sem は，最尤法により構造方程式モデリングを行う。

使用法

sem(ram, S, N, param.names = paste("Param", 1:t, sep = ""), 
    var.names = paste("V", 1:m, sep = ""), fixed.x = NULL, raw=FALSE, 
    debug = FALSE, analytic.gradient = TRUE, warn = FALSE, maxiter = 500, 
    par.size=c('ones', 'startvalues'), refit=TRUE, start.tol=1E-6, ...) 

引数

• ram
  specifyModel 関数により定義されたオブジェクト
• S
  共分散行列（多くの場合は相関係数行列）
• N
  共分散行列が計算されたデータのサンプルサイズ
• obs.variables
  観測変数の名前（デフォルトは共分散行列の行名から抽出）
• fixed.x
  外生変数の名前
• raw
  S が積和行列ならば TRUE（デフォルトは FALSE つまり，S は共分散行列）

> library(sem)

> R.DHP <- readMoments(diag=FALSE, names=c('ROccAsp', 'REdAsp', 'FOccAsp', 
+                 'FEdAsp', 'RParAsp', 'RIQ', 'RSES', 'FSES', 'FIQ', 'FParAsp'))
1:     .6247                                                              
2:     .3269  .3669                                                        
4:     .4216  .3275  .6404                                      
7:     .2137  .2742  .1124  .0839                                
11:     .4105  .4043  .2903  .2598  .1839                          
16:     .3240  .4047  .3054  .2786  .0489  .2220                    
22:     .2930  .2407  .4105  .3607  .0186  .1861  .2707              
29:     .2995  .2863  .5191  .5007  .0782  .3355  .2302  .2950        
37:     .0760  .0702  .2784  .1988  .1147  .1021  .0931 -.0438  .2087  
46: 
Read 45 items

> model.dhp <- specifyModel()
1:     RParAsp  -> RGenAsp, gam11,  NA
2:     RIQ      -> RGenAsp, gam12,  NA
3:     RSES     -> RGenAsp, gam13,  NA
4:     FSES     -> RGenAsp, gam14,  NA
5:     RSES     -> FGenAsp, gam23,  NA
6:     FSES     -> FGenAsp, gam24,  NA
7:     FIQ      -> FGenAsp, gam25,  NA
8:     FParAsp  -> FGenAsp, gam26,  NA
9:     FGenAsp  -> RGenAsp, beta12, NA
10:     RGenAsp  -> FGenAsp, beta21, NA
11:     RGenAsp  -> ROccAsp,  NA,       1
12:     RGenAsp  -> REdAsp,  lam21,  NA
13:     FGenAsp  -> FOccAsp,  NA,       1
14:     FGenAsp  -> FEdAsp,  lam42,  NA
15:     RGenAsp <-> RGenAsp, ps11,   NA
16:     FGenAsp <-> FGenAsp, ps22,   NA
17:     RGenAsp <-> FGenAsp, ps12,   NA
18:     ROccAsp <-> ROccAsp, theta1, NA
19:     REdAsp  <-> REdAsp,  theta2, NA
20:     FOccAsp <-> FOccAsp, theta3, NA
21:     FEdAsp  <-> FEdAsp,  theta4, NA
22: 
Read 21 records

> sem.dhp <- sem(model.dhp, R.DHP, 329,
+     fixed.x=c('RParAsp', 'RIQ', 'RSES', 'FSES', 'FIQ', 'FParAsp'))
 
> sem.dhp # print メソッドでは，係数しか表示されない

 Model Chisquare =  26.69722   Df =  15 

      gam11       gam12       gam13       gam14       gam23       gam24 
 0.16122243  0.24964929  0.21840307  0.07183948  0.06188722  0.22886655 
      gam25       gam26      beta12      beta21       lam21       lam42 
 0.34903584  0.15953378  0.18423260  0.23547774  1.06267796  0.92972549 
       ps11        ps22        ps12      theta1      theta2      theta3 
 0.28098701  0.26383553 -0.02260953  0.41214545  0.33614511  0.31119482 
     theta4 
 0.40460363 

 Iterations =  32 

> summary(sem.dhp) # 結果の表示は summary メソッドを使う

 Model Chisquare =  26.697   Df =  15 Pr(>Chisq) = 0.031302
 Chisquare (null model) =  872   Df =  45
 Goodness-of-fit index =  0.98439
 Adjusted goodness-of-fit index =  0.94275
 RMSEA index =  0.048759   90% CI: (0.014517, 0.078309)
 Bentler-Bonnett NFI =  0.96938
 Tucker-Lewis NNFI =  0.95757
 Bentler CFI =  0.98586
 SRMR =  0.020204
 AIC =  64.697
 AICc =  29.157
 BIC =  136.82
 CAIC =  -75.244 

 Normalized Residuals
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-0.8000 -0.1180  0.0000 -0.0120  0.0397  1.5700 

 R-square for Endogenous Variables
RGenAsp FGenAsp ROccAsp  REdAsp FOccAsp  FEdAsp 
 0.5220  0.6170  0.5879  0.6639  0.6888  0.5954 

 Parameter Estimates
       Estimate  Std Error z value  Pr(>|z|)                       
gam11   0.161222 0.038792   4.15604 3.2381e-05 RGenAsp <--- RParAsp
gam12   0.249649 0.043981   5.67631 1.3763e-08 RGenAsp <--- RIQ    
gam13   0.218403 0.044197   4.94154 7.7508e-07 RGenAsp <--- RSES   
gam14   0.071839 0.049707   1.44526 1.4838e-01 RGenAsp <--- FSES   
gam23   0.061887 0.051720   1.19659 2.3147e-01 FGenAsp <--- RSES   
gam24   0.228867 0.044162   5.18241 2.1904e-07 FGenAsp <--- FSES   
gam25   0.349036 0.045290   7.70672 1.2909e-14 FGenAsp <--- FIQ    
gam26   0.159534 0.038826   4.10895 3.9746e-05 FGenAsp <--- FParAsp
beta12  0.184233 0.094888   1.94158 5.2188e-02 RGenAsp <--- FGenAsp
beta21  0.235478 0.119389   1.97235 4.8570e-02 FGenAsp <--- RGenAsp
lam21   1.062678 0.090139  11.78937 4.4286e-32 REdAsp <--- RGenAsp 
lam42   0.929725 0.070281  13.22868 5.9934e-40 FEdAsp <--- FGenAsp 
ps11    0.280987 0.046232   6.07782 1.2183e-09 RGenAsp <--> RGenAsp
ps22    0.263836 0.044667   5.90674 3.4895e-09 FGenAsp <--> FGenAsp
ps12   -0.022610 0.051194  -0.44164 6.5875e-01 FGenAsp <--> RGenAsp
theta1  0.412145 0.051225   8.04584 8.5654e-16 ROccAsp <--> ROccAsp
theta2  0.336145 0.052100   6.45193 1.1043e-10 REdAsp <--> REdAsp  
theta3  0.311195 0.045927   6.77584 1.2369e-11 FOccAsp <--> FOccAsp
theta4  0.404604 0.046184   8.76062 1.9418e-18 FEdAsp <--> FEdAsp  

 Iterations =  32