How to compare coefficients across SEM models?

[Rick Trinkner]

Hello,

Is there a way to compare coefficients across sem models that are not nested?

For example:
Model 1: y1 <- x1 x2 x3 x4
Model 2: y1 <- x1 x2 x3 x5
Model 3: y1 <- x1 x2 x3 x6
Model 4: y1 <- x1 x2 x3 x7

I want to figure out if the coefficients associated with x4 thru x7 are significantly different from each other. Each model is identical in all respects except for those variables. (In this instance, x4 thru x6 are different ways to measure the same construct with x7 being a composite of those measures).

I know I could do this in a regression format with the suest and subsequent test commands, but suest command isn't allowed in the sem framework. I'm using an sem framework because my dataset only has 75 cases, but 16 of those cases are missing values on key variables in my model. My thinking was I could use the sem framework (with observed variables only) with FIML estimation to account for missing data, so I wouldn't have to lose those 16 cases (like I would in a standard regression model).

[Andrew Musau]

There is a -group()- option in sem, but these being separate variables will require you to restructure your data.

sysuse auto, clear
sem mpg <- turn disp gear weight, method(mlmv)
sem mpg <- turn disp gear length, method(mlmv)

*RESHAPE
rename (weight length) var=
reshape long var, i(make) j(which) string
encode which, gen(groupvar) 

*JOINT ESTIMATION
 sem (mpg <- turn disp gear var), group(groupvar) method(mlmv)

*TEST (-coeflegend- to see how coefficients are named)
test _b[mpg:1.groupvar#c.var]=  _b[mpg:2.groupvar#c.var]

Res.:

. sem mpg <- turn disp gear weight, method(mlmv)

Endogenous variables

Observed:  mpg

Exogenous variables

Observed:  turn displacement gear_ratio weight

Fitting target model:

Iteration 0:   log likelihood = -1339.1709  
Iteration 1:   log likelihood = -1339.1709  

Structural equation model                       Number of obs     =         74
Estimation method  = mlmv
Log likelihood     = -1339.1709

--------------------------------------------------------------------------------
               |                 OIM
               |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
Structural     |
  mpg          |
          turn |  -.1345925   .1746197    -0.77   0.441    -.4768408    .2076557
  displacement |   .0077091   .0112159     0.69   0.492    -.0142737    .0296919
    gear_ratio |   .5694417   1.551143     0.37   0.714    -2.470743    3.609626
        weight |  -.0059168   .0013924    -4.25   0.000    -.0086459   -.0031877
         _cons |   41.26146    7.96542     5.18   0.000     25.64953     56.8734
---------------+----------------------------------------------------------------
     var(e.mpg)|   11.34244   1.864686                       8.21807    15.65464
--------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0)   =      0.00, Prob > chi2 =      .

. 
. sem mpg <- turn disp gear length, method(mlmv)

Endogenous variables

Observed:  mpg

Exogenous variables

Observed:  turn displacement gear_ratio length

Fitting target model:

Iteration 0:   log likelihood = -1089.9339  
Iteration 1:   log likelihood = -1089.9339  

Structural equation model                       Number of obs     =         74
Estimation method  = mlmv
Log likelihood     = -1089.9339

--------------------------------------------------------------------------------
               |                 OIM
               |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
Structural     |
  mpg          |
          turn |  -.1164765   .1862625    -0.63   0.532    -.4815444    .2485914
  displacement |  -.0032826   .0102445    -0.32   0.749    -.0233615    .0167963
    gear_ratio |   1.047017   1.582798     0.66   0.508    -2.055211    4.149245
        length |   -.160631   .0419622    -3.83   0.000    -.2428755   -.0783865
         _cons |   53.59424   8.326451     6.44   0.000     37.27469    69.91378
---------------+----------------------------------------------------------------
     var(e.mpg)|   11.77787    1.93627                      8.533558    16.25562
--------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0)   =      0.00, Prob > chi2 =      .

. 

. 
. *JOINT ESTIMATION

. 
.  sem (mpg <- turn disp gear var), group(groupvar) method(mlmv)

Endogenous variables

Observed:  mpg

Exogenous variables

Observed:  turn displacement gear_ratio var

Fitting target model:

Iteration 0:   log likelihood = -2429.1049  
Iteration 1:   log likelihood = -2429.1049  

Structural equation model                       Number of obs     =        148
Grouping variable  = groupvar                   Number of groups  =          2
Estimation method  = mlmv
Log likelihood     = -2429.1049

Group              : length                     Number of obs     =         74

--------------------------------------------------------------------------------
               |                 OIM
               |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
Structural     |
  mpg          |
          turn |  -.1164765   .1862625    -0.63   0.532    -.4815444    .2485914
  displacement |  -.0032826   .0102445    -0.32   0.749    -.0233615    .0167963
    gear_ratio |   1.047017   1.582798     0.66   0.508    -2.055211    4.149245
           var |   -.160631   .0419622    -3.83   0.000    -.2428755   -.0783865
         _cons |   53.59424   8.326451     6.44   0.000     37.27469    69.91378
---------------+----------------------------------------------------------------
     var(e.mpg)|   11.77787    1.93627                      8.533558    16.25562
--------------------------------------------------------------------------------

Group              : weight                     Number of obs     =         74

--------------------------------------------------------------------------------
               |                 OIM
               |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
Structural     |
  mpg          |
          turn |  -.1345925   .1746197    -0.77   0.441    -.4768408    .2076557
  displacement |   .0077091   .0112159     0.69   0.492    -.0142737    .0296919
    gear_ratio |   .5694417   1.551143     0.37   0.714    -2.470743    3.609626
           var |  -.0059168   .0013924    -4.25   0.000    -.0086459   -.0031877
         _cons |   41.26146    7.96542     5.18   0.000     25.64953     56.8734
---------------+----------------------------------------------------------------
     var(e.mpg)|   11.34244   1.864686                       8.21807    15.65464
--------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(0)   =      0.00, Prob > chi2 =      .

. 
. 
. 
. *TEST (-coeflegend- to see how coefficients are named)

. 
. test _b[mpg:1.groupvar#c.var]=  _b[mpg:2.groupvar#c.var]

 ( 1)  [mpg]1bn.groupvar#c.var - [mpg]2.groupvar#c.var = 0

           chi2(  1) =   13.58
         Prob > chi2 =    0.0002

.

[Rick Trinkner]

Thanks Andrew! This is very helpful