.30  0.11 -0.04 -0.23 -0.03  0.22  0.15 -0.11  0.02 -0.06  0.02
N1 -0.43  0.65  0.06  0.09 -0.27 -0.13  0.13 -0.12  0.01  0.05  0.05 -0.03
N2 -0.42  0.65  0.12  0.05 -0.22 -0.21  0.15  0.00  0.14  0.05  0.09 -0.01
N3 -0.40  0.63  0.06  0.06 -0.01 -0.01 -0.13 -0.10  0.03 -0.11 -0.16  0.05
N4 -0.54  0.42  0.09 -0.04  0.23  0.08 -0.11 -0.02 -0.06 -0.08 -0.22 -0.02
N5 -0.36  0.44 -0.05  0.22  0.13  0.05 -0.27  0.02 -0.15 -0.03  0.18 -0.01
O1  0.33  0.18  0.24 -0.36  0.02  0.16  0.14 -0.01 -0.09  0.01 -0.02  0.10
O2 -0.20  0.09 -0.33  0.39 -0.05  0.15  0.10  0.15 -0.01 -0.01  0.01  0.01
O3  0.40  0.28  0.19 -0.47  0.03  0.13 -0.05 -0.03 -0.08  0.05  0.11 -0.11
O4 -0.09  0.24  0.18 -0.24  0.31  0.07  0.01  0.08  0.08 -0.08  0.06  0.18
O5 -0.20 -0.05 -0.29  0.44 -0.15  0.21  0.06  0.06 -0.07 -0.05 -0.02 -0.06
    MR13  MR14  MR15  MR16  MR17  MR18  MR19  MR20  MR21  MR22  MR23 MR24 MR25
A1  0.05  0.17  0.00  0.08 -0.02 -0.02 -0.03  0.03  0.02 -0.01  0.00    0    0
A2  0.07  0.07 -0.07  0.07  0.00  0.05 -0.01  0.02  0.00  0.03  0.00    0    0
A3  0.01 -0.02  0.06  0.02 -0.08  0.01 -0.06  0.02  0.00 -0.05  0.00    0    0
A4  0.02  0.02  0.07  0.00 -0.01 -0.03  0.04  0.00  0.00  0.00  0.01    0    0
A5  0.04  0.09 -0.03 -0.05  0.06 -0.09  0.01 -0.03  0.03  0.02  0.00    0    0
C1  0.08 -0.03 -0.03 -0.07 -0.13  0.00 -0.01  0.01 -0.04  0.01  0.01    0    0
C2 -0.08 -0.02  0.01  0.03  0.04  0.00  0.02 -0.03  0.01  0.00 -0.01    0    0
C3  0.09  0.01  0.12  0.12  0.02 -0.04  0.03 -0.02 -0.01  0.00  0.00    0    0
C4  0.10 -0.06 -0.03  0.03 -0.08 -0.02  0.06 -0.05 -0.02 -0.02 -0.01    0    0
C5  0.02  0.07  0.10  0.01  0.03  0.00 -0.01 -0.01  0.01  0.02  0.01    0    0
E1  0.03 -0.05 -0.15  0.02  0.03  0.02  0.00 -0.02  0.00  0.02  0.01    0    0
E2  0.01  0.10  0.06 -0.09  0.01  0.07  0.02  0.05 -0.01  0.00 -0.01    0    0
E3 -0.14  0.06  0.04 -0.02 -0.02  0.05  0.05  0.00 -0.04  0.03  0.01    0    0
E4  0.04 -0.06 -0.06  0.03  0.09  0.06  0.00  0.02 -0.03  0.00 -0.01    0    0
E5  0.01  0.04 -0.07 -0.15  0.01 -0.03  0.04  0.02  0.03 -0.03  0.00    0    0
N1  0.06 -0.10  0.03 -0.03 -0.01 -0.08 -0.03  0.02 -0.01  0.05 -0.01    0    0
N2 -0.04  0.02 -0.03  0.07  0.06  0.05  0.03 -0.03 -0.01 -0.03  0.01    0    0
N3  0.02  0.03  0.02 -0.01 -0.07  0.08  0.02 -0.03  0.05  0.01 -0.01    0    0
N4  0.00  0.02 -0.01  0.01  0.08 -0.06  0.01  0.05 -0.04 -0.02  0.00    0    0
N5  0.01  0.05 -0.08 -0.05  0.00 -0.02 -0.06 -0.03  0.00 -0.01  0.01    0    0
O1 -0.02 -0.01  0.06 -0.04  0.06  0.03 -0.10 -0.05 -0.02  0.00  0.00    0    0
O2 -0.21 -0.01 -0.05  0.06 -0.06 -0.03 -0.03  0.02  0.00  0.01  0.00    0    0
O3  0.07 -0.07 -0.04  0.09 -0.01  0.02  0.01  0.06  0.04  0.00  0.01    0    0
O4 -0.11 -0.13  0.04  0.00  0.00 -0.04  0.02  0.01  0.04  0.00  0.00    0    0
O5  0.07 -0.12  0.09 -0.08  0.06  0.07  0.00  0.02  0.03  0.00  0.01    0    0
     h2   u2 com
A1 0.41 0.59 3.6
A2 0.65 0.35 5.2
A3 0.60 0.40 3.7
A4 0.48 0.52 5.1
A5 0.58 0.42 2.8
C1 0.48 0.52 3.7
C2 0.61 0.39 4.5
C3 0.46 0.54 5.0
C4 0.63 0.37 3.9
C5 0.62 0.38 4.4
E1 0.57 0.43 6.0
E2 0.66 0.34 2.5
E3 0.58 0.42 3.2
E4 0.69 0.31 2.9
E5 0.56 0.44 3.4
N1 0.77 0.23 2.7
N2 0.77 0.23 2.8
N3 0.65 0.35 2.3
N4 0.62 0.38 3.2
N5 0.54 0.46 4.6
O1 0.41 0.59 4.9
O2 0.42 0.58 4.5
O3 0.57 0.43 4.0
O4 0.35 0.65 6.4
O5 0.45 0.55 4.1

                       MR1  MR2  MR3  MR4  MR5  MR6  MR7  MR8  MR9 MR10 MR11
SS loadings           4.67 2.41 1.70 1.40 1.07 0.63 0.39 0.34 0.24 0.24 0.21
Proportion Var        0.19 0.10 0.07 0.06 0.04 0.03 0.02 0.01 0.01 0.01 0.01
Cumulative Var        0.19 0.28 0.35 0.41 0.45 0.47 0.49 0.50 0.51 0.52 0.53
Proportion Explained  0.33 0.17 0.12 0.10 0.08 0.04 0.03 0.02 0.02 0.02 0.01
Cumulative Proportion 0.33 0.50 0.62 0.72 0.80 0.84 0.87 0.89 0.91 0.93 0.94
                      MR12 MR13 MR14 MR15 MR16 MR17 MR18 MR19 MR20 MR21 MR22
SS loadings           0.16 0.13 0.12 0.10 0.10 0.07 0.05 0.03 0.02 0.02 0.01
Proportion Var        0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Cumulative Var        0.54 0.54 0.55 0.55 0.56 0.56 0.56 0.56 0.56 0.56 0.56
Proportion Explained  0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00
Cumulative Proportion 0.95 0.96 0.97 0.98 0.99 0.99 0.99 1.00 1.00 1.00 1.00
                      MR23 MR24 MR25
SS loadings           0.00 0.00 0.00
Proportion Var        0.00 0.00 0.00
Cumulative Var        0.56 0.56 0.56
Proportion Explained  0.00 0.00 0.00
Cumulative Proportion 1.00 1.00 1.00

Mean item complexity =  4
Test of the hypothesis that 25 factors are sufficient.

df null model =  300  with the objective function =  7.41 with Chi Square =  16484.78
df of  the model are -25  and the objective function was  0 

The root mean square of the residuals (RMSR) is  0 
The df corrected root mean square of the residuals is  NA 

The harmonic n.obs is  2236 with the empirical chi square  0  with prob <  NA 
The total n.obs was  2236  with Likelihood Chi Square =  0  with prob <  NA 

Tucker Lewis Index of factoring reliability =  1.019
Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                                   MR1  MR2  MR3  MR4  MR5  MR6
Correlation of (regression) scores with factors   0.96 0.94 0.89 0.86 0.85 0.78
Multiple R square of scores with factors          0.92 0.88 0.80 0.75 0.72 0.60
Minimum correlation of possible factor scores     0.85 0.76 0.59 0.49 0.44 0.20
                                                    MR7   MR8   MR9  MR10  MR11
Correlation of (regression) scores with factors    0.70  0.66  0.61  0.59  0.59
Multiple R square of scores with factors           0.49  0.43  0.37  0.35  0.35
Minimum correlation of possible factor scores     -0.02 -0.13 -0.25 -0.30 -0.29
                                                   MR12  MR13  MR14  MR15  MR16
Correlation of (regression) scores with factors    0.50  0.47  0.46  0.43  0.42
Multiple R square of scores with factors           0.25  0.22  0.21  0.19  0.18
Minimum correlation of possible factor scores     -0.49 -0.57 -0.58 -0.62 -0.64
                                                   MR17  MR18  MR19  MR20  MR21
Correlation of (regression) scores with factors    0.39  0.36  0.26  0.23  0.19
Multiple R square of scores with factors           0.15  0.13  0.07  0.05  0.04
Minimum correlation of possible factor scores     -0.70 -0.75 -0.86 -0.90 -0.93
                                                   MR22  MR23  MR24 MR25
Correlation of (regression) scores with factors    0.17  0.06  0.01    0
Multiple R square of scores with factors           0.03  0.00  0.00    0
Minimum correlation of possible factor scores     -0.94 -0.99 -1.00   -1

sum(Full$loadings[,1]*Full$loadings[,1])

[1] 4.669779

Different rotations

EFA_Varimax <- fa(Data_Factorial, nfactors = 5, rotate = "varimax")

EFA_Varimax

Factor Analysis using method =  minres
Call: fa(r = Data_Factorial, nfactors = 5, rotate = "varimax")
Standardized loadings (pattern matrix) based upon correlation matrix
     MR2   MR1   MR3   MR5   MR4   h2   u2 com
A1  0.11  0.04  0.03 -0.42 -0.09 0.20 0.80 1.3
A2  0.04  0.22  0.14  0.61  0.04 0.44 0.56 1.4
A3  0.01  0.32  0.11  0.64  0.05 0.53 0.47 1.6
A4 -0.06  0.20  0.22  0.43 -0.13 0.30 0.70 2.2
A5 -0.12  0.38  0.09  0.53  0.05 0.46 0.54 2.0
C1  0.02  0.06  0.54  0.03  0.21 0.34 0.66 1.3
C2  0.09  0.02  0.64  0.11  0.10 0.44 0.56 1.2
C3 -0.03  0.03  0.56  0.11 -0.01 0.33 0.67 1.1
C4  0.24 -0.07 -0.63 -0.03 -0.10 0.47 0.53 1.4
C5  0.28 -0.18 -0.56 -0.04  0.04 0.43 0.57 1.7
E1  0.03 -0.57  0.03 -0.12 -0.06 0.34 0.66 1.1
E2  0.24 -0.68 -0.10 -0.11 -0.05 0.55 0.45 1.4
E3  0.02  0.55  0.09  0.26  0.28 0.46 0.54 2.0
E4 -0.12  0.64  0.10  0.32 -0.08 0.54 0.46 1.7
E5  0.04  0.51  0.32  0.09  0.20 0.42 0.58 2.1
N1  0.79  0.08 -0.04 -0.21 -0.08 0.68 0.32 1.2
N2  0.75  0.04 -0.02 -0.19 -0.01 0.61 0.39 1.1
N3  0.73 -0.06 -0.06 -0.02  0.00 0.55 0.45 1.0
N4  0.59 -0.35 -0.18  0.01  0.08 0.51 0.49 1.9
N5  0.54 -0.16 -0.05  0.11 -0.16 0.35 0.65 1.5
O1 -0.01  0.21  0.12  0.05  0.50 0.32 0.68 1.5
O2  0.18  0.00 -0.10  0.10 -0.48 0.28 0.72 1.5
O3  0.03  0.31  0.07  0.12  0.60 0.48 0.52 1.6
O4  0.22 -0.19 -0.04  0.14  0.37 0.24 0.76 2.7
O5  0.08 -0.01 -0.06 -0.02 -0.54 0.31 0.69 1.1

                       MR2  MR1  MR3  MR5  MR4
SS loadings           2.71 2.49 2.02 1.79 1.54
Proportion Var        0.11 0.10 0.08 0.07 0.06
Cumulative Var        0.11 0.21 0.29 0.36 0.42
Proportion Explained  0.26 0.24 0.19 0.17 0.15
Cumulative Proportion 0.26 0.49 0.68 0.85 1.00

Mean item complexity =  1.5
Test of the hypothesis that 5 factors are sufficient.

df null model =  300  with the objective function =  7.41 with Chi Square =  16484.78
df of  the model are 185  and the objective function was  0.63 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic n.obs is  2236 with the empirical chi square  1046.45  with prob <  3.1e-120 
The total n.obs was  2236  with Likelihood Chi Square =  1400.38  with prob <  1.6e-185 

Tucker Lewis Index of factoring reliability =  0.878
RMSEA index =  0.054  and the 90 % confidence intervals are  0.052 0.057
BIC =  -26.42
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   MR2  MR1  MR3  MR5  MR4
Correlation of (regression) scores with factors   0.92 0.88 0.86 0.84 0.83
Multiple R square of scores with factors          0.85 0.77 0.74 0.70 0.69
Minimum correlation of possible factor scores     0.71 0.54 0.48 0.41 0.38

EFA_varimin <- fa(Data_Factorial, nfactors = 5, rotate = "varimin")

EFA_varimin

Factor Analysis using method =  minres
Call: fa(r = Data_Factorial, nfactors = 5, rotate = "varimin")
Standardized loadings (pattern matrix) based upon correlation matrix
     MR1   MR2   MR3   MR4   MR5   h2   u2 com
A1 -0.25 -0.15  0.18  0.12 -0.25 0.20 0.80 4.0
A2  0.40  0.31 -0.21  0.19  0.31 0.44 0.56 3.9
A3  0.45  0.36 -0.27  0.23  0.26 0.53 0.47 3.9
A4  0.32  0.07 -0.24  0.27  0.24 0.30 0.70 3.9
A5  0.48  0.28 -0.31  0.19  0.11 0.46 0.54 2.9
C1  0.39 -0.13  0.34  0.23  0.09 0.34 0.66 3.0
C2  0.37 -0.16  0.33  0.34  0.23 0.44 0.56 4.1
C3  0.34 -0.23  0.17  0.30  0.19 0.33 0.67 4.0
C4 -0.50  0.35 -0.19 -0.22 -0.05 0.47 0.53 2.6
C5 -0.46  0.36 -0.03 -0.30  0.01 0.43 0.57 2.7
E1 -0.27 -0.29  0.19 -0.25  0.29 0.34 0.66 4.7
E2 -0.46 -0.14  0.27 -0.31  0.39 0.55 0.45 3.7
E3  0.46  0.39 -0.04  0.23 -0.19 0.46 0.54 2.9
E4  0.42  0.23 -0.36  0.40 -0.16 0.54 0.46 3.9
E5  0.44  0.18  0.10  0.37 -0.20 0.42 0.58 2.9
N1 -0.50  0.37  0.37  0.39  0.02 0.68 0.32 3.7
N2 -0.45  0.36  0.41  0.32  0.04 0.61 0.39 3.8
N3 -0.41  0.40  0.34  0.24  0.20 0.55 0.45 4.1
N4 -0.45  0.31  0.33 -0.08  0.31 0.51 0.49 3.7
N5 -0.37  0.24  0.13  0.19  0.32 0.35 0.65 3.6
O1  0.40  0.23  0.26 -0.07 -0.16 0.32 0.68 2.9
O2 -0.33  0.00 -0.28  0.26  0.17 0.28 0.72 3.5
O3  0.47  0.38  0.26 -0.07 -0.20 0.48 0.52 3.0
O4  0.05  0.27  0.29 -0.21  0.19 0.24 0.76 3.7
O5 -0.34 -0.15 -0.29  0.26  0.10 0.31 0.69 3.5

                       MR1  MR2  MR3  MR4  MR5
SS loadings           4.07 1.90 1.78 1.67 1.12
Proportion Var        0.16 0.08 0.07 0.07 0.04
Cumulative Var        0.16 0.24 0.31 0.38 0.42
Proportion Explained  0.39 0.18 0.17 0.16 0.11
Cumulative Proportion 0.39 0.57 0.74 0.89 1.00

Mean item complexity =  3.5
Test of the hypothesis that 5 factors are sufficient.

df null model =  300  with the objective function =  7.41 with Chi Square =  16484.78
df of  the model are 185  and the objective function was  0.63 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic n.obs is  2236 with the empirical chi square  1046.45  with prob <  3.1e-120 
The total n.obs was  2236  with Likelihood Chi Square =  1400.38  with prob <  1.6e-185 

Tucker Lewis Index of factoring reliability =  0.878
RMSEA index =  0.054  and the 90 % confidence intervals are  0.052 0.057
BIC =  -26.42
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   MR1  MR2  MR3  MR4  MR5
Correlation of (regression) scores with factors   0.93 0.88 0.87 0.85 0.81
Multiple R square of scores with factors          0.86 0.77 0.75 0.73 0.65
Minimum correlation of possible factor scores     0.73 0.53 0.50 0.45 0.30

EFA_oblimin <- fa(Data_Factorial, nfactors = 5, rotate = "oblimin")

EFA_oblimin

Factor Analysis using method =  minres
Call: fa(r = Data_Factorial, nfactors = 5, rotate = "oblimin")
Standardized loadings (pattern matrix) based upon correlation matrix
     MR2   MR1   MR3   MR5   MR4   h2   u2 com
A1  0.21 -0.18  0.08 -0.43 -0.07 0.20 0.80 2.0
A2 -0.02 -0.01  0.07  0.64  0.02 0.44 0.56 1.0
A3 -0.02 -0.11  0.03  0.67  0.03 0.53 0.47 1.1
A4 -0.06 -0.07  0.19  0.45 -0.17 0.30 0.70 1.7
A5 -0.12 -0.22  0.00  0.54  0.04 0.46 0.54 1.5
C1  0.08  0.04  0.55  0.00  0.16 0.34 0.66 1.2
C2  0.15  0.10  0.66  0.09  0.04 0.44 0.56 1.2
C3  0.03  0.05  0.58  0.08 -0.07 0.33 0.67 1.1
C4  0.15  0.01 -0.64  0.04 -0.04 0.47 0.53 1.1
C5  0.17  0.15 -0.56  0.03  0.09 0.43 0.57 1.4
E1 -0.07  0.54  0.10 -0.11 -0.10 0.34 0.66 1.3
E2  0.09  0.67 -0.02 -0.07 -0.07 0.55 0.45 1.1
E3  0.09 -0.42  0.01  0.24  0.30 0.46 0.54 2.6
E4 -0.01 -0.57  0.02  0.32 -0.07 0.54 0.46 1.6
E5  0.16 -0.43  0.27  0.07  0.21 0.42 0.58 2.6
N1  0.83 -0.10  0.00 -0.10 -0.05 0.68 0.32 1.1
N2  0.78 -0.04  0.01 -0.10  0.02 0.61 0.39 1.0
N3  0.70  0.12 -0.03  0.09  0.02 0.55 0.45 1.1
N4  0.46  0.41 -0.14  0.10  0.09 0.51 0.49 2.3
N5  0.48  0.21 -0.02  0.21 -0.16 0.35 0.65 2.0
O1  0.00 -0.09  0.08  0.00  0.52 0.32 0.68 1.1
O2  0.19 -0.06 -0.08  0.17 -0.48 0.28 0.72 1.7
O3  0.04 -0.16  0.00  0.07  0.62 0.48 0.52 1.2
O4  0.11  0.33 -0.05  0.16  0.37 0.24 0.76 2.6
O5  0.12 -0.10 -0.03  0.04 -0.55 0.31 0.69 1.2

                       MR2  MR1  MR3  MR5  MR4
SS loadings           2.56 2.21 2.07 2.04 1.65
Proportion Var        0.10 0.09 0.08 0.08 0.07
Cumulative Var        0.10 0.19 0.27 0.36 0.42
Proportion Explained  0.24 0.21 0.20 0.19 0.16
Cumulative Proportion 0.24 0.45 0.65 0.84 1.00

 With factor correlations of 
      MR2   MR1   MR3   MR5   MR4
MR2  1.00  0.21 -0.19 -0.03  0.00
MR1  0.21  1.00 -0.25 -0.33 -0.17
MR3 -0.19 -0.25  1.00  0.19  0.19
MR5 -0.03 -0.33  0.19  1.00  0.17
MR4  0.00 -0.17  0.19  0.17  1.00

Mean item complexity =  1.5
Test of the hypothesis that 5 factors are sufficient.

df null model =  300  with the objective function =  7.41 with Chi Square =  16484.78
df of  the model are 185  and the objective function was  0.63 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic n.obs is  2236 with the empirical chi square  1046.45  with prob <  3.1e-120 
The total n.obs was  2236  with Likelihood Chi Square =  1400.38  with prob <  1.6e-185 

Tucker Lewis Index of factoring reliability =  0.878
RMSEA index =  0.054  and the 90 % confidence intervals are  0.052 0.057
BIC =  -26.42
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   MR2  MR1  MR3  MR5  MR4
Correlation of (regression) scores with factors   0.93 0.89 0.88 0.88 0.85
Multiple R square of scores with factors          0.86 0.79 0.77 0.77 0.72
Minimum correlation of possible factor scores     0.71 0.59 0.55 0.55 0.44

loadings <- EFA_oblimin$loadings
loadings


Loadings:
   MR2    MR1    MR3    MR5    MR4   
A1  0.205 -0.178        -0.426       
A2                       0.638       
A3        -0.107         0.667       
A4                0.185  0.450 -0.167
A5 -0.121 -0.217         0.535       
C1                0.550         0.160
C2  0.145  0.104  0.659              
C3                0.576              
C4  0.154        -0.637              
C5  0.167  0.150 -0.562              
E1         0.539  0.104 -0.113       
E2         0.672                     
E3        -0.423         0.242  0.298
E4        -0.572         0.318       
E5  0.164 -0.426  0.268         0.207
N1  0.833 -0.103        -0.103       
N2  0.781                            
N3  0.701  0.116                     
N4  0.465  0.411 -0.137              
N5  0.478  0.207         0.206 -0.161
O1                              0.515
O2  0.188                0.170 -0.481
O3        -0.159                0.623
O4  0.110  0.330         0.161  0.366
O5  0.117                      -0.551

                MR2   MR1   MR3   MR5   MR4
SS loadings    2.49 1.957 1.956 1.863 1.587
Proportion Var 0.10 0.078 0.078 0.075 0.063
Cumulative Var 0.10 0.178 0.256 0.331 0.394

fa.diagram(EFA_oblimin)

communalities <- EFA_oblimin$communality
communalities

       A1        A2        A3        A4        A5        C1        C2        C3 
0.1977705 0.4403525 0.5263649 0.2989709 0.4553709 0.3397847 0.4392911 0.3269120 
       C4        C5        E1        E2        E3        E4        E5        N1 
0.4686006 0.4312841 0.3412718 0.5468470 0.4558448 0.5445540 0.4157993 0.6787696 
       N2        N3        N4        N5        O1        O2        O3        O4 
0.6057681 0.5456634 0.5065663 0.3536267 0.3155269 0.2828237 0.4753585 0.2421532 
       O5 
0.3068156

uniquenesses <- EFA_oblimin$uniquenesses
uniquenesses

       A1        A2        A3        A4        A5        C1        C2        C3 
0.8022295 0.5596475 0.4736351 0.7010291 0.5446291 0.6602153 0.5607089 0.6730880 
       C4        C5        E1        E2        E3        E4        E5        N1 
0.5313994 0.5687159 0.6587282 0.4531530 0.5441552 0.4554460 0.5842007 0.3212304 
       N2        N3        N4        N5        O1        O2        O3        O4 
0.3942319 0.4543366 0.4934337 0.6463733 0.6844731 0.7171763 0.5246415 0.7578468 
       O5 
0.6931844

communalities + uniquenesses

A1 A2 A3 A4 A5 C1 C2 C3 C4 C5 E1 E2 E3 E4 E5 N1 N2 N3 N4 N5 O1 O2 O3 O4 O5 
 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1

factor_correlations <- EFA_oblimin$Phi
factor_correlations

             MR2        MR1        MR3         MR5          MR4
MR2  1.000000000  0.2146213 -0.1854540 -0.02606769 -0.002886653
MR1  0.214621297  1.0000000 -0.2451715 -0.33238603 -0.166980342
MR3 -0.185454002 -0.2451715  1.0000000  0.18935459  0.185444183
MR5 -0.026067686 -0.3323860  0.1893546  1.00000000  0.170964071
MR4 -0.002886653 -0.1669803  0.1854442  0.17096407  1.000000000

Esimation method

EFA <- fa(Data_Factorial, nfactors = 5, rotate = "oblimin", fm = "pa")

EFA

Factor Analysis using method =  pa
Call: fa(r = Data_Factorial, nfactors = 5, rotate = "oblimin", fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
     PA2   PA1   PA3   PA5   PA4   h2   u2 com
A1  0.21 -0.18  0.08 -0.43 -0.07 0.20 0.80 2.0
A2 -0.02 -0.01  0.07  0.64  0.02 0.44 0.56 1.0
A3 -0.02 -0.11  0.03  0.67  0.03 0.53 0.47 1.1
A4 -0.06 -0.07  0.19  0.45 -0.17 0.30 0.70 1.7
A5 -0.12 -0.22  0.00  0.54  0.04 0.46 0.54 1.5
C1  0.08  0.04  0.55  0.00  0.16 0.34 0.66 1.2
C2  0.15  0.10  0.66  0.09  0.04 0.44 0.56 1.2
C3  0.03  0.05  0.58  0.08 -0.07 0.33 0.67 1.1
C4  0.15  0.01 -0.64  0.04 -0.04 0.47 0.53 1.1
C5  0.17  0.15 -0.56  0.03  0.09 0.43 0.57 1.4
E1 -0.07  0.54  0.10 -0.11 -0.10 0.34 0.66 1.3
E2  0.09  0.67 -0.02 -0.06 -0.07 0.55 0.45 1.1
E3  0.09 -0.42  0.01  0.24  0.30 0.46 0.54 2.6
E4 -0.01 -0.57  0.02  0.32 -0.07 0.54 0.46 1.6
E5  0.16 -0.43  0.27  0.07  0.21 0.42 0.58 2.6
N1  0.83 -0.10  0.00 -0.10 -0.05 0.68 0.32 1.1
N2  0.78 -0.04  0.01 -0.10  0.02 0.61 0.39 1.0
N3  0.70  0.12 -0.03  0.09  0.02 0.55 0.45 1.1
N4  0.47  0.41 -0.14  0.10  0.09 0.51 0.49 2.3
N5  0.48  0.21 -0.02  0.21 -0.16 0.35 0.65 2.0
O1  0.00 -0.09  0.08  0.00  0.52 0.32 0.68 1.1
O2  0.19 -0.06 -0.08  0.17 -0.48 0.28 0.72 1.7
O3  0.04 -0.16  0.00  0.07  0.62 0.48 0.52 1.2
O4  0.11  0.33 -0.05  0.16  0.37 0.24 0.76 2.6
O5  0.12 -0.10 -0.03  0.04 -0.55 0.31 0.69 1.2

                       PA2  PA1  PA3  PA5  PA4
SS loadings           2.56 2.21 2.07 2.04 1.65
Proportion Var        0.10 0.09 0.08 0.08 0.07
Cumulative Var        0.10 0.19 0.27 0.36 0.42
Proportion Explained  0.24 0.21 0.20 0.19 0.16
Cumulative Proportion 0.24 0.45 0.65 0.84 1.00

 With factor correlations of 
      PA2   PA1   PA3   PA5   PA4
PA2  1.00  0.21 -0.19 -0.03  0.00
PA1  0.21  1.00 -0.25 -0.33 -0.17
PA3 -0.19 -0.25  1.00  0.19  0.19
PA5 -0.03 -0.33  0.19  1.00  0.17
PA4  0.00 -0.17  0.19  0.17  1.00

Mean item complexity =  1.5
Test of the hypothesis that 5 factors are sufficient.

df null model =  300  with the objective function =  7.41 with Chi Square =  16484.78
df of  the model are 185  and the objective function was  0.63 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic n.obs is  2236 with the empirical chi square  1046.45  with prob <  3.1e-120 
The total n.obs was  2236  with Likelihood Chi Square =  1400.57  with prob <  1.5e-185 

Tucker Lewis Index of factoring reliability =  0.878
RMSEA index =  0.054  and the 90 % confidence intervals are  0.052 0.057
BIC =  -26.23
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   PA2  PA1  PA3  PA5  PA4
Correlation of (regression) scores with factors   0.93 0.89 0.88 0.88 0.85
Multiple R square of scores with factors          0.86 0.79 0.77 0.77 0.72
Minimum correlation of possible factor scores     0.71 0.59 0.55 0.55 0.44

EFA <- fa(Data_Factorial, nfactors = 5, rotate = "oblimin", fm = "ml")

EFA

Factor Analysis using method =  ml
Call: fa(r = Data_Factorial, nfactors = 5, rotate = "oblimin", fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
     ML2   ML5   ML3   ML1   ML4   h2   u2 com
A1  0.20 -0.37  0.05 -0.16 -0.05 0.16 0.84 2.0
A2 -0.01  0.61  0.08  0.01  0.02 0.40 0.60 1.0
A3 -0.03  0.68  0.04 -0.06  0.04 0.52 0.48 1.0
A4 -0.06  0.48  0.19 -0.05 -0.17 0.31 0.69 1.6
A5 -0.14  0.58  0.00 -0.16  0.06 0.48 0.52 1.3
C1  0.07  0.02  0.54  0.07  0.17 0.33 0.67 1.3
C2  0.12  0.12  0.63  0.14  0.06 0.42 0.58 1.3
C3  0.03  0.10  0.57  0.07 -0.06 0.33 0.67 1.1
C4  0.10  0.07 -0.66  0.04 -0.02 0.48 0.52 1.1
C5  0.13  0.02 -0.58  0.17  0.09 0.44 0.56 1.3
E1 -0.10 -0.13  0.09  0.55 -0.11 0.36 0.64 1.3
E2  0.06 -0.11 -0.03  0.65 -0.09 0.55 0.45 1.1
E3  0.07  0.30  0.00 -0.34  0.33 0.46 0.54 3.1
E4 -0.02  0.39  0.01 -0.51 -0.04 0.54 0.46 1.9
E5  0.19  0.10  0.27 -0.39  0.23 0.42 0.58 3.1
N1  0.86 -0.08  0.00 -0.09 -0.04 0.72 0.28 1.0
N2  0.82 -0.09  0.02 -0.04  0.01 0.66 0.34 1.0
N3  0.66  0.11 -0.04  0.16  0.02 0.53 0.47 1.2
N4  0.41  0.09 -0.16  0.44  0.09 0.50 0.50 2.4
N5  0.43  0.22 -0.04  0.25 -0.15 0.34 0.66 2.5
O1 -0.02  0.01  0.07 -0.05  0.54 0.32 0.68 1.1
O2  0.16  0.21 -0.10 -0.04 -0.47 0.28 0.72 1.8
O3  0.02  0.08 -0.01 -0.11  0.65 0.48 0.52 1.1
O4  0.07  0.13 -0.06  0.36  0.36 0.24 0.76 2.4
O5  0.10  0.09 -0.05 -0.08 -0.53 0.29 0.71 1.2

                       ML2  ML5  ML3  ML1  ML4
SS loadings           2.48 2.18 2.08 2.07 1.71
Proportion Var        0.10 0.09 0.08 0.08 0.07
Cumulative Var        0.10 0.19 0.27 0.35 0.42
Proportion Explained  0.24 0.21 0.20 0.20 0.16
Cumulative Proportion 0.24 0.44 0.64 0.84 1.00

 With factor correlations of 
      ML2   ML5   ML3   ML1   ML4
ML2  1.00 -0.02 -0.20  0.24  0.00
ML5 -0.02  1.00  0.19 -0.32  0.21
ML3 -0.20  0.19  1.00 -0.23  0.19
ML1  0.24 -0.32 -0.23  1.00 -0.18
ML4  0.00  0.21  0.19 -0.18  1.00

Mean item complexity =  1.6
Test of the hypothesis that 5 factors are sufficient.

df null model =  300  with the objective function =  7.41 with Chi Square =  16484.78
df of  the model are 185  and the objective function was  0.61 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic n.obs is  2236 with the empirical chi square  1105.41  with prob <  7.4e-131 
The total n.obs was  2236  with Likelihood Chi Square =  1357.5  with prob <  1.9e-177 

Tucker Lewis Index of factoring reliability =  0.882
RMSEA index =  0.053  and the 90 % confidence intervals are  0.051 0.056
BIC =  -69.3
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   ML2  ML5  ML3  ML1  ML4
Correlation of (regression) scores with factors   0.93 0.89 0.88 0.88 0.85
Multiple R square of scores with factors          0.87 0.79 0.78 0.78 0.73
Minimum correlation of possible factor scores     0.74 0.57 0.55 0.56 0.46

Factor scores

EFA_Regression <- fa(Data_Factorial, nfactors = 5, 
                     rotate = "oblimin", fm = "ml",
                     scores = "regression")

EFA_Bartlett <- fa(Data_Factorial, nfactors = 5, 
                   rotate = "oblimin", fm = "ml",
                   scores = "Bartlett")

EFA_Regression$scores %>% head()

             ML2         ML5        ML3         ML1        ML4
[1,]  0.30873404  0.45862492  1.3448145 -1.02741580  0.6367320
[2,]  0.70593522 -2.31022642 -1.0898323  1.31514996 -0.9807953
[3,] -0.08509873 -0.01506444 -0.1860651 -0.34842066 -0.2911984
[4,] -0.22502025 -1.57492864  0.5910568 -0.23058982 -0.2983634
[5,] -1.00253868  0.43265136 -1.3295963 -0.38402365  0.3184753
[6,]  0.93529784  1.08099814 -0.3139529  0.07351537  0.9746317

EFA_Bartlett$scores %>% head()

            ML2         ML5        ML3        ML1        ML4
[1,]  0.4486268  0.34140036  1.7104774 -1.2952806  0.6828470
[2,]  0.7575002 -2.86823907 -1.1688183  1.2628264 -1.0865940
[3,] -0.0855193 -0.05712183 -0.2579873 -0.5173620 -0.4259007
[4,] -0.2142354 -2.21120219  0.8706525 -0.5774081 -0.3844496
[5,] -1.2094331  0.60464790 -1.9293863 -0.4224337  0.5368255
[6,]  1.0629121  1.42903246 -0.4825082  0.2518345  1.3271042

EFA_RegressionScores <- EFA_Regression$scores
EFA_RegressionScores <- as.data.frame(EFA_RegressionScores)

EFA_BartlettScores <- EFA_Bartlett$scores
EFA_BartlettScores <- as.data.frame(EFA_BartlettScores)

cor(EFA_RegressionScores)

            ML2         ML5        ML3        ML1         ML4
ML2  1.00000000 -0.03481771 -0.2442405  0.2877761 -0.01028316
ML5 -0.03481771  1.00000000  0.2508227 -0.4381019  0.27568464
ML3 -0.24424048  0.25082267  1.0000000 -0.3091870  0.26106726
ML1  0.28777606 -0.43810188 -0.3091870  1.0000000 -0.25085056
ML4 -0.01028316  0.27568464  0.2610673 -0.2508506  1.00000000

cor(EFA_BartlettScores)

              ML2          ML5        ML3        ML1           ML4
ML2  1.0000000000 -0.009939055 -0.1578319  0.1810329 -0.0000110718
ML5 -0.0099390555  1.000000000  0.1313984 -0.1891665  0.1421161944
ML3 -0.1578319410  0.131398393  1.0000000 -0.1614366  0.1281681906
ML1  0.1810328980 -0.189166515 -0.1614366  1.0000000 -0.1036455537
ML4 -0.0000110718  0.142116194  0.1281682 -0.1036456  1.0000000000

cor(EFA_RegressionScores$ML1, EFA_BartlettScores$ML1)

[1] 0.9860482

cor(EFA_RegressionScores$ML2, EFA_BartlettScores$ML2)

[1] 0.9988308

Pre-EFA

Multivariate normality?

See this.

library(MVN)

Warning: package 'MVN' was built under R version 4.3.3

mvn(data = Data_Factorial, 
    mvnTest = "mardia")

$multivariateNormality
             Test        Statistic p value Result
1 Mardia Skewness  11107.275452718       0     NO
2 Mardia Kurtosis 69.4941876094799       0     NO
3             MVN             <NA>    <NA>     NO

$univariateNormality
               Test  Variable Statistic   p value Normality
1  Anderson-Darling    A1      123.3975  <0.001      NO    
2  Anderson-Darling    A2      126.8146  <0.001      NO    
3  Anderson-Darling    A3      115.0270  <0.001      NO    
4  Anderson-Darling    A4      156.7147  <0.001      NO    
5  Anderson-Darling    A5      101.8863  <0.001      NO    
6  Anderson-Darling    C1      101.5975  <0.001      NO    
7  Anderson-Darling    C2       94.7464  <0.001      NO    
8  Anderson-Darling    C3       85.6328  <0.001      NO    
9  Anderson-Darling    C4       97.4888  <0.001      NO    
10 Anderson-Darling    C5       69.2777  <0.001      NO    
11 Anderson-Darling    E1       77.5202  <0.001      NO    
12 Anderson-Darling    E2       70.5265  <0.001      NO    
13 Anderson-Darling    E3       68.2524  <0.001      NO    
14 Anderson-Darling    E4      114.1723  <0.001      NO    
15 Anderson-Darling    E5       97.0157  <0.001      NO    
16 Anderson-Darling    N1       74.8028  <0.001      NO    
17 Anderson-Darling    N2       58.1987  <0.001      NO    
18 Anderson-Darling    N3       69.0141  <0.001      NO    
19 Anderson-Darling    N4       62.1158  <0.001      NO    
20 Anderson-Darling    N5       80.5125  <0.001      NO    
21 Anderson-Darling    O1      113.7106  <0.001      NO    
22 Anderson-Darling    O2       96.3713  <0.001      NO    
23 Anderson-Darling    O3       89.7691  <0.001      NO    
24 Anderson-Darling    O4      149.2474  <0.001      NO    
25 Anderson-Darling    O5       99.6713  <0.001      NO    

$Descriptives
      n     Mean  Std.Dev Median Min Max 25th 75th        Skew    Kurtosis
A1 2236 2.365385 1.391968      2   1   6    1    3  0.88433371 -0.16693828
A2 2236 4.834079 1.156915      5   1   6    4    6 -1.14884458  1.14040256
A3 2236 4.629249 1.289373      5   1   6    4    6 -1.03448938  0.56428174
A4 2236 4.749553 1.447941      5   1   6    4    6 -1.09407464  0.23498989
A5 2236 4.584973 1.255833      5   1   6    4    6 -0.88005636  0.23767503
C1 2236 4.569767 1.216611      5   1   6    4    5 -0.89411758  0.41557496
C2 2236 4.401163 1.311310      5   1   6    4    5 -0.76927522 -0.09261008
C3 2236 4.322898 1.287153      5   1   6    4    5 -0.69211877 -0.10994138
C4 2236 2.500894 1.362817      2   1   6    1    4  0.64057056 -0.56219060
C5 2236 3.255367 1.629590      3   1   6    2    5  0.09185556 -1.23156045
E1 2236 2.969589 1.618121      3   1   6    2    4  0.38233076 -1.06810482
E2 2236 3.121199 1.605660      3   1   6    2    4  0.25430774 -1.12643645
E3 2236 4.009839 1.342438      4   1   6    3    5 -0.47932428 -0.43210992
E4 2236 4.430680 1.459100      5   1   6    4    6 -0.84560593 -0.26772160
E5 2236 4.418605 1.330117      5   1   6    4    5 -0.81068649 -0.02830899
N1 2236 2.908318 1.564455      3   1   6    2    4  0.38955663 -0.99020110
N2 2236 3.485689 1.534764      4   1   6    2    5 -0.06321150 -1.06829840
N3 2236 3.198569 1.596394      3   1   6    2    4  0.16527086 -1.17968936
N4 2236 3.175313 1.560600      3   1   6    2    4  0.21687387 -1.05942427
N5 2236 2.952147 1.621980      3   1   6    2    4  0.39924902 -1.05494210
O1 2236 4.821556 1.120043      5   1   6    4    6 -0.90755246  0.46521123
O2 2236 2.689177 1.545865      2   1   6    1    4  0.60609718 -0.76799127
O3 2236 4.483005 1.193261      5   1   6    4    5 -0.79209737  0.40098728
O4 2236 4.948122 1.175435      5   1   6    4    6 -1.25933720  1.26086859
O5 2236 2.455277 1.329501      2   1   6    1    3  0.78355138 -0.16476654

mvn(data = Data_Factorial, 
    mvnTest = "hz")

$multivariateNormality
           Test       HZ p value MVN
1 Henze-Zirkler 1.051814       0  NO

$univariateNormality
               Test  Variable Statistic   p value Normality
1  Anderson-Darling    A1      123.3975  <0.001      NO    
2  Anderson-Darling    A2      126.8146  <0.001      NO    
3  Anderson-Darling    A3      115.0270  <0.001      NO    
4  Anderson-Darling    A4      156.7147  <0.001      NO    
5  Anderson-Darling    A5      101.8863  <0.001      NO    
6  Anderson-Darling    C1      101.5975  <0.001      NO    
7  Anderson-Darling    C2       94.7464  <0.001      NO    
8  Anderson-Darling    C3       85.6328  <0.001      NO    
9  Anderson-Darling    C4       97.4888  <0.001      NO    
10 Anderson-Darling    C5       69.2777  <0.001      NO    
11 Anderson-Darling    E1       77.5202  <0.001      NO    
12 Anderson-Darling    E2       70.5265  <0.001      NO    
13 Anderson-Darling    E3       68.2524  <0.001      NO    
14 Anderson-Darling    E4      114.1723  <0.001      NO    
15 Anderson-Darling    E5       97.0157  <0.001      NO    
16 Anderson-Darling    N1       74.8028  <0.001      NO    
17 Anderson-Darling    N2       58.1987  <0.001      NO    
18 Anderson-Darling    N3       69.0141  <0.001      NO    
19 Anderson-Darling    N4       62.1158  <0.001      NO    
20 Anderson-Darling    N5       80.5125  <0.001      NO    
21 Anderson-Darling    O1      113.7106  <0.001      NO    
22 Anderson-Darling    O2       96.3713  <0.001      NO    
23 Anderson-Darling    O3       89.7691  <0.001      NO    
24 Anderson-Darling    O4      149.2474  <0.001      NO    
25 Anderson-Darling    O5       99.6713  <0.001      NO    

$Descriptives
      n     Mean  Std.Dev Median Min Max 25th 75th        Skew    Kurtosis
A1 2236 2.365385 1.391968      2   1   6    1    3  0.88433371 -0.16693828
A2 2236 4.834079 1.156915      5   1   6    4    6 -1.14884458  1.14040256
A3 2236 4.629249 1.289373      5   1   6    4    6 -1.03448938  0.56428174
A4 2236 4.749553 1.447941      5   1   6    4    6 -1.09407464  0.23498989
A5 2236 4.584973 1.255833      5   1   6    4    6 -0.88005636  0.23767503
C1 2236 4.569767 1.216611      5   1   6    4    5 -0.89411758  0.41557496
C2 2236 4.401163 1.311310      5   1   6    4    5 -0.76927522 -0.09261008
C3 2236 4.322898 1.287153      5   1   6    4    5 -0.69211877 -0.10994138
C4 2236 2.500894 1.362817      2   1   6    1    4  0.64057056 -0.56219060
C5 2236 3.255367 1.629590      3   1   6    2    5  0.09185556 -1.23156045
E1 2236 2.969589 1.618121      3   1   6    2    4  0.38233076 -1.06810482
E2 2236 3.121199 1.605660      3   1   6    2    4  0.25430774 -1.12643645
E3 2236 4.009839 1.342438      4   1   6    3    5 -0.47932428 -0.43210992
E4 2236 4.430680 1.459100      5   1   6    4    6 -0.84560593 -0.26772160
E5 2236 4.418605 1.330117      5   1   6    4    5 -0.81068649 -0.02830899
N1 2236 2.908318 1.564455      3   1   6    2    4  0.38955663 -0.99020110
N2 2236 3.485689 1.534764      4   1   6    2    5 -0.06321150 -1.06829840
N3 2236 3.198569 1.596394      3   1   6    2    4  0.16527086 -1.17968936
N4 2236 3.175313 1.560600      3   1   6    2    4  0.21687387 -1.05942427
N5 2236 2.952147 1.621980      3   1   6    2    4  0.39924902 -1.05494210
O1 2236 4.821556 1.120043      5   1   6    4    6 -0.90755246  0.46521123
O2 2236 2.689177 1.545865      2   1   6    1    4  0.60609718 -0.76799127
O3 2236 4.483005 1.193261      5   1   6    4    5 -0.79209737  0.40098728
O4 2236 4.948122 1.175435      5   1   6    4    6 -1.25933720  1.26086859
O5 2236 2.455277 1.329501      2   1   6    1    3  0.78355138 -0.16476654

mvn(data = Data_Factorial, 
    mvnTest = "dh")

$multivariateNormality
            Test        E df p value MVN
1 Doornik-Hansen 1737.887 50       0  NO

$univariateNormality
               Test  Variable Statistic   p value Normality
1  Anderson-Darling    A1      123.3975  <0.001      NO    
2  Anderson-Darling    A2      126.8146  <0.001      NO    
3  Anderson-Darling    A3      115.0270  <0.001      NO    
4  Anderson-Darling    A4      156.7147  <0.001      NO    
5  Anderson-Darling    A5      101.8863  <0.001      NO    
6  Anderson-Darling    C1      101.5975  <0.001      NO    
7  Anderson-Darling    C2       94.7464  <0.001      NO    
8  Anderson-Darling    C3       85.6328  <0.001      NO    
9  Anderson-Darling    C4       97.4888  <0.001      NO    
10 Anderson-Darling    C5       69.2777  <0.001      NO    
11 Anderson-Darling    E1       77.5202  <0.001      NO    
12 Anderson-Darling    E2       70.5265  <0.001      NO    
13 Anderson-Darling    E3       68.2524  <0.001      NO    
14 Anderson-Darling    E4      114.1723  <0.001      NO    
15 Anderson-Darling    E5       97.0157  <0.001      NO    
16 Anderson-Darling    N1       74.8028  <0.001      NO    
17 Anderson-Darling    N2       58.1987  <0.001      NO    
18 Anderson-Darling    N3       69.0141  <0.001      NO    
19 Anderson-Darling    N4       62.1158  <0.001      NO    
20 Anderson-Darling    N5       80.5125  <0.001      NO    
21 Anderson-Darling    O1      113.7106  <0.001      NO    
22 Anderson-Darling    O2       96.3713  <0.001      NO    
23 Anderson-Darling    O3       89.7691  <0.001      NO    
24 Anderson-Darling    O4      149.2474  <0.001      NO    
25 Anderson-Darling    O5       99.6713  <0.001      NO    

$Descriptives
      n     Mean  Std.Dev Median Min Max 25th 75th        Skew    Kurtosis
A1 2236 2.365385 1.391968      2   1   6    1    3  0.88433371 -0.16693828
A2 2236 4.834079 1.156915      5   1   6    4    6 -1.14884458  1.14040256
A3 2236 4.629249 1.289373      5   1   6    4    6 -1.03448938  0.56428174
A4 2236 4.749553 1.447941      5   1   6    4    6 -1.09407464  0.23498989
A5 2236 4.584973 1.255833      5   1   6    4    6 -0.88005636  0.23767503
C1 2236 4.569767 1.216611      5   1   6    4    5 -0.89411758  0.41557496
C2 2236 4.401163 1.311310      5   1   6    4    5 -0.76927522 -0.09261008
C3 2236 4.322898 1.287153      5   1   6    4    5 -0.69211877 -0.10994138
C4 2236 2.500894 1.362817      2   1   6    1    4  0.64057056 -0.56219060
C5 2236 3.255367 1.629590      3   1   6    2    5  0.09185556 -1.23156045
E1 2236 2.969589 1.618121      3   1   6    2    4  0.38233076 -1.06810482
E2 2236 3.121199 1.605660      3   1   6    2    4  0.25430774 -1.12643645
E3 2236 4.009839 1.342438      4   1   6    3    5 -0.47932428 -0.43210992
E4 2236 4.430680 1.459100      5   1   6    4    6 -0.84560593 -0.26772160
E5 2236 4.418605 1.330117      5   1   6    4    5 -0.81068649 -0.02830899
N1 2236 2.908318 1.564455      3   1   6    2    4  0.38955663 -0.99020110
N2 2236 3.485689 1.534764      4   1   6    2    5 -0.06321150 -1.06829840
N3 2236 3.198569 1.596394      3   1   6    2    4  0.16527086 -1.17968936
N4 2236 3.175313 1.560600      3   1   6    2    4  0.21687387 -1.05942427
N5 2236 2.952147 1.621980      3   1   6    2    4  0.39924902 -1.05494210
O1 2236 4.821556 1.120043      5   1   6    4    6 -0.90755246  0.46521123
O2 2236 2.689177 1.545865      2   1   6    1    4  0.60609718 -0.76799127
O3 2236 4.483005 1.193261      5   1   6    4    5 -0.79209737  0.40098728
O4 2236 4.948122 1.175435      5   1   6    4    6 -1.25933720  1.26086859
O5 2236 2.455277 1.329501      2   1   6    1    3  0.78355138 -0.16476654

KMO

Remember: The Kaiser-Meyer-Olkin (KMO) measure is a statistic that indicates the proportion of variance among the variables that might be common variance (i.e., that might be caused by underlying factors). It is used to examine the appropriateness of factor analysis. High values (close to 1) indicate that a factor analysis may be useful with your data. Low values (close to 0) suggest that factor analysis may not be appropriate.

KMO(Data_Factorial)

Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = Data_Factorial)
Overall MSA =  0.85
MSA for each item = 
  A1   A2   A3   A4   A5   C1   C2   C3   C4   C5   E1   E2   E3   E4   E5   N1 
0.74 0.83 0.87 0.87 0.90 0.84 0.79 0.85 0.82 0.86 0.84 0.88 0.89 0.88 0.89 0.78 
  N2   N3   N4   N5   O1   O2   O3   O4   O5 
0.78 0.86 0.89 0.86 0.86 0.78 0.83 0.78 0.76

KMO(Data_Factorial %>% select(A1, A2, A3, A4, A5))

Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = Data_Factorial %>% select(A1, A2, A3, A4, A5))
Overall MSA =  0.76
MSA for each item = 
  A1   A2   A3   A4   A5 
0.78 0.76 0.73 0.82 0.77

Reliability

Data_Factorial %>% names()

 [1] "A1" "A2" "A3" "A4" "A5" "C1" "C2" "C3" "C4" "C5" "E1" "E2" "E3" "E4" "E5"
[16] "N1" "N2" "N3" "N4" "N5" "O1" "O2" "O3" "O4" "O5"

alpha(Data_Factorial %>% select(A1, A2, A3, A4, A5))

Warning in alpha(Data_Factorial %>% select(A1, A2, A3, A4, A5)): 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 ( A1 ) 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


Reliability analysis   
Call: alpha(x = Data_Factorial %>% select(A1, A2, A3, A4, A5))

  raw_alpha std.alpha G6(smc) average_r  S/N   ase mean   sd median_r
      0.44      0.46    0.54      0.15 0.86 0.018  4.2 0.73     0.33

    95% confidence boundaries 
         lower alpha upper
Feldt      0.4  0.44  0.47
Duhachek   0.4  0.44  0.47

 Reliability if an item is dropped:
   raw_alpha std.alpha G6(smc) average_r  S/N alpha se  var.r med.r
A1      0.72      0.73    0.68     0.401 2.67   0.0096 0.0058 0.380
A2      0.29      0.31    0.39     0.100 0.45   0.0242 0.1116 0.086
A3      0.18      0.21    0.31     0.062 0.26   0.0278 0.1021 0.086
A4      0.25      0.30    0.43     0.097 0.43   0.0257 0.1595 0.098
A5      0.22      0.25    0.37     0.076 0.33   0.0263 0.1330 0.099

 Item statistics 
      n raw.r std.r r.cor r.drop mean  sd
A1 2236  0.06 0.024 -0.39  -0.31  2.4 1.4
A2 2236  0.63 0.663  0.58   0.37  4.8 1.2
A3 2236  0.73 0.746  0.72   0.48  4.6 1.3
A4 2236  0.69 0.671  0.52   0.38  4.7 1.4
A5 2236  0.70 0.715  0.63   0.44  4.6 1.3

Non missing response frequency for each item
      1    2    3    4    5    6 miss
A1 0.34 0.30 0.14 0.12 0.07 0.03    0
A2 0.02 0.04 0.05 0.19 0.37 0.32    0
A3 0.03 0.06 0.07 0.20 0.36 0.28    0
A4 0.04 0.07 0.06 0.16 0.24 0.42    0
A5 0.02 0.06 0.09 0.22 0.35 0.26    0

alpha(Data_Factorial %>% select(A1, A2, A3, A4, A5), 
      check.keys = TRUE)

Warning in alpha(Data_Factorial %>% select(A1, A2, A3, A4, A5), check.keys = TRUE): Some items were negatively correlated with the first principal component and were automatically reversed.
 This is indicated by a negative sign for the variable name.


Reliability analysis   
Call: alpha(x = Data_Factorial %>% select(A1, A2, A3, A4, A5), check.keys = TRUE)

  raw_alpha std.alpha G6(smc) average_r  S/N    ase mean   sd median_r
      0.71      0.46    0.54      0.15 0.86 0.0099  4.7 0.89     0.33

    95% confidence boundaries 
         lower alpha upper
Feldt     0.69  0.71  0.72
Duhachek  0.69  0.71  0.72

 Reliability if an item is dropped:
    raw_alpha std.alpha G6(smc) average_r  S/N alpha se  var.r med.r
A1-      0.72      0.73    0.68     0.401 2.67   0.0096 0.0058 0.380
A2       0.62      0.31    0.39     0.100 0.45   0.0132 0.1116 0.086
A3       0.60      0.21    0.31     0.062 0.26   0.0139 0.1021 0.086
A4       0.68      0.30    0.43     0.097 0.43   0.0110 0.1595 0.098
A5       0.65      0.25    0.37     0.076 0.33   0.0124 0.1330 0.099

 Item statistics 
       n raw.r std.r r.cor r.drop mean  sd
A1- 2236  0.58 0.024 -0.39   0.31  4.6 1.4
A2  2236  0.73 0.663  0.58   0.56  4.8 1.2
A3  2236  0.76 0.746  0.72   0.59  4.6 1.3
A4  2236  0.66 0.671  0.52   0.40  4.7 1.4
A5  2236  0.69 0.715  0.63   0.49  4.6 1.3

Non missing response frequency for each item
      1    2    3    4    5    6 miss
A1 0.34 0.30 0.14 0.12 0.07 0.03    0
A2 0.02 0.04 0.05 0.19 0.37 0.32    0
A3 0.03 0.06 0.07 0.20 0.36 0.28    0
A4 0.04 0.07 0.06 0.16 0.24 0.42    0
A5 0.02 0.06 0.09 0.22 0.35 0.26    0

omega(Data_Factorial %>% select(A1, A2, A3, A4, A5))

Omega 
Call: omegah(m = m, nfactors = nfactors, fm = fm, key = key, flip = flip, 
    digits = digits, title = title, sl = sl, labels = labels, 
    plot = plot, n.obs = n.obs, rotate = rotate, Phi = Phi, option = option, 
    covar = covar)
Alpha:                 0.71 
G.6:                   0.68 
Omega Hierarchical:    0.68 
Omega H asymptotic:    0.9 
Omega Total            0.76 

Schmid Leiman Factor loadings greater than  0.2 
       g   F1*   F2*   F3*   h2   u2   p2
A1- 0.35        0.45       0.33 0.67 0.37
A2  0.67        0.24       0.51 0.49 0.87
A3  0.70  0.35             0.61 0.39 0.80
A4  0.53                   0.30 0.70 0.93
A5  0.57  0.29             0.42 0.58 0.79

With Sums of squares  of:
   g  F1*  F2*  F3* 
1.67 0.21 0.27 0.02 

general/max  6.13   max/min =   12.47
mean percent general =  0.75    with sd =  0.22 and cv of  0.29 
Explained Common Variance of the general factor =  0.77 

The degrees of freedom are -2  and the fit is  0 
The number of observations was  2236  with Chi Square =  0  with prob <  NA
The root mean square of the residuals is  0 
The df corrected root mean square of the residuals is  NA

Compare this with the adequacy of just a general factor and no group factors
The degrees of freedom for just the general factor are 5  and the fit is  0.05 
The number of observations was  2236  with Chi Square =  101.8  with prob <  2.2e-20
The root mean square of the residuals is  0.05 
The df corrected root mean square of the residuals is  0.07 

RMSEA index =  0.093  and the 10 % confidence intervals are  0.078 0.109
BIC =  63.24 

Measures of factor score adequacy             
                                                 g   F1*   F2*   F3*
Correlation of scores with factors            0.84  0.43  0.52  0.15
Multiple R square of scores with factors      0.71  0.19  0.27  0.02
Minimum correlation of factor score estimates 0.42 -0.63 -0.46 -0.95

 Total, General and Subset omega for each subset
                                                 g  F1*  F2*  F3*
Omega total for total scores and subscales    0.76 0.68 0.56 0.29
Omega general for total scores and subscales  0.68 0.54 0.38 0.28
Omega group for total scores and subscales    0.08 0.14 0.18 0.01

cortest.bartlett(Data_Factorial %>% select(A1, A2, A3, A4, A5))

R was not square, finding R from data

$chisq
[1] 2098.146

$p.value
[1] 0

$df
[1] 10