RAQ
Priyank Goyal
09/04/2020
Sample Size With a little help from a few lecturer friends I collected 2571 completed questionnaires (at this point it should become apparent that this example is fictitious).
…In short, their study indicated that as communalities become lower the importance of sample size increases. With all communalities above .6, relatively small samples (less than 100) may be perfectly adequate. With communalities in the .5 range, samples between 100 and 200 can be good enough provided there are relatively few factors each with only a small number of indicator variables.
Correlations between variables
The first thing to do when conducting a factor analysis or principal components analysis is to look at the correlations of the variables.
The correlations between variables can be checked using the cor() function to create a correlation matrix of all variables.
There are essentially two potential problems: (1) correlations that are not high enough; and (2) correlations that are too high.
We can test for the first problem by visually scanning the correlation matrix and looking for correlations below about .3: if any variables have lots of correlations below this value then consider excluding them.
For the second problem, if you have reason to believe that the correlation matrix has multicollinearity then you could look through the correlation matrix for variables that correlate very highly (R > .8) and consider eliminating one of the variables (or more) before proceeding.
raqData <- read.delim("raq.dat",header=TRUE)Calculate the correlation matrix
raqmatrix <- round(cor(raqData),2) Run Barlette Test using psych package
library(psych)## Warning: package 'psych' was built under R version 3.6.1cortest.bartlett(raqData)## R was not square, finding R from data## $chisq
## [1] 19334.49
##
## $p.value
## [1] 0
##
## $df
## [1] 253The test data is highly significant and therefore factor analysis is appropriate
KMO Test
# KMO Kaiser-Meyer-Olkin Measure of Sampling Adequacy
# Function by G. Jay Kerns, Ph.D., Youngstown State University (http://tolstoy.newcastle.edu.au/R/e2/help/07/08/22816.html)
kmo = function( data ){
library(MASS)
X <- cor(as.matrix(data))
iX <- ginv(X)
S2 <- diag(diag((iX^-1)))
AIS <- S2%*%iX%*%S2 # anti-image covariance matrix
IS <- X+AIS-2*S2 # image covariance matrix
Dai <- sqrt(diag(diag(AIS)))
IR <- ginv(Dai)%*%IS%*%ginv(Dai) # image correlation matrix
AIR <- ginv(Dai)%*%AIS%*%ginv(Dai) # anti-image correlation matrix
a <- apply((AIR - diag(diag(AIR)))^2, 2, sum)
AA <- sum(a)
b <- apply((X - diag(nrow(X)))^2, 2, sum)
BB <- sum(b)
MSA <- b/(b+a) # indiv. measures of sampling adequacy
AIR <- AIR-diag(nrow(AIR))+diag(MSA)
# Examine the anti-image of the correlation matrix. That is the negative of the partial correlations, partialling out all other variables.
kmo <- BB/(AA+BB) # overall KMO statistic
# Reporting the conclusion
if (kmo >= 0.00 && kmo < 0.50){test <- 'The KMO test yields a degree of common variance unacceptable for FA.'}
else if (kmo >= 0.50 && kmo < 0.60){test <- 'The KMO test yields a degree of common variance miserable.'}
else if (kmo >= 0.60 && kmo < 0.70){test <- 'The KMO test yields a degree of common variance mediocre.'}
else if (kmo >= 0.70 && kmo < 0.80){test <- 'The KMO test yields a degree of common variance middling.' }
else if (kmo >= 0.80 && kmo < 0.90){test <- 'The KMO test yields a degree of common variance meritorious.' }
else { test <- 'The KMO test yields a degree of common variance marvelous.' }
ans <- list( overall = kmo,
report = test,
individual = MSA,
AIS = AIS,
AIR = AIR )
return(ans)
}
#To use this function:
kmo(raqData)## $overall
## [1] 0.9302245
##
## $report
## [1] "The KMO test yields a degree of common variance marvelous."
##
## $individual
## Q01 Q02 Q03 Q04 Q05 Q06 Q07
## 0.9297610 0.8747754 0.9510378 0.9553403 0.9600892 0.8913314 0.9416800
## Q08 Q09 Q10 Q11 Q12 Q13 Q14
## 0.8713055 0.8337295 0.9486858 0.9059338 0.9548324 0.9482270 0.9671722
## Q15 Q16 Q17 Q18 Q19 Q20 Q21
## 0.9404402 0.9336439 0.9306205 0.9479508 0.9407021 0.8890514 0.9293369
## Q22 Q23
## 0.8784508 0.7663994
##
## $AIS
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.627153118 -0.014264007 0.032684206 -0.103441650 -1.037583e-01
## [2,] -0.014264007 0.811755252 -0.109450940 -0.028631346 7.727771e-03
## [3,] 0.032684206 -0.109450940 0.601893661 0.050984914 2.433620e-02
## [4,] -0.103441650 -0.028631346 0.050984914 0.614852103 -8.837819e-02
## [5,] -0.103758317 0.007727771 0.024336201 -0.088378188 7.090423e-01
## [6,] 0.012088782 -0.036374795 -0.024815703 -0.004017651 -2.243144e-02
## [7,] 0.013059119 0.010812929 0.040454676 -0.049445748 -2.717225e-02
## [8,] -0.027742025 -0.021089865 -0.003996693 -0.041960612 -1.634178e-02
## [9,] -0.011472364 -0.153262421 -0.097431470 0.020499303 -1.470427e-02
## [10,] -0.008658329 -0.009762474 -0.011244544 0.004236945 -7.030633e-02
## [11,] -0.022064941 0.023201921 0.034186816 -0.011953216 -1.886611e-05
## [12,] -0.003979867 0.021383623 0.051009738 -0.091752577 -3.723802e-02
## [13,] -0.049926946 -0.005077376 -0.018181988 0.013383379 2.645271e-03
## [14,] -0.024527325 0.016237776 0.041983788 -0.002600799 -1.725476e-02
## [15,] 0.056809108 0.026845165 0.005124834 -0.039445344 9.636461e-03
## [16,] -0.153020286 -0.007522866 0.045802079 -0.020823640 -5.903514e-02
## [17,] -0.026661898 -0.018384278 0.019122891 -0.019771474 -1.076964e-02
## [18,] -0.013045034 0.011714556 0.021451839 -0.013716299 1.493170e-03
## [19,] 0.008672592 -0.023479847 -0.083483937 -0.023826851 -1.327839e-02
## [20,] -0.010925121 0.045232762 0.051626828 -0.002724226 -8.176177e-03
## [21,] 0.003767931 0.027566236 0.040049040 -0.050058353 -2.857293e-02
## [22,] 0.001054318 -0.099886582 -0.004649695 -0.023288160 2.654928e-02
## [23,] -0.044822472 -0.002060071 -0.056616249 -0.012816343 -3.825819e-03
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.012088782 0.013059119 -0.0277420250 -0.011472364 -0.008658329
## [2,] -0.036374795 0.010812929 -0.0210898651 -0.153262421 -0.009762474
## [3,] -0.024815703 0.040454676 -0.0039966925 -0.097431470 -0.011244544
## [4,] -0.004017651 -0.049445748 -0.0419606124 0.020499303 0.004236945
## [5,] -0.022431442 -0.027172245 -0.0163417807 -0.014704269 -0.070306334
## [6,] 0.573142384 -0.151630513 0.0131467843 0.007177224 -0.078722167
## [7,] -0.151630513 0.530473739 -0.0075535688 -0.019180626 -0.021520785
## [8,] 0.013146784 -0.007553569 0.5098493087 -0.062208913 0.032887772
## [9,] 0.007177224 -0.019180626 -0.0622089131 0.780016094 0.033713150
## [10,] -0.078722167 -0.021520785 0.0328877721 0.033713150 0.802646950
## [11,] -0.043447306 0.022508629 -0.2015734127 0.022405846 -0.056533948
## [12,] 0.026094115 -0.023976511 0.0180486093 -0.001900561 -0.012680730
## [13,] -0.092109464 -0.020888782 0.0009523293 0.039655398 -0.040009293
## [14,] -0.058639638 -0.030671484 -0.0130510906 -0.029714559 -0.008056592
## [15,] -0.078628196 -0.045137483 -0.0193594501 0.048849295 -0.067752682
## [16,] 0.056645166 -0.010577284 -0.0031974354 0.033607617 -0.053707659
## [17,] 0.022254595 -0.041541853 -0.1503268370 -0.042750313 0.007880771
## [18,] -0.131528207 -0.045065228 0.0122084002 -0.003463633 -0.016681035
## [19,] -0.010287564 0.044062049 0.0298246527 -0.087018152 -0.007303013
## [20,] 0.033270691 0.029839248 0.0127751183 0.028689911 0.032694075
## [21,] 0.021641617 -0.111906752 -0.0108148909 -0.019980361 0.011249010
## [22,] 0.027530455 0.008498244 -0.0148291041 -0.101440618 0.015269216
## [23,] 0.013362232 -0.005620156 0.0015036112 -0.078101774 0.012521640
## [,11] [,12] [,13] [,14] [,15]
## [1,] -2.206494e-02 -0.003979867 -0.0499269456 -0.0245273252 0.056809108
## [2,] 2.320192e-02 0.021383623 -0.0050773761 0.0162377764 0.026845165
## [3,] 3.418682e-02 0.051009738 -0.0181819885 0.0419837881 0.005124834
## [4,] -1.195322e-02 -0.091752577 0.0133833788 -0.0026007994 -0.039445344
## [5,] -1.886611e-05 -0.037238024 0.0026452706 -0.0172547624 0.009636461
## [6,] -4.344731e-02 0.026094115 -0.0921094642 -0.0586396376 -0.078628196
## [7,] 2.250863e-02 -0.023976511 -0.0208887824 -0.0306714840 -0.045137483
## [8,] -2.015734e-01 0.018048609 0.0009523293 -0.0130510906 -0.019359450
## [9,] 2.240585e-02 -0.001900561 0.0396553976 -0.0297145589 0.048849295
## [10,] -5.653395e-02 -0.012680730 -0.0400092935 -0.0080565924 -0.067752682
## [11,] 4.697590e-01 -0.002719009 -0.0503430182 0.0185809852 -0.028830917
## [12,] -2.719009e-03 0.575501008 -0.1114757308 -0.0483506266 -0.016190501
## [13,] -5.034302e-02 -0.111475731 0.5494652433 -0.0569919843 -0.004979672
## [14,] 1.858099e-02 -0.048350627 -0.0569919843 0.6070035304 -0.058969619
## [15,] -2.883092e-02 -0.016190501 -0.0049796722 -0.0589696187 0.655546920
## [16,] 2.466825e-03 -0.022213223 0.0140605358 -0.0461504852 -0.137812029
## [17,] -1.121229e-01 0.003157819 -0.0475192420 -0.0157657049 -0.049220560
## [18,] -1.091403e-02 -0.079021863 -0.0896507793 -0.0805449780 0.021891662
## [19,] -3.541011e-03 0.027194136 0.0059297117 0.0304844455 0.006757464
## [20,] -4.786649e-02 -0.041898800 0.0113005163 0.0007480665 -0.025874233
## [21,] -2.321623e-03 -0.044445498 -0.0182731673 -0.0363989731 0.020844352
## [22,] 2.142715e-02 0.012477538 0.0354047137 0.0205919013 0.018362943
## [23,] 6.291945e-03 -0.020240842 -0.0212023173 -0.0190981192 -0.018244263
## [,16] [,17] [,18] [,19] [,20]
## [1,] -0.153020286 -0.026661898 -0.013045034 0.008672592 -0.0109251211
## [2,] -0.007522866 -0.018384278 0.011714556 -0.023479847 0.0452327615
## [3,] 0.045802079 0.019122891 0.021451839 -0.083483937 0.0516268279
## [4,] -0.020823640 -0.019771474 -0.013716299 -0.023826851 -0.0027242256
## [5,] -0.059035136 -0.010769643 0.001493170 -0.013278387 -0.0081761769
## [6,] 0.056645166 0.022254595 -0.131528207 -0.010287564 0.0332706908
## [7,] -0.010577284 -0.041541853 -0.045065228 0.044062049 0.0298392484
## [8,] -0.003197435 -0.150326837 0.012208400 0.029824653 0.0127751183
## [9,] 0.033607617 -0.042750313 -0.003463633 -0.087018152 0.0286899108
## [10,] -0.053707659 0.007880771 -0.016681035 -0.007303013 0.0326940755
## [11,] 0.002466825 -0.112122917 -0.010914029 -0.003541011 -0.0478664911
## [12,] -0.022213223 0.003157819 -0.079021863 0.027194136 -0.0418987996
## [13,] 0.014060536 -0.047519242 -0.089650779 0.005929712 0.0113005163
## [14,] -0.046150485 -0.015765705 -0.080544978 0.030484446 0.0007480665
## [15,] -0.137812029 -0.049220560 0.021891662 0.006757464 -0.0258742335
## [16,] 0.536854026 -0.039461084 -0.046937807 0.030364853 -0.0033168730
## [17,] -0.039461084 0.505549313 -0.017196614 -0.029607073 0.0093954885
## [18,] -0.046937807 -0.017196614 0.507773950 0.018885098 -0.0015453311
## [19,] 0.030364853 -0.029607073 0.018885098 0.791081637 0.0689982743
## [20,] -0.003316873 0.009395489 -0.001545331 0.068998274 0.7297949321
## [21,] -0.046249347 -0.021343045 -0.037757448 0.020677430 -0.2039767910
## [22,] -0.002181511 0.006514419 -0.015627644 -0.093130611 -0.0087193817
## [23,] 0.016098449 0.037100122 0.015381707 -0.032641178 -0.0229392353
## [,21] [,22] [,23]
## [1,] 0.003767931 0.001054318 -0.044822472
## [2,] 0.027566236 -0.099886582 -0.002060071
## [3,] 0.040049040 -0.004649695 -0.056616249
## [4,] -0.050058353 -0.023288160 -0.012816343
## [5,] -0.028572928 0.026549277 -0.003825819
## [6,] 0.021641617 0.027530455 0.013362232
## [7,] -0.111906752 0.008498244 -0.005620156
## [8,] -0.010814891 -0.014829104 0.001503611
## [9,] -0.019980361 -0.101440618 -0.078101774
## [10,] 0.011249010 0.015269216 0.012521640
## [11,] -0.002321623 0.021427154 0.006291945
## [12,] -0.044445498 0.012477538 -0.020240842
## [13,] -0.018273167 0.035404714 -0.021202317
## [14,] -0.036398973 0.020591901 -0.019098119
## [15,] 0.020844352 0.018362943 -0.018244263
## [16,] -0.046249347 -0.002181511 0.016098449
## [17,] -0.021343045 0.006514419 0.037100122
## [18,] -0.037757448 -0.015627644 0.015381707
## [19,] 0.020677430 -0.093130611 -0.032641178
## [20,] -0.203976791 -0.008719382 -0.022939235
## [21,] 0.546465907 -0.016292080 0.009011910
## [22,] -0.016292080 0.832994213 -0.153800018
## [23,] 0.009011910 -0.153800018 0.914348653
##
## $AIR
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.929761030 -0.019991353 0.053197504 -0.166580176 -1.555966e-01
## [2,] -0.019991353 0.874775439 -0.156583882 -0.040526946 1.018605e-02
## [3,] 0.053197504 -0.156583882 0.951037838 0.083810123 3.725262e-02
## [4,] -0.166580176 -0.040526946 0.083810123 0.955340346 -1.338516e-01
## [5,] -0.155596577 0.010186046 0.037252619 -0.133851633 9.600892e-01
## [6,] 0.020163434 -0.053328178 -0.042250849 -0.006767926 -3.518762e-02
## [7,] 0.022640977 0.016477785 0.071594044 -0.086578823 -4.430549e-02
## [8,] -0.049060328 -0.032782369 -0.007214728 -0.074943776 -2.717956e-02
## [9,] -0.016402662 -0.192606681 -0.142196068 0.029600700 -1.977223e-02
## [10,] -0.012203517 -0.012094420 -0.016177808 0.006031221 -9.319575e-02
## [11,] -0.040651671 0.037572822 0.064292632 -0.022241387 -3.268952e-05
## [12,] -0.006624586 0.031285686 0.086670274 -0.154244574 -5.829449e-02
## [13,] -0.085050739 -0.007602504 -0.031616325 0.023025567 4.238029e-03
## [14,] -0.039752806 0.023132278 0.069458617 -0.004257218 -2.630130e-02
## [15,] 0.088599095 0.036800323 0.008158644 -0.062131025 1.413447e-02
## [16,] -0.263714560 -0.011395743 0.080574423 -0.036244591 -9.568555e-02
## [17,] -0.047350276 -0.028698042 0.034666651 -0.035462712 -1.798802e-02
## [18,] -0.023116560 0.018246436 0.038803369 -0.024548017 2.488502e-03
## [19,] 0.012312649 -0.029300299 -0.120985239 -0.034164154 -1.772959e-02
## [20,] -0.016148755 0.058767894 0.077895996 -0.004066842 -1.136616e-02
## [21,] 0.006436276 0.041388851 0.069831391 -0.086359414 -4.590258e-02
## [22,] 0.001458692 -0.121471280 -0.006566645 -0.032540847 3.454583e-02
## [23,] -0.059190649 -0.002391188 -0.076317703 -0.017093180 -4.751519e-03
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.020163434 0.022640977 -0.049060328 -0.016402662 -0.012203517
## [2,] -0.053328178 0.016477785 -0.032782369 -0.192606681 -0.012094420
## [3,] -0.042250849 0.071594044 -0.007214728 -0.142196068 -0.016177808
## [4,] -0.006767926 -0.086578823 -0.074943776 0.029600700 0.006031221
## [5,] -0.035187615 -0.044305485 -0.027179557 -0.019772226 -0.093195746
## [6,] 0.891331392 -0.274994113 0.024320212 0.010734293 -0.116065594
## [7,] -0.274994113 0.941679984 -0.014524438 -0.029818037 -0.032981005
## [8,] 0.024320212 -0.014524438 0.871305451 -0.098646099 0.051410433
## [9,] 0.010734293 -0.029818037 -0.098646099 0.833729475 0.042607424
## [10,] -0.116065594 -0.032981005 0.051410433 0.042607424 0.948685759
## [11,] -0.083732492 0.045089926 -0.411883847 0.037014508 -0.092068161
## [12,] 0.045434763 -0.043394132 0.033319600 -0.002836658 -0.018657736
## [13,] -0.164135635 -0.038691099 0.001799269 0.060573186 -0.060246038
## [14,] -0.099417859 -0.054051436 -0.023460123 -0.043183904 -0.011542330
## [15,] -0.128275927 -0.076542651 -0.033486535 0.068313199 -0.093403322
## [16,] 0.102118277 -0.019820478 -0.006111569 0.051934725 -0.081817431
## [17,] 0.041343446 -0.080218060 -0.296096886 -0.068077838 0.012371565
## [18,] -0.243810514 -0.086830924 0.023993999 -0.005503575 -0.026129164
## [19,] -0.015278145 0.068017723 0.046961702 -0.110776444 -0.009164929
## [20,] 0.051443456 0.047957387 0.020943227 0.038025680 0.042717552
## [21,] 0.038670243 -0.207846545 -0.020488949 -0.030603423 0.016985193
## [22,] 0.039843834 0.012784279 -0.022754799 -0.125845912 0.018673832
## [23,] 0.018458306 -0.008069758 0.002202210 -0.092481145 0.014616488
## [,11] [,12] [,13] [,14] [,15]
## [1,] -4.065167e-02 -0.006624586 -0.085050739 -0.039752806 0.088599095
## [2,] 3.757282e-02 0.031285686 -0.007602504 0.023132278 0.036800323
## [3,] 6.429263e-02 0.086670274 -0.031616325 0.069458617 0.008158644
## [4,] -2.224139e-02 -0.154244574 0.023025567 -0.004257218 -0.062131025
## [5,] -3.268952e-05 -0.058294488 0.004238029 -0.026301304 0.014134472
## [6,] -8.373249e-02 0.045434763 -0.164135635 -0.099417859 -0.128275927
## [7,] 4.508993e-02 -0.043394132 -0.038691099 -0.054051436 -0.076542651
## [8,] -4.118838e-01 0.033319600 0.001799269 -0.023460123 -0.033486535
## [9,] 3.701451e-02 -0.002836658 0.060573186 -0.043183904 0.068313199
## [10,] -9.206816e-02 -0.018657736 -0.060246038 -0.011542330 -0.093403322
## [11,] 9.059338e-01 -0.005229377 -0.099090396 0.034796500 -0.051954001
## [12,] -5.229377e-03 0.954832379 -0.198238120 -0.081805679 -0.026359390
## [13,] -9.909040e-02 -0.198238120 0.948226989 -0.098684298 -0.008297146
## [14,] 3.479650e-02 -0.081805679 -0.098684298 0.967172178 -0.093482608
## [15,] -5.195400e-02 -0.026359390 -0.008297146 -0.093482608 0.940440197
## [16,] 4.912162e-03 -0.039963215 0.025888307 -0.080844887 -0.232304235
## [17,] -2.300780e-01 0.005854400 -0.090160774 -0.028460074 -0.085499366
## [18,] -2.234664e-02 -0.146180354 -0.169726145 -0.145080035 0.037943870
## [19,] -5.808701e-03 0.040303389 0.008993999 0.043991831 0.009383637
## [20,] -8.175110e-02 -0.064651427 0.017845460 0.001123943 -0.037408060
## [21,] -4.582184e-03 -0.079254366 -0.033347416 -0.063199259 0.034826111
## [22,] 3.425358e-02 0.018021248 0.052332319 0.028958752 0.024849600
## [23,] 9.600446e-03 -0.027902917 -0.029912816 -0.025635340 -0.023565058
## [,16] [,17] [,18] [,19] [,20]
## [1,] -0.263714560 -0.04735028 -0.023116560 0.012312649 -0.016148755
## [2,] -0.011395743 -0.02869804 0.018246436 -0.029300299 0.058767894
## [3,] 0.080574423 0.03466665 0.038803369 -0.120985239 0.077895996
## [4,] -0.036244591 -0.03546271 -0.024548017 -0.034164154 -0.004066842
## [5,] -0.095685554 -0.01798802 0.002488502 -0.017729586 -0.011366160
## [6,] 0.102118277 0.04134345 -0.243810514 -0.015278145 0.051443456
## [7,] -0.019820478 -0.08021806 -0.086830924 0.068017723 0.047957387
## [8,] -0.006111569 -0.29609689 0.023993999 0.046961702 0.020943227
## [9,] 0.051934725 -0.06807784 -0.005503575 -0.110776444 0.038025680
## [10,] -0.081817431 0.01237157 -0.026129164 -0.009164929 0.042717552
## [11,] 0.004912162 -0.23007798 -0.022346645 -0.005808701 -0.081751099
## [12,] -0.039963215 0.00585440 -0.146180354 0.040303389 -0.064651427
## [13,] 0.025888307 -0.09016077 -0.169726145 0.008993999 0.017845460
## [14,] -0.080844887 -0.02846007 -0.145080035 0.043991831 0.001123943
## [15,] -0.232304235 -0.08549937 0.037943870 0.009383637 -0.037408060
## [16,] 0.933643945 -0.07574590 -0.089899957 0.046594261 -0.005299078
## [17,] -0.075745901 0.93062054 -0.033941105 -0.046816943 0.015468108
## [18,] -0.089899957 -0.03394110 0.947950841 0.029797058 -0.002538551
## [19,] 0.046594261 -0.04681694 0.029797058 0.940702074 0.090808637
## [20,] -0.005299078 0.01546811 -0.002538551 0.090808637 0.889051429
## [21,] -0.085387827 -0.04060627 -0.071678001 0.031448821 -0.322997230
## [22,] -0.003262183 0.01003859 -0.024029089 -0.114725725 -0.011183153
## [23,] 0.022977354 0.05456795 0.022574254 -0.038379495 -0.028081649
## [,21] [,22] [,23]
## [1,] 0.006436276 0.001458692 -0.059190649
## [2,] 0.041388851 -0.121471280 -0.002391188
## [3,] 0.069831391 -0.006566645 -0.076317703
## [4,] -0.086359414 -0.032540847 -0.017093180
## [5,] -0.045902583 0.034545829 -0.004751519
## [6,] 0.038670243 0.039843834 0.018458306
## [7,] -0.207846545 0.012784279 -0.008069758
## [8,] -0.020488949 -0.022754799 0.002202210
## [9,] -0.030603423 -0.125845912 -0.092481145
## [10,] 0.016985193 0.018673832 0.014616488
## [11,] -0.004582184 0.034253576 0.009600446
## [12,] -0.079254366 0.018021248 -0.027902917
## [13,] -0.033347416 0.052332319 -0.029912816
## [14,] -0.063199259 0.028958752 -0.025635340
## [15,] 0.034826111 0.024849600 -0.023565058
## [16,] -0.085387827 -0.003262183 0.022977354
## [17,] -0.040606268 0.010038594 0.054567953
## [18,] -0.071678001 -0.024029089 0.022574254
## [19,] 0.031448821 -0.114725725 -0.038379495
## [20,] -0.322997230 -0.011183153 -0.028081649
## [21,] 0.929336944 -0.024147602 0.012749096
## [22,] -0.024147602 0.878450848 -0.176229853
## [23,] 0.012749096 -0.176229853 0.766399409Overall KMO and individual KMO is more than 0.5 hence we can use it for the analysis
Lets see the determinant of correlation matrix.
det(raqmatrix)## [1] 0.0005293425It is more than 0.00001 Now Extracting Factors. First set number of factors equal to that of variables.
pc1 <- principal(raqData,nfactors=23,rotate="none")
pc1## Principal Components Analysis
## Call: principal(r = raqData, nfactors = 23, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## Q01 0.59 0.18 -0.22 0.12 -0.40 -0.11 -0.22 -0.08 0.01 -0.10 0.11
## Q02 -0.30 0.55 0.15 0.01 -0.03 -0.38 0.19 -0.39 0.01 -0.12 0.30
## Q03 -0.63 0.29 0.21 -0.07 0.02 0.00 0.01 -0.05 0.20 0.10 0.15
## Q04 0.63 0.14 -0.15 0.15 -0.20 -0.12 -0.06 0.11 -0.11 -0.01 -0.03
## Q05 0.56 0.10 -0.07 0.14 -0.42 -0.17 -0.06 0.11 0.24 0.09 -0.30
## Q06 0.56 0.10 0.57 -0.05 0.17 0.01 0.00 0.05 0.00 0.00 -0.13
## Q07 0.69 0.04 0.25 0.10 0.17 -0.08 0.05 0.03 -0.08 0.13 -0.27
## Q08 0.55 0.40 -0.32 -0.42 0.15 0.10 -0.07 -0.04 0.01 -0.05 -0.09
## Q09 -0.28 0.63 -0.01 0.10 0.17 -0.27 -0.01 -0.03 0.16 0.32 -0.22
## Q10 0.44 0.03 0.36 -0.10 -0.34 0.22 0.44 -0.03 0.37 -0.22 -0.11
## Q11 0.65 0.25 -0.21 -0.40 0.13 0.18 -0.01 0.03 0.10 -0.14 0.00
## Q12 0.67 -0.05 0.05 0.25 0.04 -0.08 -0.14 0.08 0.01 -0.11 0.19
## Q13 0.67 0.08 0.28 -0.01 0.13 0.03 -0.21 0.05 0.08 -0.22 0.24
## Q14 0.66 0.02 0.20 0.14 0.08 -0.03 -0.10 -0.06 -0.14 0.16 0.08
## Q15 0.59 0.01 0.12 -0.11 -0.07 0.29 0.32 -0.12 -0.27 0.41 0.15
## Q16 0.68 0.01 -0.14 0.08 -0.32 0.00 0.12 -0.14 -0.19 0.15 0.16
## Q17 0.64 0.33 -0.21 -0.34 0.10 0.05 -0.02 0.03 -0.04 0.02 0.01
## Q18 0.70 0.03 0.30 0.13 0.15 -0.09 -0.10 0.06 -0.06 -0.12 0.05
## Q19 -0.43 0.39 0.10 -0.01 -0.15 0.07 0.05 0.68 0.02 0.16 0.29
## Q20 0.44 -0.21 -0.40 0.30 0.33 -0.01 0.34 0.03 0.33 0.02 0.21
## Q21 0.66 -0.06 -0.19 0.28 0.24 -0.15 0.18 0.10 0.12 0.08 -0.02
## Q22 -0.30 0.47 -0.12 0.38 0.07 0.12 0.31 0.12 -0.41 -0.39 -0.19
## Q23 -0.14 0.37 -0.02 0.51 0.02 0.62 -0.28 -0.22 0.18 0.08 0.00
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22
## Q01 -0.12 0.30 -0.25 0.18 0.12 -0.05 -0.17 0.16 -0.01 -0.21 0.05
## Q02 0.27 -0.02 0.01 -0.24 -0.05 -0.08 0.00 0.01 -0.02 -0.02 0.03
## Q03 0.03 0.10 0.13 0.40 -0.06 0.43 0.08 0.09 0.05 0.01 0.00
## Q04 0.34 -0.32 -0.17 0.12 0.31 0.19 0.05 -0.21 0.04 0.09 -0.02
## Q05 0.16 0.12 0.48 -0.07 -0.08 -0.04 0.01 -0.04 0.00 -0.02 0.02
## Q06 0.20 0.24 -0.03 0.08 0.20 -0.14 0.05 0.09 -0.07 0.04 -0.32
## Q07 0.20 0.04 -0.22 0.00 -0.23 0.03 -0.15 0.20 0.16 0.14 0.24
## Q08 0.03 -0.01 0.04 -0.04 0.03 0.10 0.07 0.12 -0.15 0.06 0.16
## Q09 -0.37 -0.17 -0.07 0.12 0.11 -0.19 -0.02 -0.08 -0.03 0.04 -0.01
## Q10 -0.21 -0.17 -0.15 -0.07 0.03 0.07 -0.01 0.00 0.04 -0.03 0.02
## Q11 0.03 0.02 0.03 -0.02 0.07 -0.05 0.07 0.07 -0.18 0.06 0.00
## Q12 -0.07 -0.45 0.17 0.09 -0.10 -0.08 0.04 0.36 0.00 -0.04 -0.10
## Q13 -0.08 0.01 0.12 0.14 -0.11 -0.06 -0.32 -0.30 -0.06 0.16 0.08
## Q14 -0.29 0.07 0.14 -0.37 0.25 0.34 -0.09 0.06 0.02 0.03 -0.01
## Q15 0.09 -0.09 0.16 0.16 0.06 -0.12 -0.10 -0.04 -0.07 -0.19 0.10
## Q16 -0.19 0.12 -0.08 0.06 -0.22 -0.03 0.22 -0.02 -0.04 0.35 -0.12
## Q17 -0.03 -0.01 -0.01 -0.05 -0.18 0.04 -0.04 -0.10 0.42 -0.15 -0.23
## Q18 -0.11 0.09 0.00 0.03 -0.01 -0.06 0.45 -0.15 0.08 -0.18 0.23
## Q19 0.04 0.06 -0.09 -0.16 -0.03 -0.06 0.01 0.05 -0.02 0.02 0.04
## Q20 0.04 0.17 0.07 0.05 0.22 -0.09 0.00 0.04 0.18 0.10 0.06
## Q21 0.04 0.03 -0.15 -0.04 -0.27 0.20 -0.03 -0.11 -0.31 -0.20 -0.13
## Q22 -0.10 0.08 0.15 0.09 0.01 0.04 -0.06 0.02 0.00 0.01 -0.01
## Q23 0.13 -0.01 -0.07 -0.12 -0.06 -0.03 0.05 -0.03 0.01 -0.01 -0.02
## PC23 h2 u2 com
## Q01 0.01 1 -1.1e-15 6.0
## Q02 0.02 1 -3.8e-15 6.1
## Q03 0.05 1 6.7e-16 4.4
## Q04 0.02 1 -1.1e-15 4.9
## Q05 0.01 1 -6.7e-16 5.2
## Q06 -0.11 1 -4.4e-16 4.4
## Q07 0.09 1 -4.4e-16 4.1
## Q08 -0.36 1 -1.3e-15 5.7
## Q09 0.03 1 -1.3e-15 5.0
## Q10 -0.04 1 2.2e-16 7.7
## Q11 0.41 1 -1.3e-15 4.1
## Q12 -0.02 1 -1.6e-15 3.8
## Q13 -0.05 1 -1.6e-15 4.2
## Q14 0.05 1 -1.1e-15 4.3
## Q15 0.00 1 -6.7e-16 5.6
## Q16 -0.01 1 -1.8e-15 4.0
## Q17 -0.01 1 -1.6e-15 4.3
## Q18 0.01 1 -1.1e-15 3.4
## Q19 -0.02 1 -8.9e-16 3.5
## Q20 -0.04 1 4.4e-16 8.7
## Q21 -0.01 1 -2.2e-16 4.6
## Q22 0.01 1 0.0e+00 7.2
## Q23 0.00 1 1.1e-16 4.2
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
## SS loadings 7.29 1.74 1.32 1.23 0.99 0.90 0.81 0.78 0.75 0.72
## Proportion Var 0.32 0.08 0.06 0.05 0.04 0.04 0.04 0.03 0.03 0.03
## Cumulative Var 0.32 0.39 0.45 0.50 0.55 0.59 0.62 0.65 0.69 0.72
## Proportion Explained 0.32 0.08 0.06 0.05 0.04 0.04 0.04 0.03 0.03 0.03
## Cumulative Proportion 0.32 0.39 0.45 0.50 0.55 0.59 0.62 0.65 0.69 0.72
## PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20
## SS loadings 0.68 0.67 0.61 0.58 0.55 0.52 0.51 0.46 0.42 0.41
## Proportion Var 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02
## Cumulative Var 0.75 0.78 0.80 0.83 0.85 0.88 0.90 0.92 0.94 0.95
## Proportion Explained 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02
## Cumulative Proportion 0.75 0.78 0.80 0.83 0.85 0.88 0.90 0.92 0.94 0.95
## PC21 PC22 PC23
## SS loadings 0.38 0.36 0.33
## Proportion Var 0.02 0.02 0.01
## Cumulative Var 0.97 0.99 1.00
## Proportion Explained 0.02 0.02 0.01
## Cumulative Proportion 0.97 0.99 1.00
##
## Mean item complexity = 5
## Test of the hypothesis that 23 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0
## with the empirical chi square 0 with prob < NA
##
## Fit based upon off diagonal values = 1SS loading or eigen values suggests that only first four components are sufficient. Also fit based on off diagonal values is greater than 0.96 Scree plot
plot(pc1$values,type="b")
Rerunning the analysis with 4 factors
pc2 <- principal(raqData,nfactors=4,rotate="none")
pc2## Principal Components Analysis
## Call: principal(r = raqData, nfactors = 4, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 PC4 h2 u2 com
## Q01 0.59 0.18 -0.22 0.12 0.43 0.57 1.6
## Q02 -0.30 0.55 0.15 0.01 0.41 0.59 1.7
## Q03 -0.63 0.29 0.21 -0.07 0.53 0.47 1.7
## Q04 0.63 0.14 -0.15 0.15 0.47 0.53 1.3
## Q05 0.56 0.10 -0.07 0.14 0.34 0.66 1.2
## Q06 0.56 0.10 0.57 -0.05 0.65 0.35 2.1
## Q07 0.69 0.04 0.25 0.10 0.55 0.45 1.3
## Q08 0.55 0.40 -0.32 -0.42 0.74 0.26 3.5
## Q09 -0.28 0.63 -0.01 0.10 0.48 0.52 1.5
## Q10 0.44 0.03 0.36 -0.10 0.33 0.67 2.1
## Q11 0.65 0.25 -0.21 -0.40 0.69 0.31 2.2
## Q12 0.67 -0.05 0.05 0.25 0.51 0.49 1.3
## Q13 0.67 0.08 0.28 -0.01 0.54 0.46 1.4
## Q14 0.66 0.02 0.20 0.14 0.49 0.51 1.3
## Q15 0.59 0.01 0.12 -0.11 0.38 0.62 1.2
## Q16 0.68 0.01 -0.14 0.08 0.49 0.51 1.1
## Q17 0.64 0.33 -0.21 -0.34 0.68 0.32 2.4
## Q18 0.70 0.03 0.30 0.13 0.60 0.40 1.4
## Q19 -0.43 0.39 0.10 -0.01 0.34 0.66 2.1
## Q20 0.44 -0.21 -0.40 0.30 0.48 0.52 3.2
## Q21 0.66 -0.06 -0.19 0.28 0.55 0.45 1.6
## Q22 -0.30 0.47 -0.12 0.38 0.46 0.54 2.8
## Q23 -0.14 0.37 -0.02 0.51 0.41 0.59 2.0
##
## PC1 PC2 PC3 PC4
## SS loadings 7.29 1.74 1.32 1.23
## Proportion Var 0.32 0.08 0.06 0.05
## Cumulative Var 0.32 0.39 0.45 0.50
## Proportion Explained 0.63 0.15 0.11 0.11
## Cumulative Proportion 0.63 0.78 0.89 1.00
##
## Mean item complexity = 1.8
## Test of the hypothesis that 4 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.06
## with the empirical chi square 4006.15 with prob < 0
##
## Fit based upon off diagonal values = 0.96As scree plot gave only 2 factors lets rerun with 2 factors and see Lets see if the factors are correct, we find the corr matrix from pc2
loadings <- factor.model(pc2$loadings)
communality <- diag(loadings)
communality## Q01 Q02 Q03 Q04 Q05 Q06 Q07
## 0.4346477 0.4137525 0.5297160 0.4685890 0.3430498 0.6539317 0.5452943
## Q08 Q09 Q10 Q11 Q12 Q13 Q14
## 0.7394635 0.4844805 0.3347726 0.6896049 0.5133281 0.5358284 0.4882649
## Q15 Q16 Q17 Q18 Q19 Q20 Q21
## 0.3779918 0.4870822 0.6828085 0.5973378 0.3432423 0.4839965 0.5499069
## Q22 Q23
## 0.4635443 0.4121913The diagonals of this matrix contains the communalities after extraction. Lets see the difference it is called residual
residuals <- factor.residuals(raqmatrix,pc2$loadings)
uniqueness <- diag(residuals)
uniqueness## Q01 Q02 Q03 Q04 Q05 Q06 Q07
## 0.5653523 0.5862475 0.4702840 0.5314110 0.6569502 0.3460683 0.4547057
## Q08 Q09 Q10 Q11 Q12 Q13 Q14
## 0.2605365 0.5155195 0.6652274 0.3103951 0.4866719 0.4641716 0.5117351
## Q15 Q16 Q17 Q18 Q19 Q20 Q21
## 0.6220082 0.5129178 0.3171915 0.4026622 0.6567577 0.5160035 0.4500931
## Q22 Q23
## 0.5364557 0.5878087The diagonal of this matrix is the uniqueness.
residuals<-as.matrix(residuals[upper.tri(residuals)])This command re-creates the object residuals by using only the upper triangle of the original matrix. We now have an object called residuals that contains the residuals stored in a column. This is handy because it makes it easy to calculate various things.
large.resid<-abs(residuals) > 0.05
# proportion of the large residuals
sum(large.resid)/nrow(residuals)## [1] 0.3636364Some other residuals stats, such as the mean, are skipped here.
Rotation
Orthogonal Rotation
We can set rotate=“varimax” in the principal() function. But there are too many things to see.
print.psych() command prints the factor loading matrix associated with the model pc3, but displaying only loadings above .3 (cut = 0.3) and sorting items by the size of their loadings (sort = TRUE).
pc3 <- principal(raqData, nfactors=4, rotate="varimax")
print.psych(pc3, cut = 0.3, sort = TRUE)## Principal Components Analysis
## Call: principal(r = raqData, nfactors = 4, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item RC3 RC1 RC4 RC2 h2 u2 com
## Q06 6 0.80 0.65 0.35 1.0
## Q18 18 0.68 0.33 0.60 0.40 1.5
## Q13 13 0.65 0.54 0.46 1.6
## Q07 7 0.64 0.33 0.55 0.45 1.7
## Q14 14 0.58 0.36 0.49 0.51 1.8
## Q10 10 0.55 0.33 0.67 1.2
## Q15 15 0.46 0.38 0.62 2.6
## Q20 20 0.68 0.48 0.52 1.1
## Q21 21 0.66 0.55 0.45 1.5
## Q03 3 -0.57 0.37 0.53 0.47 2.3
## Q12 12 0.47 0.52 0.51 0.49 2.1
## Q04 4 0.32 0.52 0.31 0.47 0.53 2.4
## Q16 16 0.33 0.51 0.31 0.49 0.51 2.6
## Q01 1 0.50 0.36 0.43 0.57 2.4
## Q05 5 0.32 0.43 0.34 0.66 2.5
## Q08 8 0.83 0.74 0.26 1.1
## Q17 17 0.75 0.68 0.32 1.5
## Q11 11 0.75 0.69 0.31 1.5
## Q09 9 0.65 0.48 0.52 1.3
## Q22 22 0.65 0.46 0.54 1.2
## Q23 23 0.59 0.41 0.59 1.4
## Q02 2 -0.34 0.54 0.41 0.59 1.7
## Q19 19 -0.37 0.43 0.34 0.66 2.2
##
## RC3 RC1 RC4 RC2
## SS loadings 3.73 3.34 2.55 1.95
## Proportion Var 0.16 0.15 0.11 0.08
## Cumulative Var 0.16 0.31 0.42 0.50
## Proportion Explained 0.32 0.29 0.22 0.17
## Cumulative Proportion 0.32 0.61 0.83 1.00
##
## Mean item complexity = 1.8
## Test of the hypothesis that 4 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.06
## with the empirical chi square 4006.15 with prob < 0
##
## Fit based upon off diagonal values = 0.96According to the results and the screenshot of questionnaires above, we could find the questions that load highly on factor 1 are Q6 (“I have little experience of computers”) with the highest loading of .80, Q18 (“R always crashes when I try to use it”), Q13 (“I worry I will cause irreparable damage …”), Q7 (“All computers hate me”), Q14 (“Computers have minds of their own …”), Q10 (“Computers are only for games”), and Q15 (“Computers are out to get me”) with the lowest loading of .46. All these items seem to relate to using computers or R. Therefore we might label this factor fear of computers.
Similarly, we might label the factor 2 as fear of statistics, factor 3 fear of mathematics, and factor 4 peer evaluation.
Factor Scores
By setting scores=TRUE:
library(GPArotation)
pc5 <- principal(raqData, nfactors = 4, rotate = "oblimin", scores = TRUE)
# head(pc5$scores) # access scores by pc5$scores
raqData <- cbind(raqData, pc5$scores)
# bind the factor scores to raqData dataframe for other use
head(raqData)## Q01 Q02 Q03 Q04 Q05 Q06 Q07 Q08 Q09 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18
## 1 4 5 2 4 4 4 3 5 5 4 5 4 4 4 4 3 5 4
## 2 5 5 2 3 4 4 4 4 1 4 4 3 5 3 2 3 4 4
## 3 4 3 4 4 2 5 4 4 4 4 3 3 4 2 4 3 4 3
## 4 3 5 5 2 3 3 2 4 4 2 4 4 4 3 3 3 4 2
## 5 4 5 3 4 4 3 3 4 2 4 4 3 3 4 4 4 4 3
## 6 4 5 3 4 2 2 2 4 2 3 4 2 3 3 1 4 3 1
## Q19 Q20 Q21 Q22 Q23 TC1 TC4 TC3 TC2
## 1 3 4 4 4 1 0.37296709 1.8808424 0.95979596 0.3910711
## 2 3 2 2 2 4 0.63334164 0.2374679 0.29090777 -0.3504080
## 3 5 2 3 4 4 0.39712768 -0.1056263 -0.09333769 0.9249353
## 4 4 2 2 2 3 -0.78741595 0.2956628 -0.77703307 0.2605666
## 5 3 2 4 2 2 0.04425942 0.6815179 0.59786611 -0.6912687
## 6 5 1 3 5 2 -1.70018648 0.2091685 0.02784164 0.6653081Reliability Analysis
If you’re using factor analysis to validate a questionnaire, it is useful to check the reliability of your scale.
Reliability means that a measure (or in this case questionnaire) should consistently reflect the construct that it is measuring. One way to think of this is that, other things being equal, a person should get the same score on a questionnaire if they complete it at two different points in time (we have already discovered that this is called test–retest reliability).
The simplest way to do this in practice is to use split-half reliability. This method randomly splits the data set into two. A score for each participant is then calculated based on each half of the scale. If a scale is very reliable a person’s score on one half of the scale should be the same (or similar) to their score on the other half: two halves should correlate very highly.
Cronbach’s alpha, α
This method is loosely equivalent to splitting data in two in every possible way and computing the correlation coefficient for each split, and then compute the average of these values.
Recall that we have four factors: fear of computers, fear of statistics, fear of mathematics, and peer evaluation. Each factor stands for several questions in the questionnaire. For example, fear of computers includes question 6, 7, 10, …, 18.
computerFear<-raqData[, c(6, 7, 10, 13, 14, 15, 18)]
statisticsFear <- raqData[, c(1, 3, 4, 5, 12, 16, 20, 21)]
mathFear <- raqData[, c(8, 11, 17)]
peerEvaluation <- raqData[, c(2, 9, 19, 22, 23)]Reliability analysis is done with the alpha() function, which is found in the psych package.
So for computerFear, which has only positively scored items, we would use:
keys = c(1, 1, 1, 1, 1, 1, 1)but for statisticsFear, which has item 3 (Question 3, the negatively scored item) as its second item, we would use:
keys = c(1, -1, 1, 1, 1, 1, 1, 1)
alpha(computerFear)##
## Reliability analysis
## Call: alpha(x = computerFear)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.82 0.81 0.4 4.6 0.0052 3.4 0.71 0.39
##
## lower alpha upper 95% confidence boundaries
## 0.81 0.82 0.83
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Q06 0.79 0.79 0.77 0.38 3.7 0.0063 0.0081 0.38
## Q07 0.79 0.79 0.77 0.38 3.7 0.0063 0.0079 0.36
## Q10 0.82 0.82 0.80 0.44 4.7 0.0053 0.0043 0.44
## Q13 0.79 0.79 0.77 0.39 3.8 0.0062 0.0081 0.38
## Q14 0.80 0.80 0.77 0.39 3.9 0.0060 0.0085 0.36
## Q15 0.81 0.81 0.79 0.41 4.2 0.0056 0.0095 0.44
## Q18 0.79 0.78 0.76 0.38 3.6 0.0064 0.0058 0.38
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Q06 2571 0.75 0.74 0.68 0.62 3.8 1.12
## Q07 2571 0.75 0.73 0.68 0.62 3.1 1.10
## Q10 2571 0.54 0.57 0.44 0.40 3.7 0.88
## Q13 2571 0.72 0.73 0.67 0.61 3.6 0.95
## Q14 2571 0.70 0.70 0.64 0.58 3.1 1.00
## Q15 2571 0.64 0.64 0.54 0.49 3.2 1.01
## Q18 2571 0.76 0.76 0.72 0.65 3.4 1.05
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## Q06 0.06 0.10 0.13 0.44 0.27 0
## Q07 0.09 0.24 0.26 0.34 0.07 0
## Q10 0.02 0.10 0.18 0.57 0.14 0
## Q13 0.03 0.12 0.25 0.48 0.12 0
## Q14 0.07 0.18 0.38 0.31 0.06 0
## Q15 0.06 0.18 0.30 0.39 0.07 0
## Q18 0.06 0.12 0.31 0.37 0.14 0# alpha(statisticsFear, keys = c(1, -1, 1, 1, 1, 1, 1, 1))
# alpha(mathFear)
# alpha(peerEvaluation)To reiterate, we’re looking for values in the range of .7 to .8 (or thereabouts) bearing in mind what we’ve already noted about effects from the number of items.
In this case, α of computerFear is slightly above .8, and is certainly in the region indicated by Kline (1999), so this probably indicates good reliability.
r.drop is the correlation of that item with the scale total if that item isn’t included in the scale total. If any of these values of r.drop are less than about .3 then we’ve got problems, because it means that a particular item does not correlate very well with the scale overall.
In this case, all data are above .3, which is encouraging.
The analysis of other three factors is very similar and thus skipped.