Factor Analysis
Hannah Andrews
4/30/2021
Sample: There are 6157 complete cases on CAM variables at Wave 1.
Describe Data
Table: Frequencies and percentages on each variable
## Item Category Frequency Percent Pcnt_of_nonMissing
## 1 aAcupuncture 0 6083 98.8 98.8
## 2 aAcupuncture 1 74 1.2 1.2
## 3 aBiofeedback 0 6109 99.2 99.2
## 4 aBiofeedback 1 48 0.8 0.8
## 5 aChiropractic 0 5418 88.0 88.0
## 6 aChiropractic 1 739 12.0 12.0
## 7 aEnergyHeal 0 6064 98.5 98.5
## 8 aEnergyHeal 1 93 1.5 1.5
## 9 aExerciseMove 0 5079 82.5 82.5
## 10 aExerciseMove 1 1078 17.5 17.5
## 11 aHerbal 0 5856 95.1 95.1
## 12 aHerbal 1 301 4.9 4.9
## 13 aVitamins 0 5875 95.4 95.4
## 14 aVitamins 1 282 4.6 4.6
## 15 aHomeopathy 0 6015 97.7 97.7
## 16 aHomeopathy 1 142 2.3 2.3
## 17 aHypnosis 0 6085 98.8 98.8
## 18 aHypnosis 1 72 1.2 1.2
## 19 aImageryTech 0 5973 97.0 97.0
## 20 aImageryTech 1 184 3.0 3.0
## 21 aMassage 0 5638 91.6 91.6
## 22 aMassage 1 519 8.4 8.4
## 23 aPrayer 0 4315 70.1 70.1
## 24 aPrayer 1 1842 29.9 29.9
## 25 aRelaxMeditate 0 5344 86.8 86.8
## 26 aRelaxMeditate 1 813 13.2 13.2
## 27 aSpecialDiet 0 5488 89.1 89.1
## 28 aSpecialDiet 1 669 10.9 10.9
## 29 aSpiritHeal 0 5961 96.8 96.8
## 30 aSpiritHeal 1 196 3.2 3.2Visualization of frequencies
# Correlation matrix Create and plot the tetrachoric correlation matrix for all CAMs. 
Check that items are not perfectly correlated with each other.
## aA aB aC aEH aEM aHr aV aHm aHy aI aM aP aR aSD aSH
## aAcupuncture 1
## aBiofeedback . 1
## aChiropractic . 1
## aEnergyHeal . . . 1
## aExerciseMove . . 1
## aHerbal , . . , . 1
## aVitamins . . . , 1
## aHomeopathy . . . , . , , 1
## aHypnosis . . . . 1
## aImageryTech . . , . . . . . 1
## aMassage . . . , . . . . . . 1
## aPrayer . . . . . . 1
## aRelaxMeditate . , , . . . . . + . . 1
## aSpecialDiet . . . . . . . . . . 1
## aSpiritHeal . . . . . . , . . 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1Test for correlation adequacy
I will test for correlation adequacy using Bartlett’s Sphericity test. This test tests the hypothesis that correlations between variables are greater than would be expected by chance. The null hypothesis states that all off diagonal are 0. If the null hypothesis is rejected there is correlation adequacy.
## $chisq
## [1] 66329.56
##
## $p.value
## [1] 0
##
## $df
## [1] 105I reject the null hypothesis. The CAM items are adequately correlated.
Test for sampling adequacy
I will test for sampling adequacy using the Kaiser-Meyer-Olkin (KMO) test.MSA refers to the overall measure of sampling adequacy. MSAi refer to the measure of sampling adequacy for each item. MSA is a measure of the proportion of variance among variables that might be common variance. The lower the proportion of variance that is common the more suited the data are for factor analysis.
MSA cutoffs: >.9 marvelous, .8s meritorious, .7s middling, .6s mediocre, .5s miserable, less than .5 is unacceptable.
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = het.mat)
## Overall MSA = 0.76
## MSA for each item =
## aAcupuncture aBiofeedback aChiropractic aEnergyHeal aExerciseMove
## 0.85 0.75 0.73 0.89 0.77
## aHerbal aVitamins aHomeopathy aHypnosis aImageryTech
## 0.91 0.81 0.88 0.72 0.82
## aMassage aPrayer aRelaxMeditate aSpecialDiet aSpiritHeal
## 0.81 0.53 0.64 0.88 0.51Items that may be a concern with regard to sampling adequacy: prayer or other spiritual practices, relaxation or meditation, and spiritual healing. Overall MSA indicates sampling adequacy.
Determining the number of factors
First, I will run a parallel analysis. From RDocumentation: “``Parallel” analyis is a technique that compares the scree of factors of the observed data with that of a random data matrix of the same size as the original."
## Parallel analysis suggests that the number of factors = 6 and the number of components = NAI received many warning messages stating “A cell entry of 0 was replaced with correct = 0.5. Check your data!” This has to do with continuity when computing a tetrachoric correlation matrix. I added 1 to all values in the dataframe to check that the issue was not the 0/1 values. The results were the same.
From Statistics of DOOM notes: i. The dark line is set at one, which is part of the Kaiser criterion. This method is an older rule of thumb that is not well supported anymore. You would look at the number of eigenvalues that are greater than 1 (or .70 in new literature). This rule tends to overestimate the number of factors/components needed. ii. The red dotted line is the random data set used to test this analysis. Your data is randomly reordered to see how many factors are better than chance. iii. The blue line and triangles are your eigenvalues from the real dataset. iv. You want to look at where the blue and red lines cross.
The parallel analysis suggests 6 factors. This is where the lines cross. Looking at the scree plot, none of the drop offs appear to be very large. Seems like there are maybe 2 factors.
Note: Scree plots are a visual depiction of the eigenvalues. Look for the large drop off to figure out how many factors to use.
Kaiser Criterion
# older kaiser criterion, number of eigenvalues greater than 1
sum(nofactors$fa.values > 1.0)## [1] 1# new kaiser criterion, number of eigenvalues greater than 0.7
sum(nofactors$fa.values > .7)## [1] 2New kaiser criterion rule (eigenvalues greater than 0.7) suggests 2 factors.
2-6 Factor Models with all CAM variables
All models run using oblique rotation (factors are allowed to correlate when rotated) and maximum likelihood estimation.
Factor loadings: 2 Factor model with all CAM variables
##
## Loadings:
## ML2 ML1
## aAcupuncture 0.719 -0.131
## aBiofeedback 0.672 -0.106
## aChiropractic 0.448
## aEnergyHeal 0.872
## aExerciseMove 0.618
## aHerbal 0.810
## aVitamins 0.559 0.105
## aHomeopathy 0.804
## aHypnosis 0.565
## aImageryTech 0.728 0.140
## aMassage 0.741 -0.104
## aPrayer 1.007
## aRelaxMeditate 0.647 0.272
## aSpecialDiet 0.415 0.174
## aSpiritHeal 0.185 0.648
##
## ML2 ML1
## SS loadings 5.949 1.622
## Proportion Var 0.397 0.108
## Cumulative Var 0.397 0.505All items only load onto one factor.
Ml1 includes spiritual healing and prayer. All other items load onto ML2.
ML2 accounts for 40% of the variance. ML1 accounts for 12% of the variance. Cumulatively this factor model accounts for 52% of the variance.
The factors are correlated (r = 0.51).
Factor Loadings: 3 Factor model all CAM variables
##
## Loadings:
## ML3 ML1 ML2
## aAcupuncture 0.679
## aBiofeedback 0.228 0.509
## aChiropractic 0.532 -0.144
## aEnergyHeal 0.548 0.275 0.245
## aExerciseMove 0.473 0.204
## aHerbal 0.878
## aVitamins 0.653
## aHomeopathy 0.871
## aHypnosis 0.188 0.343 0.122
## aImageryTech 0.192 0.658 0.140
## aMassage 0.554 0.170
## aPrayer -0.132 0.424 0.637
## aRelaxMeditate 0.992
## aSpecialDiet 0.357 0.126 0.135
## aSpiritHeal 0.998
##
## ML3 ML1 ML2
## SS loadings 3.807 2.167 1.528
## Proportion Var 0.254 0.144 0.102
## Cumulative Var 0.254 0.398 0.500Prayer loads onto two factors (ML1 and ML2). ML1: prayer, biofeedback, hypnosis, imagery techniques, meditation ML2: prayer and spiritual healing ML3: special diet, acupuncture, chiropractice, energy healing, exercise/movement, herbal, vitamins, homeopathy, and massage
Factor Loadings: 4 Factor model all CAM variables
##
## Loadings:
## ML4 ML2 ML1 ML3
## aAcupuncture 0.594 0.105 -0.124
## aBiofeedback 0.638 -0.164
## aChiropractic 0.492 -0.107
## aEnergyHeal 0.410 0.405 0.311 -0.131
## aExerciseMove 0.467 0.203
## aHerbal 0.886
## aVitamins 0.772 -0.135 0.191
## aHomeopathy 0.859
## aHypnosis 0.505 0.223 -0.220
## aImageryTech 0.759 0.163
## aMassage 0.443 0.273 -0.139
## aPrayer 0.176 0.323 0.729
## aRelaxMeditate 0.992 -0.110 0.166
## aSpecialDiet 0.392 0.119
## aSpiritHeal 0.960 0.110
##
## ML4 ML2 ML1 ML3
## SS loadings 3.470 2.568 1.251 0.758
## Proportion Var 0.231 0.171 0.083 0.051
## Cumulative Var 0.231 0.403 0.486 0.536Energy healing loads on three factors. Prayer loads on two factors. ML1: prayer, energy healing, spirit healing ML2: energy healing, biofeedback, hypnosis, imagery techniques, meditation ML3: prayer ML4: Acupuncture, Chiropractic, Exercise, Herbal, Vitamins, Homeopathy, Massage, Special Diet
Factor Loadings: 5 Factor model all CAM variables
##
## Loadings:
## ML5 ML3 ML2 ML4 ML1
## aAcupuncture 0.687 0.126 -0.152 -0.107
## aBiofeedback 0.585 0.224 -0.173
## aChiropractic 0.408 -0.114 0.128
## aEnergyHeal 0.351 0.369 0.146 0.324 -0.132
## aExerciseMove 0.985
## aHerbal 0.902
## aVitamins 0.703 0.101 -0.132 0.198
## aHomeopathy 0.831
## aHypnosis 0.140 0.503 -0.170 0.212 -0.210
## aImageryTech 0.716 0.116 0.173
## aMassage 0.275 0.207 0.350 0.103 -0.150
## aPrayer 0.188 0.317 0.727
## aRelaxMeditate 0.971 -0.109 0.168
## aSpecialDiet 0.248 0.279 0.102 0.111
## aSpiritHeal 0.964 0.106
##
## ML5 ML3 ML2 ML4 ML1
## SS loadings 2.926 2.300 1.337 1.265 0.750
## Proportion Var 0.195 0.153 0.089 0.084 0.050
## Cumulative Var 0.195 0.348 0.438 0.522 0.572Diet doesn’t load on any factors Prayer loads on two factors. Energy healing loads on three factors.
ML1: Prayer ML2: Exercise and massage ML3: Energy, Biofeedback, Hypnosis, ImageryTech, RelaxMeditate ML4: prayer, energy, spiritual healing ML5: Acupuncture, Chiropractic, Herbal, Vitamins, Homeopathy
Factor Loadings: 6 Factor model all CAM variables
##
## Loadings:
## ML5 ML3 ML2 ML4 ML6 ML1
## aAcupuncture 0.555 0.145 -0.176 0.230
## aBiofeedback 0.578 0.212 -0.147
## aChiropractic 0.100 -0.120 0.672
## aEnergyHeal 0.318 0.375 0.134 0.337 -0.124
## aExerciseMove 0.961
## aHerbal 0.857
## aVitamins 0.776 0.111 -0.107 -0.136 0.135
## aHomeopathy 0.761 0.111
## aHypnosis 0.117 0.501 -0.174 0.223 -0.194
## aImageryTech 0.108 0.704 0.125 0.191
## aMassage 0.201 0.278 0.532
## aPrayer 0.163 0.272 0.758
## aRelaxMeditate 0.946 -0.114 0.193
## aSpecialDiet 0.336 0.290 0.121 -0.153
## aSpiritHeal 0.949 0.128
##
## ML5 ML3 ML2 ML4 ML6 ML1
## SS loadings 2.484 2.226 1.239 1.224 0.876 0.745
## Proportion Var 0.166 0.148 0.083 0.082 0.058 0.050
## Cumulative Var 0.166 0.314 0.397 0.478 0.537 0.586Energy healing loads on 3 factors. Prayer and exercise are only items to load on their factors.
Diagrams of factor loadings
Compare model fit for 2, 3, 4, and 5 factor models including all variables
## Warning: executing %dopar% sequentially: no parallel backend registered## Model TLI BIC RMSR RMSEA
## 2 Factor Model Model 1 0.6147528 17875.291 0.07479222 0.1986336
## 3 Factor Model Model 2 0.7101065 11028.394 0.06324245 0.1722974
## 4 Factor Model Model 3 0.7615625 7272.309 0.05559871 0.1562511
## 5 Factor Model Model 4 0.8052751 4600.918 0.04192812 0.1411962
## 6 Factor Model Model 5 0.8210908 3151.229 0.02896826 0.1353333
## RMSEA_lower_bound RMSEA_upper_bound RMSEA_confidence CFI
## 2 Factor Model 0.1962480 0.2010624 0.9 0.7212149
## 3 Factor Model 0.1696741 0.1749637 0.9 0.8261205
## 4 Factor Model 0.1533336 0.1592143 0.9 0.8842378
## 5 Factor Model 0.1379007 0.1445433 0.9 0.9258594
## 6 Factor Model 0.1315285 0.1392000 0.9 0.9489164Reliability
##
## Reliability analysis
## Call: psych::alpha(x = acams[, ML2])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.68 0.71 0.71 0.16 2.5 0.0055 0.063 0.11 0.16
##
## lower alpha upper 95% confidence boundaries
## 0.67 0.68 0.69
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## aAcupuncture 0.68 0.71 0.71 0.17 2.4 0.0057 0.0077 0.16
## aBiofeedback 0.68 0.71 0.71 0.17 2.5 0.0057 0.0072 0.17
## aChiropractic 0.69 0.71 0.71 0.17 2.5 0.0054 0.0072 0.17
## aEnergyHeal 0.66 0.68 0.68 0.15 2.2 0.0059 0.0072 0.14
## aExerciseMove 0.66 0.69 0.69 0.16 2.2 0.0061 0.0074 0.15
## aHerbal 0.65 0.68 0.67 0.15 2.1 0.0061 0.0062 0.15
## aVitamins 0.66 0.70 0.70 0.16 2.3 0.0059 0.0075 0.15
## aHomeopathy 0.66 0.69 0.68 0.15 2.2 0.0059 0.0068 0.15
## aHypnosis 0.68 0.72 0.72 0.17 2.5 0.0056 0.0070 0.17
## aImageryTech 0.66 0.69 0.68 0.15 2.2 0.0060 0.0069 0.14
## aMassage 0.65 0.69 0.69 0.15 2.2 0.0062 0.0074 0.15
## aRelaxMeditate 0.64 0.68 0.68 0.15 2.1 0.0063 0.0068 0.14
## aSpecialDiet 0.67 0.70 0.70 0.16 2.4 0.0057 0.0077 0.16
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## aAcupuncture 6157 0.29 0.39 0.29 0.22 0.0120 0.109
## aBiofeedback 6157 0.25 0.35 0.23 0.19 0.0078 0.088
## aChiropractic 6157 0.43 0.36 0.25 0.21 0.1200 0.325
## aEnergyHeal 6157 0.47 0.56 0.51 0.39 0.0151 0.122
## aExerciseMove 6157 0.61 0.50 0.43 0.39 0.1751 0.380
## aHerbal 6157 0.56 0.60 0.57 0.44 0.0489 0.216
## aVitamins 6157 0.45 0.46 0.38 0.32 0.0458 0.209
## aHomeopathy 6157 0.48 0.54 0.50 0.39 0.0231 0.150
## aHypnosis 6157 0.24 0.33 0.21 0.16 0.0117 0.108
## aImageryTech 6157 0.50 0.54 0.50 0.40 0.0299 0.170
## aMassage 6157 0.58 0.53 0.47 0.42 0.0843 0.278
## aRelaxMeditate 6157 0.62 0.58 0.54 0.43 0.1320 0.339
## aSpecialDiet 6157 0.49 0.42 0.33 0.29 0.1087 0.311
##
## Non missing response frequency for each item
## 0 1 miss
## aAcupuncture 0.99 0.01 0
## aBiofeedback 0.99 0.01 0
## aChiropractic 0.88 0.12 0
## aEnergyHeal 0.98 0.02 0
## aExerciseMove 0.82 0.18 0
## aHerbal 0.95 0.05 0
## aVitamins 0.95 0.05 0
## aHomeopathy 0.98 0.02 0
## aHypnosis 0.99 0.01 0
## aImageryTech 0.97 0.03 0
## aMassage 0.92 0.08 0
## aRelaxMeditate 0.87 0.13 0
## aSpecialDiet 0.89 0.11 0Raw alpha for ML2 is 0.68. This is acceptable.
##
## Reliability analysis
## Call: psych::alpha(x = acams[, ML1])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.29 0.41 0.26 0.26 0.69 0.012 0.17 0.27 0.26
##
## lower alpha upper 95% confidence boundaries
## 0.27 0.29 0.31
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## aPrayer 0.666 0.26 0.065 0.26 0.34 NA 0 0.26
## aSpiritHeal 0.098 0.26 0.065 0.26 0.34 NA 0 0.26
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## aPrayer 6157 0.95 0.79 0.4 0.26 0.299 0.46
## aSpiritHeal 6157 0.55 0.79 0.4 0.26 0.032 0.18
##
## Non missing response frequency for each item
## 0 1 miss
## aPrayer 0.70 0.30 0
## aSpiritHeal 0.97 0.03 0Raw alpha for ML1 if 0.29. This is unacceptable.
It’s notable that the items that load onto factor ML1 both failed the KMO test for sampling adequacy.
Run factor model without prayer and spiritual healing
Tetrachoric correlations (excluding prayer and spiritual healing)
Test for correlation adequacy
Bartlett’s test for sphericity.
## $chisq
## [1] 51305.93
##
## $p.value
## [1] 0
##
## $df
## [1] 78Items are adequately correlated.
Test for sampling adequacy
MSA cutoffs: >.9 marvelous, .8s meritorious, .7s middling, .6s mediocre, .5s miserable, less than .5 is unacceptable.
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = het.mat13)
## Overall MSA = 0.89
## MSA for each item =
## aAcupuncture aBiofeedback aChiropractic aEnergyHeal aExerciseMove
## 0.90 0.86 0.80 0.94 0.86
## aHerbal aVitamins aHomeopathy aHypnosis aImageryTech
## 0.90 0.91 0.91 0.85 0.89
## aMassage aRelaxMeditate aSpecialDiet
## 0.88 0.86 0.89All variables meet requirements for sampling adequacy.
Determining number of factors
Parallel Analysis
## Parallel analysis suggests that the number of factors = 5 and the number of components = NAThe parallel analysis suggests 5 factors. There is a drop off on the scree plot after 4.
Kaiser Criterion
# older kaiser criterion, number of eigenvalues greater than 1
sum(nofactors13$fa.values > 1.0)## [1] 1# new kaiser criterion, number of eigenvalues greater than 0.7
sum(nofactors13$fa.values > .7)## [1] 1The Kaiser criterion suggests there is only 1 factor. The Kaiser criterion tends to over estimate factors. Doesn’t seem good that it’s only estimating 1.
Factor Loadings: 3 factor model excluding prayer and spiritual healing
##
## Loadings:
## ML3 ML1 ML2
## aAcupuncture 0.585
## aBiofeedback 0.582 0.131
## aChiropractic 0.201 -0.200 0.532
## aEnergyHeal 0.370 0.484 0.139
## aExerciseMove 0.265 0.416
## aHerbal 0.892
## aVitamins 0.708 -0.118
## aHomeopathy 0.875
## aHypnosis 0.109 0.487
## aImageryTech 0.910
## aMassage 0.923
## aRelaxMeditate 0.905
## aSpecialDiet 0.360 0.207
##
## ML3 ML1 ML2
## SS loadings 2.734 2.626 1.367
## Proportion Var 0.210 0.202 0.105
## Cumulative Var 0.210 0.412 0.517Energy healing loads on two factors.
Factor Loadings: 4 factor model excluding prayer and spiritual healing
##
## Loadings:
## ML1 ML3 ML2 ML4
## aAcupuncture 0.188 0.491 -0.203 0.291
## aBiofeedback 0.555 0.204 0.138
## aChiropractic 0.132 0.116 0.580
## aEnergyHeal 0.514 0.318 0.154
## aExerciseMove 0.852
## aHerbal 0.850
## aVitamins 0.750 0.114 -0.217
## aHomeopathy 0.821 0.105
## aHypnosis 0.597 -0.241 0.133
## aImageryTech 0.894
## aMassage 0.178 0.339 0.507
## aRelaxMeditate 0.919
## aSpecialDiet 0.106 0.397 0.273 -0.179
##
## ML1 ML3 ML2 ML4
## SS loadings 2.668 2.501 1.095 0.844
## Proportion Var 0.205 0.192 0.084 0.065
## Cumulative Var 0.205 0.398 0.482 0.547Massage and energy heal load on two factors.
Factor loadings: 5 factor model excluding prayer and spiritual healing
##
## Loadings:
## ML2 ML3 ML4 ML1 ML5
## aAcupuncture 0.504 0.148 -0.378
## aBiofeedback 0.982
## aChiropractic 0.139 -0.182 0.536 -0.164
## aEnergyHeal 0.345 0.411 0.165 0.155
## aExerciseMove 0.157 0.427 0.151 0.445
## aHerbal 0.827
## aVitamins 0.740 0.224
## aHomeopathy 0.839
## aHypnosis 0.668 -0.167 -0.263
## aImageryTech 0.852
## aMassage 0.908
## aRelaxMeditate 0.745 0.191
## aSpecialDiet 0.415 0.158 0.282
##
## ML2 ML3 ML4 ML1 ML5
## SS loadings 2.529 1.989 1.354 1.120 0.585
## Proportion Var 0.195 0.153 0.104 0.086 0.045
## Cumulative Var 0.195 0.348 0.452 0.538 0.583Exercise/movement and energy healing load on two factors
Compare model fit for 3, 4, and 5 factor models excluding prayer and spiritual healing
## Model TLI BIC RMSR RMSEA
## 3 Factor Model Model 1 0.8381332 4139.058 0.05095690 0.13138001
## 4 Factor Model Model 2 0.8803216 2266.929 0.03003509 0.11296260
## 5 Factor Model Model 3 0.9109208 1167.187 0.02007195 0.09745208
## RMSEA_lower_bound RMSEA_upper_bound RMSEA_confidence CFI
## 3 Factor Model 0.12816309 0.1346476 0.9 0.9128694
## 4 Factor Model 0.10927667 0.1167114 0.9 0.9509225
## 5 Factor Model 0.09310654 0.1018849 0.9 0.9737473Four factor model dropping prayer, spiritual healing, biofeedback, and hypnosis.
## Factor Analysis using method = ml
## Call: fa(r = het.mat3, nfactors = 4, n.obs = nrow(acams11), rotate = "oblimin",
## fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 ML3 ML4 h2 u2 com
## aAcupuncture 0.33 0.05 0.05 -0.11 0.12 0.88 1.3
## aChiropractic 0.09 -0.06 0.33 -0.04 0.12 0.88 1.2
## aEnergyHeal 0.31 0.30 0.08 -0.07 0.28 0.72 2.2
## aExerciseMove -0.02 0.06 0.26 0.39 0.32 0.68 1.8
## aHerbal 0.65 0.02 0.02 0.02 0.46 0.54 1.0
## aVitamins 0.35 0.01 -0.09 0.24 0.22 0.78 1.9
## aHomeopathy 0.63 -0.03 0.01 0.00 0.39 0.61 1.0
## aImageryTech -0.01 0.79 -0.02 -0.01 0.61 0.39 1.0
## aMassage 0.01 0.00 0.74 0.00 0.56 0.44 1.0
## aRelaxMeditate 0.06 0.39 0.12 0.18 0.33 0.67 1.7
## aSpecialDiet 0.09 0.03 -0.04 0.44 0.23 0.77 1.1
##
## ML1 ML2 ML3 ML4
## SS loadings 1.28 0.98 0.83 0.54
## Proportion Var 0.12 0.09 0.08 0.05
## Cumulative Var 0.12 0.20 0.28 0.33
## Proportion Explained 0.35 0.27 0.23 0.15
## Cumulative Proportion 0.35 0.62 0.85 1.00
##
## With factor correlations of
## ML1 ML2 ML3 ML4
## ML1 1.00 0.44 0.43 0.38
## ML2 0.44 1.00 0.35 0.33
## ML3 0.43 0.35 1.00 0.38
## ML4 0.38 0.33 0.38 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 55 and the objective function was 1.39 with Chi Square of 8540.37
## The degrees of freedom for the model are 17 and the objective function was 0.01
##
## The root mean square of the residuals (RMSR) is 0.01
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic number of observations is 6157 with the empirical chi square 67.2 with prob < 6.5e-08
## The total number of observations was 6157 with Likelihood Chi Square = 59.08 with prob < 1.5e-06
##
## Tucker Lewis Index of factoring reliability = 0.984
## RMSEA index = 0.02 and the 90 % confidence intervals are 0.015 0.026
## BIC = -89.26
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1 ML2 ML3 ML4
## Correlation of (regression) scores with factors 0.83 0.83 0.80 0.68
## Multiple R square of scores with factors 0.69 0.69 0.65 0.47
## Minimum correlation of possible factor scores 0.38 0.38 0.29 -0.07Factor Loadings
All items now load on a factor. All items only load onto one factor (great!). Energy healing is now loading onto the same factor as acupuncture, herbal therapy, vitamins, and homeopathy. I am not sure why an item would change factors after dropping items that did not load.
Model fit
Goodness of fit statistics
TLI equals 0.985 - great! The comparitive fit index (CFI) equals
## [1] 0.9950414Also great!
Residual fit statistics
(RMSR) is 0.01, indicating excellent fit. RMSEA is 0.019, indicating excellent fit.
Reliability Assessment
##
## Reliability analysis
## Call: psych::alpha(x = acams11[, factor1])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.6 0.61 0.57 0.24 1.6 0.0074 0.029 0.1 0.24
##
## lower alpha upper 95% confidence boundaries
## 0.59 0.6 0.62
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## aAcupuncture 0.60 0.62 0.56 0.29 1.61 0.0079 0.0064 0.29
## aEnergyHeal 0.56 0.56 0.51 0.24 1.30 0.0084 0.0127 0.24
## aHerbal 0.46 0.49 0.43 0.19 0.96 0.0106 0.0052 0.19
## aVitamins 0.59 0.59 0.53 0.27 1.46 0.0077 0.0074 0.25
## aHomeopathy 0.50 0.51 0.45 0.21 1.05 0.0094 0.0073 0.20
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## aAcupuncture 6157 0.43 0.54 0.32 0.24 0.012 0.11
## aEnergyHeal 6157 0.55 0.62 0.45 0.35 0.015 0.12
## aHerbal 6157 0.77 0.72 0.63 0.49 0.049 0.22
## aVitamins 6157 0.66 0.57 0.38 0.32 0.046 0.21
## aHomeopathy 6157 0.67 0.69 0.58 0.46 0.023 0.15
##
## Non missing response frequency for each item
## 0 1 miss
## aAcupuncture 0.99 0.01 0
## aEnergyHeal 0.98 0.02 0
## aHerbal 0.95 0.05 0
## aVitamins 0.95 0.05 0
## aHomeopathy 0.98 0.02 0Raw alpha for factor 1 (acupuncture, energy healing, herbal, vitamins, and homeopathy) is 0.59 .
##
## Reliability analysis
## Call: psych::alpha(x = acams11[, factor2])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.48 0.57 0.4 0.4 1.3 0.01 0.081 0.22 0.4
##
## lower alpha upper 95% confidence boundaries
## 0.46 0.48 0.5
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## aImageryTech 0.20 0.4 0.16 0.4 0.66 NA 0 0.4
## aRelaxMeditate 0.79 0.4 0.16 0.4 0.66 NA 0 0.4
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## aImageryTech 6157 0.70 0.84 0.53 0.4 0.03 0.17
## aRelaxMeditate 6157 0.93 0.84 0.53 0.4 0.13 0.34
##
## Non missing response frequency for each item
## 0 1 miss
## aImageryTech 0.97 0.03 0
## aRelaxMeditate 0.87 0.13 0Raw alpha for factor 2 (imagery techniques and meditation) is 0.48 .
##
## Reliability analysis
## Call: psych::alpha(x = acams11[, factor3])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.4 0.41 0.25 0.25 0.68 0.015 0.1 0.24 0.25
##
## lower alpha upper 95% confidence boundaries
## 0.37 0.4 0.43
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## aChiropractic 0.30 0.25 0.065 0.25 0.34 NA 0 0.25
## aMassage 0.22 0.25 0.065 0.25 0.34 NA 0 0.25
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## aChiropractic 6157 0.83 0.79 0.4 0.25 0.120 0.33
## aMassage 6157 0.75 0.79 0.4 0.25 0.084 0.28
##
## Non missing response frequency for each item
## 0 1 miss
## aChiropractic 0.88 0.12 0
## aMassage 0.92 0.08 0Raw alpha for factor 3 ( chiropractic and massage) is 0.40 .
##
## Reliability analysis
## Call: psych::alpha(x = acams11[, factor4])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.38 0.39 0.24 0.24 0.64 0.015 0.14 0.27 0.24
##
## lower alpha upper 95% confidence boundaries
## 0.35 0.38 0.41
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## aExerciseMove 0.29 0.24 0.058 0.24 0.32 NA 0 0.24
## aSpecialDiet 0.20 0.24 0.058 0.24 0.32 NA 0 0.24
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## aExerciseMove 6157 0.83 0.79 0.39 0.24 0.18 0.38
## aSpecialDiet 6157 0.74 0.79 0.39 0.24 0.11 0.31
##
## Non missing response frequency for each item
## 0 1 miss
## aExerciseMove 0.82 0.18 0
## aSpecialDiet 0.89 0.11 0Raw alpha for factor 4 (exercise and diet) is 0.40 .