Methodological validity of vimplifying SEM Models and applying SEM to panel data with Fixed Effects

[Bui Phuong Huyen]

Hello everyone,
I would like to clarify the methodological approach I’m considering. In my SEM model, the original network of variables is very complex, with multiple feedback loops and many interconnections, which makes the model under-identified and prevents convergence. To address this, I simplified the model by removing circular paths and keeping only the most important one-way relationships.

Data Overview

• Observations: 4000
• Groups: 1440
• Variables: 8
• Time span: 11 years
• Problems:
  • Complex relationships and feedback loops.
  • Several variables act both as predictors and outcomes
  • Some variables are not independent, exhibiting bidirectional or multi-directional effects.

First SEM Attempt – Full Model

sem (GB_VL <- ROA DR SZ GQ2 TO2 ML KC A_ER) ///
  (ROA <- A_ER) (DR <- GQ2) (SZ <- DR) ///
  (GQ2 <- TO2 KC A_ER) (TO2 <- GQ2 KC A_ER) ///
  (KC <- A_ER GQ2 TO2) (ML <- A_ER) ///
  (A_ER <- KC ML GQ2 TO2), nocapslatent

==> Issues encountered:

• Model not full rank / too many parameters
• More parameters than the data can support (under-identified)
• Convergence not achieved - SEM uses iterative estimation; circular loops and under-identification prevent solution.

Second SEM Attempt – Most Simplified Version

sem (GB_VL <- ROA DR SZ GQ2 TO2 ML KC A_ER) ///
   (ROA <- A_ER) (DR <- GQ2) (SZ <- DR) ///
   (GQ2 <- KC) ///
   (TO2 <- GQ2) ///
   (KC <- A_ER) ///
   (ML <- A_ER), nocapslatent
estat mindices
estat teffects

==> No circular loops, minimal number of paths, this version converged.

My questions are:

• From a methodological standpoint, is this simplification approach acceptable?
• How would this affect the interpretation of direct and indirect effects in the SEM?
• SEM is typically designed for cross-sectional data and relies on OLS assumptions. If my dataset is panel data and I want to account for within-group fixed effects (FEM), can I still use SEM directly, or should I first transform the data using FEM techniques?

I would appreciate any guidance or suggestions on how to approach this issue.
Thank you!
Phuong Huyen

I apologize for the spelling errors in the previous title.

[Richard Williams]

For SEM with panel data, you might see if xtdpdml (available from ssc) can meet your needs.

https://www.stata-journal.com/articl...article=st0523

https://academicweb.nd.edu/~rwilliam/dynamic/index.html

[Bui Phuong Huyen]

Dear Professor Williams,

Thank you very much for your helpful response, I greatly appreciate you taking the time to share this domain-specific knowledge. I will review the paper immediately and adapt my methodology accordingly.

Sincerely,
Phuong Huyen