Measurement model and structural model having exactly same fit indices

[Alice Verlinden]

Dear community, 

I would like to ask for your help regarding a SEM analysis that I am conducting in Lavaan. 

It is a mediation model with 2 independent variables, one mediator and one outcome variable. I started by fitting the measurement model, and then switched to the structural model. The result is that both models  (measurement and structural) are identical: the fit indices are exactly the same (chisq = 116.7, df = 70, CFI = .966, TLI = .956, RMSEA = .057, SRMR = .070). 

I seems very unlikely to me that this happened  by chance.  Does anyone know what this means, and how I should interpret this?  

Thank you very much for your help! 

Alice 

[Shu Fai Cheung]

Is this what the structural part of your model is?

mediator ~ iv1 + iv2

outcome ~ mediator + iv1 + iv2

"iv1 ~~ iv2" not explicitly included but should be there by default in lavaan.

If this is your structural model, then what you found is expected. This model is saturated at the structural level, with respect to the variance-covariance matrix of the latent factors. You cannot empirically differentiate the structural model and the measurement model.

-- Shu Fai

[Alice Verlinden]

Dear Shu, 

Thanks for your clarification! Indeed, this is exactly what my structural model looks like! 

If the model is saturated at the structural level, my question is: what would you recommend me to do in order to be able to differentiate the structural from the measurement model?

I am really just discovering SEM, so my apologies for the additional question! 

Kind regards, 

Alice 

[Terrence Jorgensen]

If the model is saturated at the structural level, my question is: what would you recommend me to do in order to be able to differentiate the structural from the measurement model?

You can't.  You are using all the available information to estimate those parameters.  You can still interpret the parameters, but your structural hypotheses couldn't possibly be disconfirmed by the data.  A more restrictive hypothesized structure (e.g., full mediation) would buy you df.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen