Testing non-nested structural equation models

[Michael Chen]

Dear colleagues,

I would like to test several recursive (one-way, no feedback loops) structural equation models. All the models contain the same set of observed and latent variables. Differences exist primarily among the hypothesized directions between constructs.

For example, one part of M1 contains the path: Depression -> Coercion. However, in M2, the path is flipped: Coercion -> Depression.

Note: the LRTEST involves nested models. In my analyses, the models are not nested.

I came across the paper by Merkle et al. (2015), links:
http://quantpsy.org/pubs/merkle_you_preacher_2016.pdf
https://pdfs.semanticscholar.org/pre...642d4fda69.pdf

In it, they describe an R package that seems to be able to readily perform non-nested SEM tests.

After going through the Stata documentation, there doesn't appear to be an analogous command.

If you have any advice or guidance on how to best implement this test in Stata 14/15, please let me know.

Thank you!

[Phil Bromiley]

You'll increase your chances of a helpful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

You should try to search for Voung 1989 - see for instance
https://www.statalist.org/forums/for...nnested-models

[Michael Chen]

You should try to search for Voung 1989 - see for instance
https://www.statalist.org/forums/for...nnested-models

Thank you for that reference. Unfortunately, that's implemented in the context of single equation regression functions. I'm trying to to compare 2 un-nested SEMs.

I've attached a figure, not sure if it helps clarify what I'm trying to do. The idea is that I'd like to test Main vs. Alternate and see which model is better. The post-estimation likelihood ratio test (lrtest main alternate) would not work, since the latter model is technically not nested within the former model. I understand there are descriptive ways of comparing models (e.g., compare BICs, various fit indices, model parsimony, etc.), as described in the Merkle et al. paper cited in the original post. But what I'd really like to do is to empirically test the two competing models against each other.