SEM: How to Label path diagram and translate it into Equations

#1
Hei hou

I'm new here. So hello everybody.

I have a problem. It's about SEM (structural equation model).

I have to lable a path diagram (Lisreal Notation) and then translate it into the equations (Meassurment Model, Structural Model).

In this document you'll find the path diagram, the equations and the work I did.
https://dl.dropboxusercontent.com/u/35021035/exercise.docx

My question would be: Do you think the labeling and translation into the 3 given equations is correct?

I also need to add the covariance matrices for the structural model. As you see in the document (at the end) I did not get that. Could someone please, please help.

It'd be really cool if someone could help.
 

Lazar

Phineas Packard
#5
I assume it is homework? If so I will suggest that 1 and 2 are not quite right. For example, lets think in terms of a one factor congeneric model (or any CFA for that matter) where the expected covariance matrix is give by:

[MATH]\Sigma = \Lambda \Phi {\Lambda }' + \Theta[/MATH]

We can now expand that (assuming 6 indicator items) to:
[MATH]
\begin{Bmatrix}
\lambda_{11}
\\ \lambda_{21}
\\ \lambda_{31}
\\ \lambda_{41}
\\ \lambda_{51}
\\ \lambda_{61}
\end{Bmatrix}
\times
\phi_{1,1}
\times
[/MATH]
[MATH]
\begin{Bmatrix}
\lambda_{11} & \lambda_{21} & \lambda_{31} & \lambda_{41} & \lambda_{51} &\lambda_{61}
\end{Bmatrix}
+
\begin{Bmatrix}
\delta _{1} & 0 &0 &0 & 0 &0 \\
0& \delta _{2} &0 & 0 &0 & 0\\
0& 0 & \delta _{3} &0 &0 &0 \\
0&0 &0 &\delta _{4} &0 &0 \\
0& 0 & 0 &0 &\delta _{5} &0 \\
0& 0 &0 & 0 &0 &\delta _{6}
\end{Bmatrix}
[/MATH]

Note that the [MATH]\Phi[/MATH] and [MATH]\Theta[/MATH] matrices are square and symmetric. In yours they are not. Note also that if your tried to run this model in any SEM software it would not run as the model as you need to identify the measurement structure. You could do this either by setting [MATH] \lambda_{1,1}[/MATH] or [MATH]\phi_{1,1}[/MATH] to 1