#s C.3-1
> library(lavaan)
This is lavaan 0.5-23.1097
lavaan is BETA software! Please report any bugs.

 ̃pbP[Wt܂: elavaanf 

 ȉ̃IuWFNg epackage:psychf }XNĂ܂: 

     cor2cov 

> model0 <- #RɃRs[y[XgƂ2sڈȍ~̍ŏ+͍폜
+  'f1 =~ q1 + q2 + q3
+  f2 =~ q4 + q5 + q6
+  f3 =~ q7 + q8 + q9
+  f1 ~~ f2
+  f2 ~~ f3
+  f3 ~~ f1'
> fit0 <- sem(model=model0, data=set.data, estimator="ml")
> summary(object=fit0, fit.measure=TRUE) 
lavaan (0.5-23.1097) converged normally after  33 iterations

  Number of observations                           257

  Estimator                                         ML
  Minimum Function Test Statistic               60.107
  Degrees of freedom                                24
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic              969.982
  Degrees of freedom                                36
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.961
  Tucker-Lewis Index (TLI)                       0.942

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -2499.016
  Loglikelihood unrestricted model (H1)      -2468.963

  Number of free parameters                         21
  Akaike (AIC)                                5040.032
  Bayesian (BIC)                              5114.563
  Sample-size adjusted Bayesian (BIC)         5047.987

Root Mean Square Error of Approximation:

  RMSEA                                          0.077
  90 Percent Confidence Interval          0.053  0.101
  P-value RMSEA <= 0.05                          0.036

Standardized Root Mean Square Residual:

  SRMR                                           0.051

Parameter Estimates:

  Information                                 Expected
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  f1 =~                                               
    q1                1.000                           
    q2                0.708    0.076    9.254    0.000
    q3                0.836    0.096    8.698    0.000
  f2 =~                                               
    q4                1.000                           
    q5                0.828    0.055   15.103    0.000
    q6                0.970    0.048   20.296    0.000
  f3 =~                                               
    q7                1.000                           
    q8                0.516    0.092    5.614    0.000
    q9                0.894    0.141    6.335    0.000

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  f1 ~~                                               
    f2                0.419    0.056    7.491    0.000
  f2 ~~                                               
    f3                0.315    0.049    6.465    0.000
  f1 ~~                                               
    f3                0.275    0.048    5.762    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .q1                0.226    0.051    4.386    0.000
   .q2                0.445    0.047    9.374    0.000
   .q3                0.781    0.079    9.829    0.000
   .q4                0.123    0.023    5.316    0.000
   .q5                0.352    0.035   10.018    0.000
   .q6                0.149    0.023    6.359    0.000
   .q7                0.434    0.055    7.873    0.000
   .q8                0.280    0.028   10.000    0.000
   .q9                0.527    0.058    9.153    0.000
    f1                0.626    0.087    7.226    0.000
    f2                0.667    0.072    9.285    0.000
    f3                0.295    0.065    4.534    0.000

#s C.3-2
> subset(modificationIndices(fit0), mi>5)
   lhs op rhs     mi    epc sepc.lv sepc.all sepc.nox
26  f1 =~  q5 13.778  0.301   0.238    0.265    0.265
32  f2 =~  q2  8.413  0.292   0.238    0.273    0.273
37  f3 =~  q1  5.207 -0.568  -0.309   -0.335   -0.335
38  f3 =~  q2 10.961  0.613   0.333    0.383    0.383
40  f3 =~  q4  8.794 -0.425  -0.231   -0.260   -0.260
41  f3 =~  q5 13.634  0.599   0.325    0.362    0.362
44  q1 ~~  q3 12.424  0.232   0.232    0.228    0.228
51  q2 ~~  q3  6.783 -0.126  -0.126   -0.131   -0.131
56  q2 ~~  q8 12.840  0.089   0.089    0.170    0.170
65  q4 ~~  q6 18.905  0.195   0.195    0.249    0.249
68  q4 ~~  q9  5.719 -0.056  -0.056   -0.072   -0.072
69  q5 ~~  q6  5.707 -0.068  -0.068   -0.086   -0.086
> model1 <- #RɃRs[y[XgƂ2sڈȍ~̍ŏ+͍폜
+  'f1 =~ q1 + q2 + q3
+  f2 =~ q4 + q5 + q6
+  f3 =~ q7 + q8 + q9
+  f1 ~~ f2
+  f2 ~~ f3
+  f3 ~~ f1
+  q1 ~~ q3
+  q4 ~~ q6
+  q2 ~~ q8'
> fit1 <- sem(model=model1, data=set.data, estimator="ml")
> summary(object=fit1, fit.measure=TRUE)
lavaan (0.5-23.1097) converged normally after  37 iterations

  Number of observations                           257

  Estimator                                         ML
  Minimum Function Test Statistic               20.657
  Degrees of freedom                                21
  P-value (Chi-square)                           0.480

Model test baseline model:

  Minimum Function Test Statistic              969.982
  Degrees of freedom                                36
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    1.000
  Tucker-Lewis Index (TLI)                       1.001

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -2479.291
  Loglikelihood unrestricted model (H1)      -2468.963

  Number of free parameters                         24
  Akaike (AIC)                                5006.583
  Bayesian (BIC)                              5091.761
  Sample-size adjusted Bayesian (BIC)         5015.673

Root Mean Square Error of Approximation:

  RMSEA                                          0.000
  90 Percent Confidence Interval          0.000  0.052
  P-value RMSEA <= 0.05                          0.939

Standardized Root Mean Square Residual:

  SRMR                                           0.023

Parameter Estimates:

  Information                                 Expected
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  f1 =~                                               
    q1                1.000                           
    q2                0.843    0.096    8.755    0.000
    q3                0.762    0.099    7.724    0.000
  f2 =~                                               
    q4                1.000                           
    q5                1.046    0.085   12.298    0.000
    q6                0.963    0.049   19.647    0.000
  f3 =~                                               
    q7                1.000                           
    q8                0.532    0.094    5.688    0.000
    q9                0.918    0.144    6.387    0.000

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  f1 ~~                                               
    f2                0.398    0.055    7.265    0.000
  f2 ~~                                               
    f3                0.302    0.047    6.376    0.000
  f1 ~~                                               
    f3                0.258    0.046    5.588    0.000
 .q1 ~~                                               
   .q3                0.166    0.057    2.892    0.004
 .q4 ~~                                               
   .q6                0.154    0.036    4.274    0.000
 .q2 ~~                                               
   .q8                0.077    0.025    3.038    0.002

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .q1                0.335    0.057    5.849    0.000
   .q2                0.392    0.049    7.994    0.000
   .q3                0.918    0.095    9.638    0.000
   .q4                0.271    0.040    6.707    0.000
   .q5                0.240    0.040    6.019    0.000
   .q6                0.295    0.041    7.188    0.000
   .q7                0.444    0.055    8.135    0.000
   .q8                0.278    0.028    9.983    0.000
   .q9                0.523    0.057    9.129    0.000
    f1                0.517    0.085    6.104    0.000
    f2                0.519    0.073    7.098    0.000
    f3                0.286    0.064    4.486    0.000

#s C.3-3
> standardizedSolution(fit1)
   lhs op rhs est.std    se      z pvalue
1   f1 =~  q1   0.779 0.044 17.580  0.000
2   f1 =~  q2   0.696 0.046 15.144  0.000
3   f1 =~  q3   0.496 0.063  7.919  0.000
4   f2 =~  q4   0.811 0.033 24.384  0.000
5   f2 =~  q5   0.838 0.031 26.949  0.000
6   f2 =~  q6   0.788 0.035 22.427  0.000
7   f3 =~  q7   0.626 0.056 11.105  0.000
8   f3 =~  q8   0.475 0.062  7.699  0.000
9   f3 =~  q9   0.561 0.058  9.636  0.000
10  f1 ~~  f2   0.769 0.050 15.483  0.000
11  f2 ~~  f3   0.785 0.060 12.998  0.000
12  f1 ~~  f3   0.671 0.074  9.096  0.000
13  q1 ~~  q3   0.299 0.081  3.704  0.000
14  q4 ~~  q6   0.544 0.065  8.348  0.000
15  q2 ~~  q8   0.232 0.071  3.292  0.001
16  q1 ~~  q1   0.393 0.069  5.689  0.000
17  q2 ~~  q2   0.516 0.064  8.079  0.000
18  q3 ~~  q3   0.754 0.062 12.112  0.000
19  q4 ~~  q4   0.343 0.054  6.366  0.000
20  q5 ~~  q5   0.297 0.052  5.702  0.000
21  q6 ~~  q6   0.380 0.055  6.864  0.000
22  q7 ~~  q7   0.609 0.070  8.632  0.000
23  q8 ~~  q8   0.774 0.059 13.199  0.000
24  q9 ~~  q9   0.685 0.065 10.470  0.000
25  f1 ~~  f1   1.000 0.000     NA     NA
26  f2 ~~  f2   1.000 0.000     NA     NA
27  f3 ~~  f3   1.000 0.000     NA     NA

#s C.3-4
> model2 <- 'f1 =~ q1 + q2 + q3 #RɃRs[y[XgƂ2sڈȍ~̍ŏ+͍폜
+  f2 =~ q4 + q5 + q6
+  f3 =~ q7 + q8 + q9
+  f3 ~ f2
+  f2 ~ f1
+  q1 ~~ q3
+  q4 ~~ q6
+  q2 ~~ q8'
> fit2 <- sem(model=model2, data=set.data, estimator="ml")
> summary(object=fit2, fit.measure=T)
lavaan (0.5-23.1097) converged normally after  33 iterations

  Number of observations                           257

  Estimator                                         ML
  Minimum Function Test Statistic               21.617
  Degrees of freedom                                22
  P-value (Chi-square)                           0.483

Model test baseline model:

  Minimum Function Test Statistic              969.982
  Degrees of freedom                                36
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    1.000
  Tucker-Lewis Index (TLI)                       1.001

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -2479.771
  Loglikelihood unrestricted model (H1)      -2468.963

  Number of free parameters                         23
  Akaike (AIC)                                5005.542
  Bayesian (BIC)                              5087.171
  Sample-size adjusted Bayesian (BIC)         5014.254

Root Mean Square Error of Approximation:

  RMSEA                                          0.000
  90 Percent Confidence Interval          0.000  0.051
  P-value RMSEA <= 0.05                          0.944

Standardized Root Mean Square Residual:

  SRMR                                           0.024

Parameter Estimates:

  Information                                 Expected
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  f1 =~                                               
    q1                1.000                           
    q2                0.844    0.097    8.741    0.000
    q3                0.762    0.099    7.720    0.000
  f2 =~                                               
    q4                1.000                           
    q5                1.047    0.084   12.463    0.000
    q6                0.965    0.049   19.644    0.000
  f3 =~                                               
    q7                1.000                           
    q8                0.535    0.094    5.693    0.000
    q9                0.916    0.144    6.353    0.000

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  f3 ~                                                
    f2                0.594    0.077    7.742    0.000
  f2 ~                                                
    f1                0.782    0.095    8.244    0.000

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
 .q1 ~~                                               
   .q3                0.168    0.057    2.925    0.003
 .q4 ~~                                               
   .q6                0.157    0.035    4.477    0.000
 .q2 ~~                                               
   .q8                0.080    0.025    3.217    0.001

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .q1                0.337    0.057    5.909    0.000
   .q2                0.392    0.049    7.989    0.000
   .q3                0.919    0.095    9.656    0.000
   .q4                0.275    0.040    6.958    0.000
   .q5                0.244    0.039    6.297    0.000
   .q6                0.297    0.040    7.391    0.000
   .q7                0.446    0.055    8.167    0.000
   .q8                0.277    0.028    9.975    0.000
   .q9                0.526    0.057    9.167    0.000
    f1                0.514    0.084    6.090    0.000
   .f2                0.200    0.044    4.556    0.000
   .f3                0.102    0.037    2.740    0.006

#s C.3-5
> standardizedSolution(fit2)
   lhs op rhs est.std    se      z pvalue
1   f1 =~  q1   0.777 0.044 17.532      0
2   f1 =~  q2   0.695 0.046 15.123      0
3   f1 =~  q3   0.496 0.063  7.913      0
4   f2 =~  q4   0.807 0.033 24.683      0
5   f2 =~  q5   0.835 0.030 27.441      0
6   f2 =~  q6   0.786 0.035 22.756      0
7   f3 =~  q7   0.623 0.056 11.045      0
8   f3 =~  q8   0.476 0.062  7.730      0
9   f3 =~  q9   0.558 0.058  9.550      0
10  f3  ~  f2   0.801 0.058 13.873      0
11  f2  ~  f1   0.781 0.047 16.455      0
12  q1 ~~  q3   0.301 0.080  3.750      0
13  q4 ~~  q6   0.549 0.063  8.756      0
14  q2 ~~  q8   0.242 0.069  3.484      0
15  q1 ~~  q1   0.396 0.069  5.748      0
16  q2 ~~  q2   0.517 0.064  8.081      0
17  q3 ~~  q3   0.754 0.062 12.158      0
18  q4 ~~  q4   0.348 0.053  6.591      0
19  q5 ~~  q5   0.302 0.051  5.945      0
20  q6 ~~  q6   0.382 0.054  7.047      0
21  q7 ~~  q7   0.611 0.070  8.685      0
22  q8 ~~  q8   0.773 0.059 13.178      0
23  q9 ~~  q9   0.689 0.065 10.562      0
24  f1 ~~  f1   1.000 0.000     NA     NA
25  f2 ~~  f2   0.389 0.074  5.248      0
26  f3 ~~  f3   0.359 0.092  3.878      0

#s C.3-6
> library(semPlot) 
> semPaths(fit1, "model1", "std", style="lisrel", rotation=2, nDigits=3,
+ edge.label.cex=1.0, curve=1.8, edge.color="black", edge.label.position=.4)
> semPaths(fit2, "model2", "std", style="lisrel", rotation=2, nDigits=3,
+ edge.label.cex=1.0, curve=1.8, edge.color="black", edge.label.position=.4)
