R: sem: 因子分析

Rによる共分散構造分析。因子分析をやってみる。狩野・三浦(2002) p.74の例題。

##
## データは狩野・三浦(2002) p.74より
##
library(sem)

n <- 220
R <- readMoments(diag = FALSE,
                 names = c("X1", "X2", "X3", "X4", "X5", "X6"))            
0.439
0.410 0.351
0.288 0.354 0.164
0.329 0.320 0.190 0.595
0.248 0.329 0.181 0.470 0.484

# model 1
model1 <- specifyModel()
X1 <-  F1, lambda1
X2 <-  F1, lambda2
X3 <-  F1, lambda3
X4 <-  F1, lambda4
X5 <-  F1, lambda5
X6 <-  F1, lambda6
F1 <-> F1, NA, 1
X1 <-> X1, e1
X2 <-> X2, e2
X3 <-> X3, e3
X4 <-> X4, e4
X5 <-> X5, e5
X6 <-> X6, e6

s1 <- sem(model1, S = R, N = n)
summary(s1)

# model 2
model2 <- specifyModel()
X1 <-  F1, lambda1
X2 <-  F1, lambda2
X3 <-  F1, lambda3
X4 <-  F2, lambda4
X5 <-  F2, lambda5
X6 <-  F2, lambda6
F1 <-> F1, NA, 1
F2 <-> F2, NA, 1
F1 <-> F2, phi12
X1 <-> X1, e1
X2 <-> X2, e2
X3 <-> X3, e3
X4 <-> X4, e4
X5 <-> X5, e5
X6 <-> X6, e6

s2 <- sem(model2, S = R, N = n)
summary(s2)

結果

> summary(s1)

 Model Chisquare =  53.245   Df =  9 Pr(>Chisq) = 2.6267e-08
 Chisquare (null model) =  318.29   Df =  15
 Goodness-of-fit index =  0.91393
 Adjusted goodness-of-fit index =  0.79916
 RMSEA index =  0.14983   90% CI: (0.11244, 0.1899)
 Bentler-Bonnett NFI =  0.83272
 Tucker-Lewis NNFI =  0.75687
 Bentler CFI =  0.85412
 SRMR =  0.084726
 AIC =  77.245
 AICc =  54.752
 BIC =  117.97
 CAIC =  -4.298 

 Normalized Residuals
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-1.2500 -0.8320 -0.0273  0.1730  0.2630  3.5200 

 R-square for Endogenous Variables
    X1     X2     X3     X4     X5     X6 
0.2406 0.2832 0.1188 0.5310 0.5511 0.3913 

 Parameter Estimates
        Estimate Std Error z value Pr(>|z|)             
lambda1 0.49050  0.071142   6.8947 5.3996e-12 X1 <--- F1
lambda2 0.53214  0.070323   7.5672 3.8150e-14 X2 <--- F1
lambda3 0.34471  0.073521   4.6886 2.7509e-06 X3 <--- F1
lambda4 0.72866  0.066294  10.9913 4.2063e-28 X4 <--- F1
lambda5 0.74235  0.066047  11.2397 2.6039e-29 X5 <--- F1
lambda6 0.62557  0.068334   9.1545 5.4602e-20 X6 <--- F1
e1      0.75941  0.079194   9.5893 8.8693e-22 X1 <--> X1
e2      0.71683  0.076513   9.3687 7.3449e-21 X2 <--> X2
e3      0.88117  0.087286  10.0953 5.7980e-24 X3 <--> X3
e4      0.46905  0.064961   7.2205 5.1814e-13 X4 <--> X4
e5      0.44892  0.064531   6.9566 3.4848e-12 X5 <--> X5
e6      0.60866  0.070311   8.6567 4.8567e-18 X6 <--> X6

 Iterations =  13 

> summary(s2)

 Model Chisquare =  7.7844   Df =  8 Pr(>Chisq) = 0.45481
 Chisquare (null model) =  318.29   Df =  15
 Goodness-of-fit index =  0.98816
 Adjusted goodness-of-fit index =  0.96892
 RMSEA index =  0   90% CI: (NA, 0.077836)
 Bentler-Bonnett NFI =  0.97554
 Tucker-Lewis NNFI =  1.0013
 Bentler CFI =  1
 SRMR =  0.031955
 AIC =  33.784
 AICc =  9.5513
 BIC =  77.902
 CAIC =  -43.365 

 Normalized Residuals
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-1.0900 -0.2600 -0.0312 -0.0180  0.1260  1.1300 

 R-square for Endogenous Variables
    X1     X2     X3     X4     X5     X6 
0.4727 0.4506 0.2842 0.5730 0.6069 0.3935 

 Parameter Estimates
        Estimate Std Error z value Pr(>|z|)             
lambda1 0.68756  0.075701   9.0826 1.0599e-19 X1 <--- F1
lambda2 0.67129  0.075566   8.8836 6.4756e-19 X2 <--- F1
lambda3 0.53312  0.075615   7.0504 1.7834e-12 X3 <--- F1
lambda4 0.75700  0.067113  11.2794 1.6581e-29 X4 <--- F2
lambda5 0.77901  0.066942  11.6371 2.6692e-31 X5 <--- F2
lambda6 0.62732  0.068494   9.1587 5.2508e-20 X6 <--- F2
phi12   0.59481  0.071772   8.2876 1.1558e-16 F2 <--> F1
e1      0.52726  0.082350   6.4027 1.5270e-10 X1 <--> X1
e2      0.54937  0.081687   6.7253 1.7520e-11 X2 <--> X2
e3      0.71578  0.082010   8.7279 2.5938e-18 X3 <--> X3
e4      0.42695  0.067242   6.3495 2.1607e-10 X4 <--> X4
e5      0.39314  0.067591   5.8164 6.0135e-09 X5 <--> X5
e6      0.60647  0.070501   8.6022 7.8212e-18 X6 <--> X6

 Iterations =  17 

タグ：R SEM