Correlations

EFA

## Parallel analysis suggests that the number of factors =  1  and the number of components =  1

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 = dataf1, nfactors = 2, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
##         MR1   MR2   h2    u2 com
## beck  -0.34 -0.47 0.46 0.544 1.8
## Ak.As  0.44  0.30 0.38 0.617 1.8
## Bo     0.36  0.46 0.46 0.539 1.9
## Ca     0.70  0.17 0.61 0.393 1.1
## To.As  0.79  0.03 0.65 0.353 1.0
## Sp.As -0.28 -0.37 0.28 0.717 1.9
## Ak     0.20  0.32 0.19 0.810 1.7
## To     0.96 -0.15 0.85 0.152 1.0
## Sp    -0.02  0.88 0.77 0.234 1.0
## Us    -0.05  0.98 0.93 0.074 1.0
## Ud     0.54  0.19 0.40 0.598 1.2
## Po     0.11  0.38 0.19 0.813 1.2
## 
##                        MR1  MR2
## SS loadings           3.16 2.99
## Proportion Var        0.26 0.25
## Cumulative Var        0.26 0.51
## Proportion Explained  0.51 0.49
## Cumulative Proportion 0.51 1.00
## 
##  With factor correlations of 
##      MR1  MR2
## MR1 1.00 0.36
## MR2 0.36 1.00
## 
## Mean item complexity =  1.4
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  66  and the objective function was  8.15 with Chi Square of  237.6
## The degrees of freedom for the model are 43  and the objective function was  2.69 
## 
## The root mean square of the residuals (RMSR) is  0.1 
## The df corrected root mean square of the residuals is  0.13 
## 
## The harmonic number of observations is  35 with the empirical chi square  48.78  with prob <  0.25 
## The total number of observations was  35  with Likelihood Chi Square =  75.01  with prob <  0.0018 
## 
## Tucker Lewis Index of factoring reliability =  0.694
## RMSEA index =  0.143  and the 90 % confidence intervals are  0.09 0.203
## BIC =  -77.87
## Fit based upon off diagonal values = 0.94
## Measures of factor score adequacy             
##                                                    MR1  MR2
## Correlation of (regression) scores with factors   0.96 1.00
## Multiple R square of scores with factors          0.92 0.99
## Minimum correlation of possible factor scores     0.85 0.99

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 = 0.51 Proportion Explained varies from 0.49 to 0.51. 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) 79.57 74.30 – 84.84 <0.001 25.57 23.38 – 27.76 <0.001 26.71 24.87 – 28.56 <0.001 27.60 25.79 – 29.41 <0.001
MR1 1.15 -4.86 – 7.15 0.700 0.31 -2.19 – 2.81 0.801 -0.11 -2.21 – 2.00 0.919 1.15 -0.92 – 3.21 0.266
MR2 0.16 -5.63 – 5.95 0.957 0.68 -1.72 – 3.09 0.567 0.09 -1.93 – 2.12 0.925 -0.50 -2.49 – 1.49 0.613
Observations 35 35 35 35
R2 / R2 adjusted 0.006 / -0.056 0.018 / -0.043 0.000 / -0.062 0.039 / -0.021

Vars only

  ALL PK EK SK
Predictors Estimates CI p Estimates CI p Estimates CI p Estimates CI p
(Intercept) 173.96 78.52 – 269.41 0.001 65.50 29.13 – 101.86 0.001 50.47 20.64 – 80.30 0.002 51.13 12.23 – 90.03 0.012
beck -1.17 -2.26 – -0.07 0.039 -0.53 -0.95 – -0.11 0.016 -0.17 -0.51 – 0.18 0.329 -0.45 -0.90 – 0.00 0.050
Ak-As 0.00 -0.57 – 0.57 0.997 -0.09 -0.31 – 0.13 0.396 0.13 -0.05 – 0.30 0.158 -0.06 -0.29 – 0.18 0.620
Bo -0.50 -1.42 – 0.41 0.268 -0.30 -0.65 – 0.05 0.091 -0.06 -0.35 – 0.23 0.667 -0.16 -0.53 – 0.21 0.379
Ca 0.49 -0.47 – 1.46 0.303 0.16 -0.21 – 0.53 0.374 0.09 -0.21 – 0.40 0.522 0.26 -0.13 – 0.65 0.187
To-As 0.63 -0.33 – 1.58 0.188 0.23 -0.13 – 0.60 0.199 0.38 0.09 – 0.68 0.014 0.03 -0.36 – 0.42 0.859
Sp-As -0.57 -1.58 – 0.44 0.254 -0.26 -0.64 – 0.12 0.173 -0.15 -0.46 – 0.17 0.339 -0.11 -0.52 – 0.30 0.591
Ak 0.01 -0.60 – 0.62 0.973 0.03 -0.21 – 0.26 0.817 -0.06 -0.25 – 0.13 0.517 0.10 -0.15 – 0.34 0.433
To -0.46 -1.35 – 0.43 0.292 -0.04 -0.38 – 0.30 0.796 -0.35 -0.63 – -0.07 0.016 -0.10 -0.46 – 0.26 0.572
Sp -0.39 -1.35 – 0.57 0.408 -0.09 -0.46 – 0.27 0.607 -0.10 -0.40 – 0.20 0.492 -0.21 -0.60 – 0.18 0.284
Us 0.14 -1.17 – 1.45 0.825 0.18 -0.32 – 0.68 0.453 0.00 -0.41 – 0.41 0.994 -0.02 -0.56 – 0.51 0.934
Ud -0.85 -1.47 – -0.23 0.010 -0.41 -0.65 – -0.17 0.002 -0.24 -0.43 – -0.04 0.019 -0.14 -0.40 – 0.11 0.263
Po -0.23 -1.30 – 0.84 0.660 -0.15 -0.56 – 0.26 0.447 -0.13 -0.47 – 0.21 0.431 0.05 -0.39 – 0.49 0.806
Observations 35 35 35 35
R2 / R2 adjusted 0.477 / 0.192 0.567 / 0.331 0.581 / 0.352 0.290 / -0.097

for XPN

EFA

## Parallel analysis suggests that the number of factors =  1  and the number of components =  1

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 = dataf1, nfactors = 2, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
##         MR1   MR2   h2   u2 com
## beck  -0.76 -0.01 0.58 0.42 1.0
## Ak.As  0.82  0.12 0.75 0.25 1.0
## Bo     0.69  0.14 0.56 0.44 1.1
## Ca     0.91 -0.03 0.81 0.19 1.0
## To.As  0.94 -0.06 0.86 0.14 1.0
## Sp.As -0.55 -0.49 0.73 0.27 2.0
## Ak     0.26  0.30 0.21 0.79 2.0
## To     0.88 -0.13 0.72 0.28 1.0
## Sp     0.00  0.87 0.76 0.24 1.0
## Us     0.11  0.89 0.88 0.12 1.0
## Ud     0.42  0.30 0.35 0.65 1.8
## Po    -0.16  0.88 0.70 0.30 1.1
## 
##                        MR1  MR2
## SS loadings           4.95 2.95
## Proportion Var        0.41 0.25
## Cumulative Var        0.41 0.66
## Proportion Explained  0.63 0.37
## Cumulative Proportion 0.63 1.00
## 
##  With factor correlations of 
##      MR1  MR2
## MR1 1.00 0.34
## MR2 0.34 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  66  and the objective function was  35.7 with Chi Square of  327.26
## The degrees of freedom for the model are 43  and the objective function was  26.74 
## 
## The root mean square of the residuals (RMSR) is  0.09 
## The df corrected root mean square of the residuals is  0.12 
## 
## The harmonic number of observations is  15 with the empirical chi square  17.54  with prob <  1 
## The total number of observations was  15  with Likelihood Chi Square =  209.45  with prob <  9.5e-24 
## 
## Tucker Lewis Index of factoring reliability =  -0.196
## RMSEA index =  0.503  and the 90 % confidence intervals are  0.456 0.598
## BIC =  93
## Fit based upon off diagonal values = 0.97

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 = 0.51 Proportion Explained varies from 0.49 to 0.51. 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) 77.13 69.60 – 84.67 <0.001 24.20 21.26 – 27.14 <0.001 26.47 23.44 – 29.50 <0.001 26.47 23.77 – 29.16 <0.001
MR1 7.22 -1.08 – 15.52 0.082 2.34 -0.90 – 5.58 0.142 3.04 -0.30 – 6.38 0.071 1.84 -1.13 – 4.81 0.201
MR2 -3.38 -11.85 – 5.10 0.402 -0.66 -3.97 – 2.64 0.670 -1.98 -5.39 – 1.42 0.229 -0.73 -3.76 – 2.30 0.610
Observations 15 15 15 15
R2 / R2 adjusted 0.232 / 0.104 0.172 / 0.034 0.262 / 0.139 0.132 / -0.012

for hyper

EFA

## Parallel analysis suggests that the number of factors =  1  and the number of components =  1

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 = dataf1, nfactors = 2, cor = "mixed")
## Standardized loadings (pattern matrix) based upon correlation matrix
##         MR1   MR2   h2     u2 com
## beck  -0.71 -0.18 0.61  0.386 1.1
## Ak.As  0.10  0.98 1.02 -0.018 1.0
## Bo     0.74  0.07 0.59  0.414 1.0
## Ca     0.51  0.29 0.42  0.578 1.6
## To.As  0.45  0.45 0.52  0.477 2.0
## Sp.As -0.65  0.59 0.55  0.445 2.0
## Ak     0.21  0.47 0.32  0.678 1.4
## To     0.43  0.37 0.40  0.598 2.0
## Sp     0.75  0.14 0.65  0.354 1.1
## Us     0.89 -0.09 0.76  0.244 1.0
## Ud     0.44  0.36 0.40  0.596 1.9
## Po     0.31  0.22 0.18  0.817 1.8
## 
##                        MR1  MR2
## SS loadings           4.04 2.39
## Proportion Var        0.34 0.20
## Cumulative Var        0.34 0.54
## Proportion Explained  0.63 0.37
## Cumulative Proportion 0.63 1.00
## 
##  With factor correlations of 
##      MR1  MR2
## MR1 1.00 0.27
## MR2 0.27 1.00
## 
## Mean item complexity =  1.5
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  66  and the objective function was  12.22 with Chi Square of  173.18
## The degrees of freedom for the model are 43  and the objective function was  6.31 
## 
## The root mean square of the residuals (RMSR) is  0.12 
## The df corrected root mean square of the residuals is  0.15 
## 
## The harmonic number of observations is  20 with the empirical chi square  38.83  with prob <  0.65 
## The total number of observations was  20  with Likelihood Chi Square =  81.01  with prob <  4e-04 
## 
## Tucker Lewis Index of factoring reliability =  0.358
## RMSEA index =  0.204  and the 90 % confidence intervals are  0.142 0.287
## BIC =  -47.81
## Fit based upon off diagonal values = 0.92

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 = 0.51 Proportion Explained varies from 0.49 to 0.51. 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 74.01 – 88.79 <0.001 26.60 23.68 – 29.52 <0.001 26.90 24.51 – 29.29 <0.001 28.45 25.74 – 31.16 <0.001
MR1 1.26 -6.83 – 9.35 0.747 1.89 -1.31 – 5.09 0.230 -0.55 -3.17 – 2.07 0.662 0.14 -2.83 – 3.11 0.923
MR2 -4.40 -11.49 – 2.69 0.208 -3.12 -5.92 – -0.31 0.032 -0.30 -2.60 – 1.99 0.785 -0.64 -3.24 – 1.96 0.610
Observations 20 20 20 20
R2 / R2 adjusted 0.092 / -0.015 0.256 / 0.168 0.022 / -0.093 0.016 / -0.100