Correlations

EFA

## Parallel analysis suggests that the number of factors =  4  and the number of components =  4

The suggested number of factors is 4, so we will start with a model with 4 factors.

Each factor consist of minimum 3 variables. None of the variables have loadings less than 0.3 None of the variables have equal loadings for more than one factor, which is good for our model.

## Factor Analysis using method =  minres
## Call: fa(r = dataf1, nfactors = 4, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
##         MR3   MR1   MR2   MR4   h2   u2 com
## beck  -0.50 -0.35 -0.09 -0.09 0.49 0.51 2.0
## Ak.As  0.26  0.41 -0.06  0.60 0.71 0.29 2.2
## Bo     0.57  0.34 -0.06 -0.11 0.55 0.45 1.7
## Ca     0.21  0.69 -0.18 -0.05 0.64 0.36 1.3
## To.As  0.04  0.82 -0.17 -0.04 0.72 0.28 1.1
## Sp.As -0.40 -0.34  0.16  0.32 0.45 0.55 3.3
## Ak     0.35  0.12  0.22  0.52 0.49 0.51 2.3
## To    -0.09  0.94  0.14  0.02 0.85 0.15 1.1
## Sp     0.88  0.02  0.15  0.11 0.81 0.19 1.1
## Us     0.84  0.07  0.01  0.03 0.74 0.26 1.0
## Ud     0.21  0.52 -0.08  0.12 0.41 0.59 1.5
## Po     0.29  0.17 -0.06  0.15 0.17 0.83 2.3
## glo1   0.24  0.17  0.07 -0.35 0.22 0.78 2.4
## glo2   0.13  0.19  0.19 -0.77 0.68 0.32 1.3
## glo3  -0.26  0.25  0.75 -0.12 0.66 0.34 1.5
## glo4  -0.68  0.27  0.23  0.24 0.54 0.46 1.9
## glo5   0.28 -0.21  0.86 -0.09 0.86 0.14 1.4
## glo6  -0.09 -0.04  0.69  0.11 0.49 0.51 1.1
## 
##                        MR3  MR1  MR2  MR4
## SS loadings           3.47 3.32 2.08 1.63
## Proportion Var        0.19 0.18 0.12 0.09
## Cumulative Var        0.19 0.38 0.49 0.58
## Proportion Explained  0.33 0.32 0.20 0.16
## Cumulative Proportion 0.33 0.65 0.84 1.00
## 
##  With factor correlations of 
##       MR3   MR1   MR2   MR4
## MR3  1.00  0.27 -0.01  0.01
## MR1  0.27  1.00 -0.03  0.10
## MR2 -0.01 -0.03  1.00 -0.05
## MR4  0.01  0.10 -0.05  1.00
## 
## Mean item complexity =  1.7
## Test of the hypothesis that 4 factors are sufficient.
## 
## The degrees of freedom for the null model are  153  and the objective function was  15.35 with Chi Square of  417.03
## The degrees of freedom for the model are 87  and the objective function was  6.5 
## 
## The root mean square of the residuals (RMSR) is  0.08 
## The df corrected root mean square of the residuals is  0.1 
## 
## The harmonic number of observations is  35 with the empirical chi square  65.02  with prob <  0.96 
## The total number of observations was  35  with Likelihood Chi Square =  159.18  with prob <  3.8e-06 
## 
## Tucker Lewis Index of factoring reliability =  0.431
## RMSEA index =  0.151  and the 90 % confidence intervals are  0.117 0.194
## BIC =  -150.14
## Fit based upon off diagonal values = 0.94
## Measures of factor score adequacy             
##                                                    MR3  MR1  MR2  MR4
## Correlation of (regression) scores with factors   0.96 0.98 0.97 0.93
## Multiple R square of scores with factors          0.92 0.97 0.95 0.87
## Minimum correlation of possible factor scores     0.84 0.93 0.89 0.75

The mixed type of correlation was used which is automatically includes rotation in the model. As can be seen, there are correlations between factors presented. There is non-orthogonal rotation, There is a a medium positive correlation between factors 1 and 2. Therefore, such rotation is approved, the factors are connected with each other.

Cumulative Var = 0.58 Proportion Explained varies from 0.16 to 0.3. The variables should be equally distributed between factors,and here we have a kind of bad distribution. Proportion Variance: each factor should describe at least 10%, all of the factors do.

Regression

factors

  ALL PK EK SK
Predictors Estimates CI p Estimates CI p Estimates CI p Estimates CI p
(Intercept) 79.57 74.32 – 84.82 <0.001 25.57 23.40 – 27.74 <0.001 26.71 24.99 – 28.44 <0.001 27.60 25.71 – 29.49 <0.001
MR1 1.46 -4.28 – 7.19 0.608 0.71 -1.67 – 3.08 0.548 0.12 -1.77 – 2.01 0.896 0.81 -1.26 – 2.87 0.431
MR2 -3.16 -8.67 – 2.34 0.250 -0.69 -2.96 – 1.59 0.542 -2.21 -4.03 – -0.40 0.018 -0.39 -2.37 – 1.59 0.690
MR3 -0.28 -6.09 – 5.53 0.923 0.48 -1.92 – 2.88 0.687 -0.14 -2.05 – 1.77 0.882 -0.51 -2.59 – 1.58 0.625
MR4 -3.13 -8.89 – 2.64 0.277 -1.91 -4.30 – 0.47 0.112 -0.73 -2.63 – 1.17 0.437 -0.12 -2.19 – 1.95 0.906
Observations 35 35 35 35
R2 / R2 adjusted 0.082 / -0.041 0.103 / -0.016 0.182 / 0.073 0.030 / -0.099

Vars only

  ALL PK EK SK
Predictors Estimates CI p Estimates CI p Estimates CI p Estimates CI p
(Intercept) 167.78 59.40 – 276.16 0.005 60.75 20.17 – 101.33 0.006 48.23 15.52 – 80.94 0.007 51.50 4.50 – 98.50 0.034
beck -1.46 -2.67 – -0.24 0.022 -0.60 -1.06 – -0.15 0.012 -0.08 -0.45 – 0.29 0.651 -0.72 -1.25 – -0.19 0.010
Ak-As -0.30 -1.04 – 0.44 0.409 -0.21 -0.48 – 0.07 0.135 0.18 -0.04 – 0.41 0.103 -0.28 -0.60 – 0.05 0.088
Bo -0.37 -1.47 – 0.73 0.490 -0.21 -0.63 – 0.20 0.286 0.03 -0.31 – 0.36 0.870 -0.17 -0.65 – 0.30 0.451
Ca 0.43 -0.86 – 1.72 0.491 0.07 -0.41 – 0.55 0.765 -0.04 -0.43 – 0.35 0.814 0.39 -0.17 – 0.95 0.155
To-As -0.09 -1.11 – 0.92 0.846 -0.06 -0.44 – 0.32 0.746 0.13 -0.18 – 0.44 0.391 -0.12 -0.57 – 0.32 0.561
Sp-As -1.11 -2.27 – 0.05 0.059 -0.45 -0.88 – -0.01 0.045 -0.28 -0.63 – 0.07 0.111 -0.30 -0.80 – 0.21 0.227
Ak 0.26 -0.45 – 0.98 0.446 0.11 -0.16 – 0.38 0.387 0.09 -0.13 – 0.31 0.388 0.10 -0.21 – 0.41 0.490
To -0.53 -1.62 – 0.56 0.315 -0.02 -0.43 – 0.39 0.918 -0.30 -0.63 – 0.03 0.072 -0.20 -0.67 – 0.27 0.377
Sp -0.03 -1.01 – 0.95 0.950 0.05 -0.32 – 0.42 0.771 0.08 -0.22 – 0.37 0.591 -0.15 -0.57 – 0.28 0.470
Us -0.03 -1.76 – 1.71 0.973 0.21 -0.44 – 0.86 0.505 -0.19 -0.72 – 0.33 0.451 -0.03 -0.78 – 0.72 0.932
Ud -0.61 -1.35 – 0.13 0.099 -0.33 -0.61 – -0.06 0.021 -0.16 -0.39 – 0.06 0.146 -0.08 -0.40 – 0.24 0.611
Po 0.17 -0.95 – 1.28 0.755 -0.03 -0.45 – 0.38 0.869 -0.12 -0.46 – 0.22 0.460 0.29 -0.19 – 0.78 0.217
glo1 0.11 -0.66 – 0.87 0.775 0.07 -0.21 – 0.36 0.591 0.04 -0.19 – 0.28 0.689 -0.01 -0.34 – 0.32 0.957
glo2 -0.06 -0.88 – 0.76 0.873 -0.05 -0.35 – 0.26 0.748 0.18 -0.07 – 0.42 0.149 -0.17 -0.53 – 0.18 0.316
glo3 0.29 -0.72 – 1.30 0.550 0.19 -0.19 – 0.56 0.315 -0.04 -0.34 – 0.27 0.805 0.10 -0.34 – 0.53 0.651
glo4 1.18 0.19 – 2.17 0.022 0.45 0.08 – 0.82 0.020 0.24 -0.05 – 0.54 0.101 0.45 0.02 – 0.88 0.040
glo5 0.20 -0.70 – 1.11 0.637 0.02 -0.32 – 0.36 0.915 -0.10 -0.37 – 0.17 0.446 0.25 -0.15 – 0.64 0.201
glo6 -1.04 -1.94 – -0.14 0.027 -0.42 -0.76 – -0.08 0.018 -0.13 -0.40 – 0.14 0.332 -0.43 -0.82 – -0.04 0.033
Observations 35 35 35 35
R2 / R2 adjusted 0.705 / 0.372 0.764 / 0.498 0.779 / 0.531 0.546 / 0.034

for XPN

EFA

## Parallel analysis suggests that the number of factors =  2  and the number of components =  2

The suggested number of factors is 3, so we will start with a model with 2 factors.

Each factor consist of minimum 5 variables. None of the variables have loadings less than 0.3 None of the variables have equal loadings for more than one factor, which is good for our model.

## Factor Analysis using method =  minres
## Call: fa(r = data_f1, nfactors = 3, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
##         MR1   MR2   MR3   h2    u2 com
## beck  -0.74  0.07 -0.05 0.57  0.43 1.0
## Ak.As  0.84 -0.07  0.10 0.76  0.24 1.0
## Bo     0.71 -0.17  0.11 0.60  0.40 1.2
## Ca     0.92 -0.12 -0.05 0.84  0.16 1.0
## To.As  0.91 -0.02 -0.01 0.83  0.17 1.0
## Sp.As -0.60  0.27 -0.46 0.80  0.20 2.3
## Ak     0.29  0.39  0.37 0.37  0.63 2.8
## To     0.89  0.36 -0.03 0.89  0.11 1.3
## Sp     0.12  0.09  0.80 0.68  0.32 1.1
## Us     0.22 -0.08  0.84 0.86  0.14 1.2
## Ud     0.43  0.14  0.36 0.37  0.63 2.2
## Po    -0.11  0.07  0.95 0.86  0.14 1.0
## glo1   0.13  0.35 -0.50 0.41  0.59 2.0
## glo2   0.29  0.82 -0.15 0.78  0.22 1.3
## glo3   0.16  0.86 -0.24 0.87  0.13 1.2
## glo4   0.17  0.32 -0.39 0.29  0.71 2.4
## glo5  -0.21  1.00  0.22 1.02 -0.02 1.2
## glo6  -0.22  0.83  0.01 0.75  0.25 1.1
## 
##                        MR1  MR2  MR3
## SS loadings           5.28 3.82 3.45
## Proportion Var        0.29 0.21 0.19
## Cumulative Var        0.29 0.51 0.70
## Proportion Explained  0.42 0.30 0.28
## Cumulative Proportion 0.42 0.72 1.00
## 
##  With factor correlations of 
##       MR1   MR2   MR3
## MR1  1.00 -0.04  0.20
## MR2 -0.04  1.00 -0.16
## MR3  0.20 -0.16  1.00
## 
## Mean item complexity =  1.5
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  153  and the objective function was  108.73 with Chi Square of  779.23
## The degrees of freedom for the model are 102  and the objective function was  92.49 
## 
## The root mean square of the residuals (RMSR) is  0.08 
## The df corrected root mean square of the residuals is  0.1 
## 
## The harmonic number of observations is  15 with the empirical chi square  29.36  with prob <  1 
## The total number of observations was  15  with Likelihood Chi Square =  477.88  with prob <  5.8e-50 
## 
## Tucker Lewis Index of factoring reliability =  -0.379
## RMSEA index =  0.491  and the 90 % confidence intervals are  0.467 0.56
## BIC =  201.66
## Fit based upon off diagonal values = 0.96

The mixed type of correlation was used which is automatically includes rotation in the model. As can be seen, there are correlations between factors presented. There is non-orthogonal rotation, There is a a medium positive correlation between factors 1 and 2. Therefore, such rotation is approved, the factors are connected with each other.

Cumulative Var = 0.7 Proportion Explained varies from 0.28 to 0.42. The variables should be equally distributed between factors,and here we have almost ok distribution. Proportion Variance: each factor should describe at least 10%, all of the factors do.

Regression

factors

  ALL PK EK SK
Predictors Estimates CI p Estimates CI p Estimates CI p Estimates CI p
(Intercept) 77.13 69.34 – 84.92 <0.001 24.20 21.16 – 27.24 <0.001 26.47 23.46 – 29.47 <0.001 26.47 23.60 – 29.33 <0.001
MR1 3.20 -4.50 – 10.91 0.380 1.20 -1.81 – 4.21 0.400 1.35 -1.63 – 4.32 0.341 0.66 -2.17 – 3.49 0.618
MR2 -4.35 -11.35 – 2.65 0.199 -1.40 -4.13 – 1.34 0.284 -1.84 -4.54 – 0.86 0.162 -1.11 -3.68 – 1.47 0.363
MR3 -4.23 -12.42 – 3.96 0.280 -1.21 -4.41 – 1.99 0.424 -2.60 -5.76 – 0.56 0.098 -0.42 -3.44 – 2.59 0.762
Observations 15 15 15 15
R2 / R2 adjusted 0.263 / 0.061 0.204 / -0.014 0.347 / 0.168 0.119 / -0.121

for hyper

EFA

## Parallel analysis suggests that the number of factors =  2  and the number of components =  2

The suggested number of factors is 2, so we will start with a model with 2 factors.

Each factor consist of minimum 5 variables. None of the variables have loadings less than 0.3 None of the variables have equal loadings for more than one factor, which is good for our model.

## Factor Analysis using method =  minres
## Call: fa(r = data.f1, nfactors = 2, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
##         MR1   MR2     h2   u2 com
## beck  -0.61 -0.39 0.6104 0.39 1.7
## Ak.As -0.05  0.92 0.8229 0.18 1.0
## Bo     0.80  0.19 0.7359 0.26 1.1
## Ca     0.39  0.46 0.4370 0.56 2.0
## To.As  0.27  0.61 0.5124 0.49 1.4
## Sp.As -0.50  0.25 0.2613 0.74 1.5
## Ak     0.11  0.54 0.3200 0.68 1.1
## To     0.18  0.64 0.4775 0.52 1.2
## Sp     0.78  0.26 0.7460 0.25 1.2
## Us     0.77  0.18 0.6737 0.33 1.1
## Ud     0.23  0.62 0.4970 0.50 1.3
## Po     0.12  0.38 0.1798 0.82 1.2
## glo1   0.71 -0.08 0.4912 0.51 1.0
## glo2   0.59 -0.59 0.5625 0.44 2.0
## glo3  -0.02 -0.09 0.0097 0.99 1.1
## glo4  -0.84  0.19 0.6730 0.33 1.1
## glo5   0.58 -0.33 0.3718 0.63 1.6
## glo6  -0.01  0.00 0.0001 1.00 1.0
## 
##                        MR1  MR2
## SS loadings           4.77 3.62
## Proportion Var        0.26 0.20
## Cumulative Var        0.26 0.47
## Proportion Explained  0.57 0.43
## Cumulative Proportion 0.57 1.00
## 
##  With factor correlations of 
##      MR1  MR2
## MR1 1.00 0.19
## MR2 0.19 1.00
## 
## Mean item complexity =  1.3
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  153  and the objective function was  53.71 with Chi Square of  653.52
## The degrees of freedom for the model are 118  and the objective function was  45.66 
## 
## The root mean square of the residuals (RMSR) is  0.14 
## The df corrected root mean square of the residuals is  0.16 
## 
## The harmonic number of observations is  20 with the empirical chi square  128.12  with prob <  0.25 
## The total number of observations was  20  with Likelihood Chi Square =  494.68  with prob <  1.4e-47 
## 
## Tucker Lewis Index of factoring reliability =  -0.139
## RMSEA index =  0.396  and the 90 % confidence intervals are  0.373 0.448
## BIC =  141.18
## Fit based upon off diagonal values = 0.84

The mixed type of correlation was used which is automatically includes rotation in the model. As can be seen, there are correlations between factors presented. There is non-orthogonal rotation, There is a a medium positive correlation between factors 1 and 2. Therefore, such rotation is approved, the factors are connected with each other.

Cumulative Var = 0.47 Proportion Explained varies from 0.2 to 0.26. The variables should be equally distributed between factors,and here we have almost perfect distribution. Proportion Variance: each factor should describe at least 10%, all of the factors do.

Regression

factors

  ALL PK EK SK
Predictors Estimates CI p Estimates CI p Estimates CI p Estimates CI p
(Intercept) 81.40 73.90 – 88.90 <0.001 26.60 23.39 – 29.81 <0.001 26.90 24.54 – 29.26 <0.001 28.45 25.72 – 31.18 <0.001
MR1 -0.40 -5.17 – 4.38 0.863 0.14 -1.90 – 2.18 0.887 -0.23 -1.73 – 1.27 0.751 -0.15 -1.89 – 1.58 0.857
MR2 -3.25 -9.68 – 3.18 0.301 -1.68 -4.44 – 1.07 0.215 -0.87 -2.89 – 1.15 0.376 -0.30 -2.64 – 2.04 0.792
Observations 20 20 20 20
R2 / R2 adjusted 0.063 / -0.047 0.101 / -0.005 0.047 / -0.065 0.005 / -0.112