Does a poorly fitting CFA preclude SEM?

Question

Trying to help someone with a Masters dissertation.

I've run CFA in Jamovi on her questionnaire responses based on the assumed item/factor relationships.

I don't really understand the various outputs from the Jamovi CFA program,and havn't so far been able to locate an idiot's guide.

She certainly doesn't understand them, and its a fair bet that her supervisor won't understand them either, but apparently she's likely to have an external examiner who is not clueless, so the default reliance on "emperors new clothes" may be risky.

I get a poor fit on all indices apart from Chi sq/df.

Would I be right in thinking that a poorly fitting CFA model (equivalent, I believe, to the measurement model in SEM) precludes doing SEM?

If so, that'd be something of a relief.

Answer 1

A confirmatory factor analysis (CFA) is a structural equation model (SEM); as you said, it's the measurement part of the SEM. If the CFA has poor fit, then a SEM that adds variables but doesn't affect the measurement model will also have poor fit. Indeed, if there is misfit in the measurement model and the other parts of the larger SEM are estimated together with maximum likelihood, the estimates will be biased.

One way to get around this is to use model-implied instrumental variables (MIIVs) estimation of the SEM, which allows you consistently estimate structural parameters of the SEM even if the measurement model is misspecified (as long as some parts of it are correct). MIIVs can also help identify the specific parts of the model that are incorrect. This is a bit of an advanced technique, but there is a very easy-to-use package for this in R (MIIVsem) and a straightforward introductory paper (Bollen, 2018).