Estimating and interpreting structural equation models in Stata 12
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Estimating and interpreting structural equation models in Stata 12
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Estimating and interpreting structural equation models in Stata 12 David M. Drukker Director of Econometrics Stata
Stata Conference, Chicago July 14, 2011
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Purpose and outline Purpose To excite structural-equation-model (SEM) devotees by describing part of the new sem command and convince traditional simultaneous-equation-model types that the sem command is worth investigating
Outline 1
The language of SEM
2
Parameter estimation SUR with observed exogenous variables Recursive (triangular) system with correlated errors SUR with observed exogenous variables and a latent variable Nonrecursive system with a latent variable
3
Postestimation
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The language of SEM
Variables and Paths There are five types of variables in SEMs A variable is either observed or latent Observed variables are in your dataset Unobserved variables are not in your dataset, but you wish they were
A variable is either exogenous or endogenous A variable is exogenous if it is determined outside the system A variable is endogenous if is not exogenous
The concepts give rise to four possibilities Observed exogenous variable, latent exogenous variable, observed endogenous variable, and latent endogenous variable
Errors are a special type of latent exogenous variables Errors are the random shocks or effects that drive the system Errors are the random effects that cause the outcomes of “observationally equivalent individuals” to differ 3 / 31
The language of SEM
Path diagram
A path diagram is graphical specification of model A path diagram is composed of Variables in square or rectangular boxes are observed variables Variables in circles or ellipses are latent variables Straight arrows Each straight arrow indicates that the variable at the base affects the variable at the head When two variables have two arrows that point to each other there is feedback; each one affects the other
Curved two-headed arrows indicate that two variables are correlated A number along an arrow represents a constraint
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Parameter estimation
SUR with observed exogenous variables
Path diagram
x1 y1
ε1
y2
ε2
y3
ε3
x2
x3
x4
This is a path diagram for a seemingly unrelated regression (SUR) model with observed exogenous variables
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Parameter estimation
SUR with observed exogenous variables
Mathematical description of model SUR with observed exogenous variables y1 = β10 + β11 x1 + β12 x2 + ǫ1 y2 = β20 + β22 x2 + β23 x3 + ǫ2 y3 = β30 + β33 x2 + β34 x4 + ǫ3 where ǫ = (ǫ1 , ǫ2 , ǫ3 )′ , E [ǫ] = (0, 0, 0)′ , and Var [ǫ] = Σ sem (y1
