Saturated model - How to address in lavaan / proceed and write up results/discussion?

[Jordan H]

Hi, 

I hope this is the appropriate place to ask my question! I have a model with two IVs/exogenous variables, one mediator variable, and one DV. I ran this model using lavaan and learned that I ended up with a saturated or just-identified model with zero degrees of freedom and "perfect" fit statistics (e.g., CFI of 1, RMSEA of 0, etc.). The lavaan summary showed that one of my IVs had an indirect effect (in the predicted direction) on my DV through the mediator variable, but not with my other IV.

However, I'm unclear on how I should proceed from here. Is it appropriate for me to still report that I found support for one of my predicted effects, and simply acknowledge that a limitation of this finding is that I cannot assess model fit due to zero df? Or is there something else I can do in lavaan to fix this issue?

Here is an image of my model. S_R and N_C are my IVs, P_C is my mediator, and O_D is my DV. The path I found support for was S_R --> P_C --> O_D.

 

Any advice or alternative suggestions are appreciated! Forgive the potential naivety of my question; I'm a Master's student who is still very new to SEM.

Thank you,

Jordan

*Resubmitted this post with new information since I couldn't figure out how to edit my original post.

[Jeremy Miles]

If the model you want to assess has zero df,  you can still report the parameter estimates.

It's not really a limitation that you can't assess model fit. Every regression, correlation, anova, ancova, etc model also has zero df and fit can't be assessed. (And every multilevel model might not fit, but there's no such thing as a saturated model in multilevel models, so the fit also can't be assessed).

Jeremy

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[Jordan H]

Thank you for your help, Jeremy! That all makes sense.

Jordan

[Mauricio Garnier-Villarreal]

Also, I see very little use of the fit indexes for path analysis. It seems incoherent to say that the relation between variables will reproduce the covariance matrix, as we can get the saturated model by including all relations. 

Fit its useful for a measurement model, when you try to state that latent variables structure reproduce the covariance matrix. 

I had to answer a reviewer asking me for fit measure in a model just like yours (path analysis and saturated)