Ron Meeting 06/24/21
Hannah Andrews
06/23/2021
Sample: There are 6157 complete cases on CAM variables at Wave 1.
CAM Descriptives
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
## Number of CAM treatments used in the past 12 months
## totalCams
## 0 1 2 3 4 5
## 0.4866006172 0.2320935521 0.1279844080 0.0729251259 0.0328081858 0.0190027611
## 6 7 8 9 10 11
## 0.0120188403 0.0063342537 0.0040604190 0.0021114179 0.0019490011 0.0014617509
## 13 15
## 0.0004872503 0.0001624168## Category f rf rf(%) cf cf(%)
## 0 2996 0.49 48.66 2996 48.66
## 1 1429 0.23 23.21 4425 71.87
## 2 788 0.13 12.80 5213 84.67
## 3 449 0.07 7.29 5662 91.96
## 4 202 0.03 3.28 5864 95.24
## 5 117 0.02 1.90 5981 97.14
## 6 74 0.01 1.20 6055 98.34
## 7 39 0.01 0.63 6094 98.98
## 8 25 0.00 0.41 6119 99.38
## 9 13 0.00 0.21 6132 99.59
## 10 12 0.00 0.19 6144 99.79
## 11 9 0.00 0.15 6153 99.94
## 13 3 0.00 0.05 6156 99.98
## 15 1 0.00 0.02 6157 100.00Analayses including all 15 CAMs
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 completed using maximum likelihood factoring method. 
## 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.
After readings Ayers and Kronenfeld (2010), I will test the old CAM domains posted by the National Center for Complementary and Alternative Medicine (NCCAM), now the National Center for Complementary and Integrative Medicine (NCCIM). Then I will test the domains found by Ayers and Kronenfeld (2010). Finally, I will test the NCCIM’s current CAM domains before performing exploratory factor analysis on the MIDUS data.
Compare model fit for 1, 2, 3, 4, 5, 6 factor models including all CAMs
Factor method: Maximum likelihood Rotation method: Oblique
## Warning: executing %dopar% sequentially: no parallel backend registered## Model TLI BIC RMSR RMSEA
## 1 Factor Mode1 Model 1 0.5927004 22422.125 0.09183285 0.2042507
## 2 Factor Model Model 2 0.6147528 17875.291 0.07479222 0.1986336
## 3 Factor Model Model 3 0.7101065 11028.394 0.06324245 0.1722974
## 4 Factor Model Model 4 0.7615625 7272.309 0.05559871 0.1562511
## 5 Factor Model Model 5 0.8052751 4600.918 0.04192812 0.1411962
## 6 Factor Model Model 6 0.8210908 3151.229 0.02896826 0.1353333
## RMSEA_lower_bound RMSEA_upper_bound RMSEA_confidence CFI
## 1 Factor Mode1 0.2020598 0.2064837 0.9 0.6509240
## 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 0.9489164Models excluding prayer, spiritual healing, and energy healing
Tetrachoric correlation matrix
## Bartlett’s Test of Spherecity 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] 42574.65
##
## $p.value
## [1] 0
##
## $df
## [1] 66KMO 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.mat12)
## Overall MSA = 0.86
## MSA for each item =
## aAcupuncture aBiofeedback aChiropractic aExerciseMove aHerbal
## 0.87 0.85 0.80 0.83 0.87
## aVitamins aHomeopathy aHypnosis aImageryTech aMassage
## 0.89 0.89 0.86 0.87 0.87
## aRelaxMeditate aSpecialDiet
## 0.83 0.88Great.
Parallel Analysis
Maximum Likelihood
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 = 5 and the number of components = NAPrincipal axis
## Parallel analysis suggests that the number of factors = 5 and the number of components = NAMinimum Residual
## Parallel analysis suggests that the number of factors = 5 and the number of components = NAFrom 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 5 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
Old Kaiser Criterion
# older kaiser criterion, number of eigenvalues greater than 1
sum(acams12_parallelMl$fa.values > 1.0)## [1] 1New Kaiser Criterion
## [1] 1Create table for model comparisons of all models excluding prayer, spiritual healing, and energy
Factor alphas input in order from factor loadings matrix. For example, if ML3 is the first column of factors presented in the factor loadings table when called, the alpha will be input under reliabilityF1. Reliability calculated using Kuder-Richardson Formula 20 (KR-20), a measure for testing the reliability of binary items. If an item loads equally on multiple factors, I include it in the reliability calculation for all factors it loads on. In notes, I refer to factors in order of reliability columns. For example, “Massage loads onto factors 1 and 2” refers to reliabilityF1 and reliabilityF2.
(Code chunk here, does not appear in html output.)
Maximum likelihood, Three factor
Orthogonal rotation: Varimax
Massage and special diet load equally onto multiple factors. When calculating alphas, I include them for all factors they load onto.
Oblique rotation: promax
Special diet does not load on any factors. Massage loads equally on two factors.
Oblique rotation: oblimin
Massage loads fairly equally on factors 1 and 3. Special diet does not load on any factors.
Oblique rotation: cluster
All items load on one factor. Special diet is questionable - less than .1 difference factor loading between factors 1 and 3. About .12 difference in loadings on factors 1 and 3 for massage.
Principal Axis, Three factor
Orthogonal rotation: varimax
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
Principal axis factoring produces an ultra-Heywood case. Warning message states factor scorings are probably incorrect. None of the principal axis solution are included in the table. They have been left out of the results here as well.
Minimum Residual, Three Factors
Minimum residual solutions produce error message warning about ultra-Heywood case. Not included in model comparisons table or in the results here.
Maximum Likelihood, Four Factor
Orthogonal rotation: Varimax
Acupuncture loads on 1, 2, 4. Special diet loads on 2, 3.
Oblique rotation: promax
Oblique rotation: oblimin
Oblique rotation: cluster
Model fit comparison: Three and four factor models excluding prayer, spiritual healing, and energy healing
## Model TLI CFI BIC
## 1 Three Factor, Maximum Likelihood, Varimax 0.8281754 0.9141157 3395.890
## 2 Three Factor, Maximum Likelihood, Promax 0.8281754 0.9141157 3395.890
## 3 Three Factor, Maximum Likelihood, oblimin 0.8281754 0.9141157 3395.890
## 4 Three Factor, Maximum Likelihood, cluster 0.8281754 0.9141157 3395.890
## 5 Four Factor, Maximum Likelihood, Varimax 0.8722328 0.9535594 1788.721
## 6 Four Factor, Maximum Likelihood, Promax 0.8722328 0.9535594 1788.721
## 7 Four Factor, Maximum Likelihood, Oblimin 0.8722328 0.9535594 1788.721
## 8 Four Factor, Maximum Likelihood, Cluster 0.8722328 0.9535594 1788.721
## RMSEA RMSEA_lower_bound RMSEA_upper_bound RMSEA_confidence RMSR
## 1 0.1340460 0.1304178 0.1377325 0.9 0.05364173
## 2 0.1340460 0.1304178 0.1377325 0.9 0.05364173
## 3 0.1340460 0.1304178 0.1377325 0.9 0.05364173
## 4 0.1340460 0.1304178 0.1377325 0.9 0.05364173
## 5 0.1155838 0.1113305 0.1199140 0.9 0.03166634
## 6 0.1155838 0.1113305 0.1199140 0.9 0.03166634
## 7 0.1155838 0.1113305 0.1199140 0.9 0.03166634
## 8 0.1155838 0.1113305 0.1199140 0.9 0.03166634
## reliabilityF1 reliabilityF2 reliabilityF3 reliabilityF4 reliabilityF5
## 1 0.5448215 0.4907695 0.4739292 NA NA
## 2 0.5420952 0.4301535 0.4625759 NA NA
## 3 0.5420952 0.4301535 0.4625759 NA NA
## 4 0.4694976 0.4301535 0.4739292 NA NA
## 5 0.4391816 0.5211192 0.3831456 0.3519221 NA
## 6 0.4301535 0.5211192 Inf 0.4025591 NA
## 7 0.5211192 0.4301535 Inf 0.4025591 NA
## 8 0.5211192 0.4301535 Inf 0.4025591 NA
## notes
## 1 Massage loads on all three factors fairly equally. Special diet loads on factors 1 and 3.
## 2 Special diet does not load on any factors. Massage loads on factors 1 and 3.
## 3 Massage loads fairly equally on factors 1 and 3. Special diet does not load on any factors.
## 4 All items load on one factor. Special diet is questionable - less than .1 difference factor loading between factors 1 and 2. About .12 difference in loadings on factors 1 and 3 for massage.
## 5 Acupuncture loads on 1, 2, 4. Special diet loads on 2, 3.
## 6 Exercise only loads on one factor, factor 3
## 7 Exercise only loads on one factor, factor 3
## 8 Exercise only loads on one factor, factor 3