= Stata sem =

The '''`sem`''' command fits a [[Statistics/StructuralEquationModeling|SEM]].

<<TableOfContents>>

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== Usage ==

Adapted from [[https://www.stata.com/features/overview/structural-equation-modeling/explanation/]]:

{{{
. webuse sem_1fmm
(Single-factor measurement model)

. rename x4 y

. sem (x1<-X) (x2<-X) (x3<-X) (y<-X)

Endogenous variables
  Measurement: x1 x2 x3 y

Exogenous variables
  Latent: X

Fitting target model:
Iteration 0:   log likelihood = -8487.5905  
Iteration 1:   log likelihood = -8487.2358  
Iteration 2:   log likelihood = -8487.2337  
Iteration 3:   log likelihood = -8487.2337  

Structural equation model                                  Number of obs = 500
Estimation method: ml

Log likelihood = -8487.2337

 ( 1)  [x1]X = 1
------------------------------------------------------------------------------
             |                 OIM
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Measurement  |
  x1         |
           X |          1  (constrained)
       _cons |     99.518   .6412888   155.18   0.000      98.2611    100.7749
  -----------+----------------------------------------------------------------
  x2         |
           X |   1.033249   .0723898    14.27   0.000     .8913676     1.17513
       _cons |     99.954   .6341354   157.62   0.000     98.71112    101.1969
  -----------+----------------------------------------------------------------
  x3         |
           X |   1.063876   .0729725    14.58   0.000     .9208526      1.2069
       _cons |     99.052   .6372649   155.43   0.000     97.80298     100.301
  -----------+----------------------------------------------------------------
  y          |
           X |   7.276754   .4277638    17.01   0.000     6.438353    8.115156
       _cons |     94.474   3.132547    30.16   0.000     88.33432    100.6137
-------------+----------------------------------------------------------------
    var(e.x1)|   115.6865   7.790423                      101.3823    132.0089
    var(e.x2)|   105.0445    7.38755                      91.51873    120.5692
    var(e.x3)|   101.2572    7.17635                      88.12499    116.3463
     var(e.y)|   144.0406   145.2887                      19.94838    1040.069
       var(X)|   89.93921   11.07933                      70.64676    114.5001
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(2) = 1.46            Prob > chi2 = 0.4827
}}}

A more complex example:

{{{
. sem (X -> x1 x2 x3) (Z -> z1 z2 z3) (Y -> y1 y2 y3) (Y <- X Z), noanchor variance(X@1 Z@1 e.Y@1) noconstant
}}}

Note that assumptions about variances must be specified on the '''`variance`''' option. In this case, the variances of latent variables (i.e., `var(X)` and `var(Z)`) and the variance of the outcome variable's errors  (i.e. `var(e.Y)`) are all assumed to be uniform.

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== See also ==

[[Stata/Gsem|gsem]]

[[https://www.stata.com/manuals/sem.pdf#semsem|Stata manual for sem]]



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CategoryRicottone