Stata sem
The sem command fits a SEM.
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 = 0.4827A 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.