Hi all,
I am estimating a model with SEM, using the following command:
Code:
sem (visual -> v1, ) (visual -> v2, ) (visual -> v3, ) (verbal -> v4, ) ///
(verbal -> v5, ) (verbal -> v6, ) (speed -> v7, ) (speed -> v8, ) ///
(speed -> v9, ), covstruct(_lexogenous, diagonal) vce(sbentler) ///
standardized latent(visual verbal speed ) cov( visual*verbal visual*speed ///
verbal*speed) nocapslatent
The results in matrix form is:

PHP Code:

Endogenous variables on endogenous variables

                 
observed                                                                                          
            Beta 
|        v1         v2         v3         v4         v5         v6         v7         v8         v9 
    
-------------+---------------------------------------------------------------------------------------------------
    
observed     |                                                                                                   
              
v1 |         0                                                                                         
              v2 
|         0          0                                                                              
              v3 
|         0          0          0                                                                   
              v4 
|         0          0          0          0                                                        
              v5 
|         0          0          0          0          0                                             
              v6 
|         0          0          0          0          0          0                                  
              v7 
|         0          0          0          0          0          0          0                       
              v8 
|         0          0          0          0          0          0          0          0            
              v9 
|         0          0          0          0          0          0          0          0          0 
    
-----------------------------------------------------------------------------------------------------------------

Exogenous variables on endogenous variables

                 
latent                          
           Gamma 
|    visual     verbal      speed 
    
-------------+---------------------------------
    
observed     |                                 
              
v1 |         1          0          0 
              v2 
|  .4907708          0          0 
              v3 
|   1.23306          0          0 
              v4 
|         0          1          0 
              v5 
|         0   1.319723          0 
              v6 
|         0   2.247793          0 
              v7 
|         0          0          1 
              v8 
|         0          0   1.065948 
              v9 
|         0          0   1.655825 
    
-----------------------------------------------

Covariances of error variables

                 
observed                                                                                          
             Psi 
|      e.v1       e.v2       e.v3       e.v4       e.v5       e.v6       e.v7       e.v8       e.v9 
    
-------------+---------------------------------------------------------------------------------------------------
    
observed     |                                                                                                   
            
e.v1 |  25.73631                                                                                         
            e
.v2 |         0   14.38707                                                                              
            e
.v3 |         0          0   35.64868                                                                   
            e
.v4 |         0          0          0   2.837749                                                        
            e
.v5 |         0          0          0          0   6.702231                                             
            e
.v6 |         0          0          0          0          0   19.89547                                  
            e
.v7 |         0          0          0          0          0          0   317.6616                       
            e
.v8 |         0          0          0          0          0          0          0   160.4738            
            e
.v9 |         0          0          0          0          0          0          0          0   693.0864 
    
-----------------------------------------------------------------------------------------------------------------

Intercepts of endogenous variables

                    
observed                                                                                          
          alpha 
|        v1         v2         v3         v4         v5         v6         v7         v8         v9 
    
-------------+---------------------------------------------------------------------------------------------------
           
_cons |  29.57931       24.8   15.96552   9.951724   18.84828   17.28276   90.17931   109.7655   191.7793 
    
-----------------------------------------------------------------------------------------------------------------

Covariances of exogenous variables

                 
latent                          
             Phi 
|    visual     verbal      speed 
    
-------------+---------------------------------
    
latent       |                                 
          
visual |  21.73498                       
          verbal 
|  7.338981   8.477162            
           speed 
|  38.11427   15.28808   244.0304 
    
-----------------------------------------------

Means of exogenous variables

                 
latent                          
           kappa 
|    visual     verbal      speed 
    
-------------+---------------------------------
            
mean |         0          0          0 
    
----------------------------------------------- 

When I am predicting the latent variables, I get the following results:

Code:
predict visual verbal speed, latent(visual verbal speed)
sum visual verbal speed
HTML Code:
   Variable Obs Mean Std. Dev. Min Max       visual 145 -4.32e-09 4.000018 -9.592437 12.42246 verbal 145 -1.23e-09 2.746986 -7.786823 7.084102 speed 145 3.21e-08 13.91826 -40.7785 43.87231

My questions are:

1) Why the std. dev. of the predicted latent variables are smaller than the sqrt of the variances of the variables in matrix Phi?

2) If I use
Code:
estat framework, stand
the latent variables are standardized in the Phi matrix; zero mean and unit variance. Is there any way to predict standard latent variables directly, or one should always predict them first and then standardize them with:

Code:
egen vis = std(visual)
Thanks for taking the time,
Emma