#s C.2-1
> pa.data <- read.csv("http://mlab.arrow.jp/r_factor/parents.csv") #Ђɂ͏ĂȂ
> vss(pa.data, fm="ml")

Very Simple Structure
Call: vss(x = pa.data, fm = "ml")
VSS complexity 1 achieves a maximimum of 0.67  with  3  factors
VSS complexity 2 achieves a maximimum of 0.8  with  7  factors

The Velicer MAP achieves a minimum of NA  with  1  factors 
BIC achieves a minimum of  NA  with  3  factors
Sample Size adjusted BIC achieves a minimum of  NA  with  3  factors

Statistics by number of factors 
  vss1 vss2   map dof   chisq    prob sqresid  fit RMSEA   BIC SABIC complex  eChisq    SRMR eCRMS eBIC
1 0.34 0.00 0.068  20 1.7e+02 5.3e-26     7.3 0.34  0.19  64.1 127.4     1.0 3.1e+02 1.6e-01 0.192  204
2 0.56 0.59 0.080  13 7.4e+01 1.2e-10     4.5 0.59  0.15   4.9  46.1     1.2 1.1e+02 9.5e-02 0.140   38
3 0.67 0.75 0.094   7 5.8e+00 5.6e-01     2.7 0.76  0.00 -31.6  -9.4     1.3 5.7e+00 2.2e-02 0.044  -32
4 0.63 0.75 0.156   2 7.4e-01 6.9e-01     2.4 0.78  0.00 -10.0  -3.6     1.3 5.5e-01 6.8e-03 0.026  -10
5 0.63 0.76 0.285  -2 1.3e-07      NA     2.2 0.80    NA    NA    NA     1.4 1.2e-07 3.2e-06    NA   NA
6 0.58 0.78 0.486  -5 6.2e-11      NA     1.6 0.85    NA    NA    NA     1.4 6.6e-11 7.5e-08    NA   NA
7 0.58 0.80 1.000  -7 0.0e+00      NA     1.2 0.89    NA    NA    NA     1.4 2.2e-13 4.3e-09    NA   NA
8 0.60 0.68    NA  -8 2.1e+01      NA     3.2 0.71    NA    NA    NA     1.4 1.9e+01 4.0e-02    NA   NA

#s C.2-2
> fa.result <- fa(pa.data, nfactors=2, fm="ml", rotate="varimax")
> print(fa.result, cutoff=0, digits=3)
Factor Analysis using method =  ml
Call: fa(r = pa.data, nfactors = 2, rotate = "varimax", fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
      ML1    ML2     h2    u2  com
Q1 -0.088  0.779 0.6138 0.386 1.03
Q2  0.022  0.598 0.3579 0.642 1.00
Q3  0.185  0.530 0.3155 0.685 1.24
Q4  0.908  0.063 0.8287 0.171 1.01
Q5  0.611  0.079 0.3800 0.620 1.03
Q6  0.373  0.032 0.1402 0.860 1.01
Q7  0.287  0.046 0.0842 0.916 1.05
Q8 -0.121 -0.153 0.0378 0.962 1.90

                        ML1   ML2
SS loadings           1.477 1.281
Proportion Var        0.185 0.160
Cumulative Var        0.185 0.345
Proportion Explained  0.535 0.465
Cumulative Proportion 0.535 1.000

Mean item complexity =  1.2
Test of the hypothesis that 2 factors are sufficient.

The degrees of freedom for the null model are  28  and the objective function was  1.474 0 with Chi Square of  304.37
The degrees of freedom for the model are 13  and the objective function was  0.363 
 0
The root mean square of the residuals (RMSR) is  0.095 
The df corrected root mean square of the residuals is  0.14 
 0
The harmonic number of observations is  211 with the empirical chi square  107.422  with prob <  5.96e-17 
 0The total number of observations was  211  with Likelihood Chi Square =  74.452  with prob <  1.2e-10 
 0
Tucker Lewis Index of factoring reliability =  0.5177
RMSEA index =  0.1496  and the 90 % confidence intervals are  0.118 0.184 0
BIC =  4.878
Fit based upon off diagonal values = 0.83
Measures of factor score adequacy             
                                                    ML1   ML2
Correlation of (regression) scores with factors   0.922 0.848
Multiple R square of scores with factors          0.851 0.720
Minimum correlation of possible factor scores     0.701 0.440

#s C.2-3
> fa.result <- fa(pa.data, nfactors=3, fm="ml", rotate="varimax")
> print(fa.result, cutoff=0, digits=3)
Factor Analysis using method =  ml
Call: fa(r = pa.data, nfactors = 3, rotate = "varimax", fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
      ML2    ML1    ML3     h2    u2  com
Q1  0.774 -0.057 -0.059 0.6056 0.394 1.02
Q2  0.609 -0.023  0.155 0.3951 0.605 1.13
Q3  0.531  0.226 -0.015 0.3329 0.667 1.35
Q4  0.044  0.815  0.277 0.7430 0.257 1.23
Q5  0.068  0.683  0.043 0.4736 0.526 1.03
Q6  0.016  0.133  0.802 0.6605 0.339 1.06
Q7  0.038  0.081  0.652 0.4332 0.567 1.04
Q8 -0.151 -0.084 -0.144 0.0506 0.949 2.55

                        ML2   ML1   ML3
SS loadings           1.282 1.217 1.195
Proportion Var        0.160 0.152 0.149
Cumulative Var        0.160 0.312 0.462
Proportion Explained  0.347 0.330 0.323
Cumulative Proportion 0.347 0.677 1.000

Mean item complexity =  1.3
Test of the hypothesis that 3 factors are sufficient.

The degrees of freedom for the null model are  28  and the objective function was  1.474 0 with Chi Square of  304.37
The degrees of freedom for the model are 7  and the objective function was  0.029 
 0
The root mean square of the residuals (RMSR) is  0.022 
The df corrected root mean square of the residuals is  0.044 
 0
The harmonic number of observations is  211 with the empirical chi square  5.737  with prob <  0.571 
 0The total number of observations was  211  with Likelihood Chi Square =  5.835  with prob <  0.559 
 0
Tucker Lewis Index of factoring reliability =  1.017
RMSEA index =  0  and the 90 % confidence intervals are  0 0.0758 0
BIC =  -31.628
Fit based upon off diagonal values = 0.991
Measures of factor score adequacy             
                                                    ML2   ML1   ML3
Correlation of (regression) scores with factors   0.849 0.871 0.851
Multiple R square of scores with factors          0.720 0.759 0.724
Minimum correlation of possible factor scores     0.441 0.519 0.447

#s C.2-4
> fa.result <- fa(pa.data, nfactors=4, fm="ml", rotate="varimax")
> print(fa.result, cutoff=0, digits=3)
Factor Analysis using method =  ml
Call: fa(r = pa.data, nfactors = 4, rotate = "varimax", fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
      ML1    ML2    ML3    ML4    h2    u2  com
Q1 -0.015  0.991 -0.076  0.084 0.995 0.005 1.03
Q2 -0.006  0.461  0.138  0.267 0.303 0.697 1.81
Q3  0.189  0.356 -0.070  0.546 0.466 0.534 2.04
Q4  0.965  0.003  0.243  0.063 0.995 0.005 1.14
Q5  0.573  0.003  0.041  0.146 0.352 0.648 1.14
Q6  0.155  0.017  0.753  0.070 0.596 0.404 1.10
Q7  0.071  0.019  0.683  0.107 0.484 0.516 1.07
Q8 -0.058 -0.044 -0.121 -0.315 0.119 0.881 1.41

                        ML1   ML2   ML3   ML4
SS loadings           1.329 1.324 1.139 0.518
Proportion Var        0.166 0.166 0.142 0.065
Cumulative Var        0.166 0.332 0.474 0.539
Proportion Explained  0.308 0.307 0.264 0.120
Cumulative Proportion 0.308 0.616 0.880 1.000

Mean item complexity =  1.3
Test of the hypothesis that 4 factors are sufficient.

The degrees of freedom for the null model are  28  and the objective function was  1.474 0 with Chi Square of  304.37
The degrees of freedom for the model are 2  and the objective function was  0.004 
 0
The root mean square of the residuals (RMSR) is  0.007 
The df corrected root mean square of the residuals is  0.026 
 0
The harmonic number of observations is  211 with the empirical chi square  0.55  with prob <  0.759 
 0The total number of observations was  211  with Likelihood Chi Square =  0.736  with prob <  0.692 
 0
Tucker Lewis Index of factoring reliability =  1.065
RMSEA index =  0  and the 90 % confidence intervals are  0 0.1017 0
BIC =  -9.968
Fit based upon off diagonal values = 0.999
Measures of factor score adequacy             
                                                    ML1   ML2   ML3    ML4
Correlation of (regression) scores with factors   0.987 0.994 0.832  0.641
Multiple R square of scores with factors          0.974 0.988 0.693  0.410
Minimum correlation of possible factor scores     0.948 0.977 0.385 -0.179

#s C.2-5
> pa1.data <- pa.data[1:7] 
> head(pa1.data)
  Q1 Q2 Q3 Q4 Q5 Q6 Q7
1  1  2  2  4  4  4  4
2  1  1  1  1  3  3  3
3  1  2  3  2  2  3  4
4  2  4  2  4  1  3  4
5  2  4  2  1  1  3  3
6  1  2  2  4  4  3  3
> fa.result <- fa(pa1.data, nfactors=3, fm="ml", rotate="varimax")
> print(fa.result, cutoff=0, digits=3)
Factor Analysis using method =  ml
Call: fa(r = pa1.data, nfactors = 3, rotate = "varimax", fm = "ml")
Standardized loadings (pattern matrix) based upon correlation matrix
     ML2    ML1    ML3    h2    u2  com
Q1 0.801 -0.052 -0.062 0.648 0.352 1.02
Q2 0.596 -0.013  0.149 0.378 0.622 1.12
Q3 0.512  0.229 -0.023 0.316 0.684 1.39
Q4 0.039  0.823  0.269 0.751 0.249 1.22
Q5 0.061  0.681  0.036 0.469 0.531 1.02
Q6 0.021  0.140  0.808 0.672 0.328 1.06
Q7 0.039  0.089  0.645 0.425 0.575 1.05

                        ML2   ML1   ML3
SS loadings           1.267 1.224 1.168
Proportion Var        0.181 0.175 0.167
Cumulative Var        0.181 0.356 0.523
Proportion Explained  0.346 0.335 0.319
Cumulative Proportion 0.346 0.681 1.000

Mean item complexity =  1.1
Test of the hypothesis that 3 factors are sufficient.

The degrees of freedom for the null model are  21  and the objective function was  1.413 0 with Chi Square of  292.181
The degrees of freedom for the model are 3  and the objective function was  0.007 
 0
The root mean square of the residuals (RMSR) is  0.009 
The df corrected root mean square of the residuals is  0.024 
 0
The harmonic number of observations is  211 with the empirical chi square  0.743  with prob <  0.863 
 0The total number of observations was  211  with Likelihood Chi Square =  1.342  with prob <  0.719 
 0
Tucker Lewis Index of factoring reliability =  1.0432
RMSEA index =  0  and the 90 % confidence intervals are  0 0.0845 0
BIC =  -14.713
Fit based upon off diagonal values = 0.999
Measures of factor score adequacy             
                                                    ML2   ML1   ML3
Correlation of (regression) scores with factors   0.858 0.875 0.852
Multiple R square of scores with factors          0.735 0.766 0.726
Minimum correlation of possible factor scores     0.471 0.531 0.453
