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st: Replication of panel-RE/FE Models with SEM


From   "Florian Christian Esser" <florian.esser@tu-dortmund.de>
To   statalist@hsphsun2.harvard.edu
Subject   st: Replication of panel-RE/FE Models with SEM
Date   Wed, 18 Sep 2013 09:15:01 +0200

Hi everyone,

first, I am still using Stata 12.1

I want to reproduce Random and Fixed Effects Models for panel data with
structural equation models as described e.g. by Bollen/Brand (2008 -
http://www.escholarship.org/uc/item/3sr461nd). Unfortunately I do not
manage to get the same results from regular models with -xtreg (, fe)- and
sem. Are there any additional lines of code that I have to use in order to
make the sem command work or are there mistakes?

It would be great to hear back from you!
Florian

I have attached the Stata output from my .do-file:


* Regressionmodel: enter panel information
. xtset id year
       panel variable:  id (strongly balanced)
        time variable:  year, 10 to 12
                delta:  1 unit

.
. * Regression: REM
. xtreg height food

Random-effects GLS regression                   Number of obs      =      
 15
Group variable: id                              Number of groups   =      
  5

R-sq:  within  = 0.4167                         Obs per group: min =      
  3
       between = 0.6194                                        avg =      
3.0
       overall = 0.4316                                        max =      
  3

                                                Wald chi2(1)       =     
5.70
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =   
0.0169

------------------------------------------------------------------------------
      height |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
        food |   1.311973   .5493459     2.39   0.017     .2352746   
2.388671
       _cons |    159.782   5.932372    26.93   0.000     148.1548   
171.4092
-------------+----------------------------------------------------------------
     sigma_u |  10.279583
     sigma_e |  .80507649
         rho |  .99390368   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.
. * Regression: FEM
. xtreg height food, fe

Fixed-effects (within) regression               Number of obs      =      
 15
Group variable: id                              Number of groups   =      
  5

R-sq:  within  = 0.4167                         Obs per group: min =      
  3
       between = 0.6194                                        avg =      
3.0
       overall = 0.4316                                        max =      
  3

                                                F(1,9)             =     
6.43
corr(u_i, Xb)  = 0.6159                         Prob > F           =   
0.0319

------------------------------------------------------------------------------
      height |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
        food |       1.25   .4930066     2.54   0.032     .1347415   
2.365259
       _cons |   160.1167   2.670339    59.96   0.000     154.0759   
166.1574
-------------+----------------------------------------------------------------
     sigma_u |  13.822611
     sigma_e |  .80507649
         rho |  .99661917   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(4, 9) =   548.90                Prob > F =
0.0000

.
. * Reshapen in Wide Format
. reshape wide height food, i(id) j(year)
(note: j = 10 11 12)

Data                               long   ->   wide
-----------------------------------------------------------------------------
Number of obs.                       15   ->       5
Number of variables                   4   ->       7
j variable (3 values)              year   ->   (dropped)
xij variables:
                                 height   ->   height10 height11 height12
                                   food   ->   food10 food11 food12
-----------------------------------------------------------------------------

.
. * Calculate  SEM RE
. sem (food10@B -> height10) (food11@B -> height11) (food12@B -> height12)
(eta@1 -> height10) (eta@1 -> height11) (eta@1 -
> > height12), ///
> covstruct(_lexogenous,diagonal) cov(_lexogenous*_oexogenous@0) nolog
iterate(200) latent(eta ) cov( food10*food11 food10*
> food12 food11*food12 ///
> e.height10@E e.height11@E e.height12@E) nocapslatent

Endogenous variables

Observed:  height10 height11 height12

Exogenous variables

Observed:  food10 food11 food12
Latent:    eta

Structural equation model                       Number of obs      =      
  5
Estimation method  = ml
Log likelihood     = -38.399032

 ( 1)  [height10]food10 - [height12]food12 = 0
 ( 2)  [height10]eta = 1
 ( 3)  [height11]food11 - [height12]food12 = 0
 ( 4)  [height11]eta = 1
 ( 5)  [height12]eta = 1
 ( 6)  [var(e.height10)]_cons - [var(e.height12)]_cons = 0
 ( 7)  [var(e.height11)]_cons - [var(e.height12)]_cons = 0
 ( 8)  [cov(food10,eta)]_cons = 0
 ( 9)  [cov(food11,eta)]_cons = 0
 (10)  [cov(food12,eta)]_cons = 0
-------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
--------------+----------------------------------------------------------------
Structural    |
  height10 <- |
       food10 |   .1816882    .569775     0.32   0.750    -.9350502   
1.298427
          eta |          1   1.51e-15  6.6e+14   0.000            1       
   1
        _cons |   165.0916   6.412771    25.74   0.000     152.5228   
177.6604
  ------------+----------------------------------------------------------------
  height11 <- |
       food11 |   .1816882    .569775     0.32   0.750    -.9350502   
1.298427
          eta |          1  (constrained)
        _cons |   166.0189    6.51722    25.47   0.000     153.2454   
178.7924
  ------------+----------------------------------------------------------------
  height12 <- |
       food12 |   .1816882    .569775     0.32   0.750    -.9350502   
1.298427
          eta |          1  (constrained)
        _cons |   166.5462   6.627862    25.13   0.000     153.5558   
179.5366
--------------+----------------------------------------------------------------
Mean          |
       food10 |          5   .2828427    17.68   0.000     4.445638   
5.554362
       food11 |        5.4   .3577709    15.09   0.000     4.698782   
6.101218
       food12 |        5.8   .1788854    32.42   0.000     5.449391   
6.150609
--------------+----------------------------------------------------------------
Variance      |
   e.height10 |   .3453428   .1545956                       .143616   
.8304203
   e.height11 |   .3453428   .1545956                       .143616   
.8304203
   e.height12 |   .3453428   .1545956                       .143616   
.8304203
       food10 |         .4   .2529822                      .1158011   
1.381679
       food11 |        .64   .4047715                      .1852818   
2.210686
       food12 |        .16   .1011929                      .0463205   
.5526715
          eta |   164.6924   104.4409                      47.52018   
570.7805
--------------+----------------------------------------------------------------
Covariance    |
  food10      |
       food11 |         .4   .2884441     1.39   0.166    -.1653401   
.9653401
       food12 |         .2   .1442221     1.39   0.166      -.08267     
.48267
          eta |          0  (constrained)
  ------------+----------------------------------------------------------------
  food11      |
       food12 |        .28   .1901578     1.47   0.141    -.0927025   
.6527025
          eta |          0  (constrained)
  ------------+----------------------------------------------------------------
  food12      |
          eta |          0  (constrained)
-------------------------------------------------------------------------------

.
. * Calculate  SEM FE
. sem (food10@B -> height10) (food11@B -> height11) (food12@B -> height12)
(eta@1 -> height10) (eta@1 -> height11) (eta@1 -
> > height12), ///
> covstruct(_lexogenous,diagonal) cov(_lexogenous*_oexogenous@0) nolog
iterate(200) latent(eta ) ///
> cov( food10*food11 food10*food12 food10*eta food11*food12 food11*eta
food12*eta e.height10@E e.height11@E e.height12@E) n
> ocapslatent

Endogenous variables

Observed:  height10 height11 height12

Exogenous variables

Observed:  food10 food11 food12
Latent:    eta

Structural equation model                       Number of obs      =      
  5
Estimation method  = ml
Log likelihood     = -31.552533

 ( 1)  [height10]food10 - [height12]food12 = 0
 ( 2)  [height10]eta = 1
 ( 3)  [height11]food11 - [height12]food12 = 0
 ( 4)  [height11]eta = 1
 ( 5)  [height12]eta = 1
 ( 6)  [var(e.height10)]_cons - [var(e.height12)]_cons = 0
 ( 7)  [var(e.height11)]_cons - [var(e.height12)]_cons = 0
-------------------------------------------------------------------------------
              |                 OIM
              |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
--------------+----------------------------------------------------------------
Structural    |
  height10 <- |
       food10 |       .125   .5687157     0.22   0.826    -.9896622   
1.239662
          eta |          1   1.51e-15  6.6e+14   0.000            1       
   1
        _cons |    165.375   6.420632    25.76   0.000     152.7908   
177.9592
  ------------+----------------------------------------------------------------
  height11 <- |
       food11 |       .125   .5687157     0.22   0.826    -.9896622   
1.239662
          eta |          1  (constrained)
        _cons |    166.325   6.524571    25.49   0.000     153.5371   
179.1129
  ------------+----------------------------------------------------------------
  height12 <- |
       food12 |       .125   .5687157     0.22   0.826    -.9896622   
1.239662
          eta |          1  (constrained)
        _cons |    166.875   6.634683    25.15   0.000     153.8713   
179.8787
--------------+----------------------------------------------------------------
Mean          |
       food10 |          5   .2828427    17.68   0.000     4.445638   
5.554362
       food11 |        5.4   .3577709    15.09   0.000     4.698782   
6.101218
       food12 |        5.8   .1788854    32.42   0.000     5.449391   
6.150609
--------------+----------------------------------------------------------------
Variance      |
   e.height10 |       .345   .1542887                      .1435986    
.828873
   e.height11 |       .345   .1542887                      .1435986    
.828873
   e.height12 |       .345   .1542887                      .1435986    
.828873
       food10 |         .4   .2529822                      .1158011   
1.381679
       food11 |        .64   .4047715                      .1852818   
2.210686
       food12 |        .16   .1011929                      .0463205   
.5526715
          eta |   165.3479    104.855                      47.71022   
573.0415
--------------+----------------------------------------------------------------
Covariance    |
  food10      |
       food11 |         .4   .2884441     1.39   0.166    -.1653401   
.9653401
       food12 |         .2   .1442221     1.39   0.166      -.08267     
.48267
          eta |   6.891667      4.772     1.44   0.149    -2.461282   
16.24461
  ------------+----------------------------------------------------------------
  food11      |
       food12 |        .28   .1901578     1.47   0.141    -.0927025   
.6527025
          eta |   6.198333   5.378265     1.15   0.249    -4.342873   
16.73954
  ------------+----------------------------------------------------------------
  food12      |
          eta |       4.28   2.995532     1.43   0.153    -1.591135   
10.15114
-------------------------------------------------------------------------------

.
end of do-file

.

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