Which fit indices should be reported for binary WLSMV models?

[Jonathon Little]

Dear lavaan users,

For a CFA or EFA with binary items estimated using WLSMV, lavaan can return:

cfi cfi.scaled cfi.robust tli tli.scaled tli.robust rmsea rmsea.scaled rmsea.robust

Savalei (2020) showed that the traditional WLSMV CFI and RMSEA can make model fit appear too good, especially with binary data, and proposed cML-based corrections.

Could someone clarify:

1. Do cfi.robust and rmsea.robust implement Savalei’s cML(D),s corrections? and if not which correct do they use and is there a reference for the method employed?
2. Is tli.robust based on the same correction?
3. For binary WLSMV models, should the .robust values be reported in preference to the .scaled values?
4. What do the unqualified values represent in this setting?

Many thanks.

Jonathon

[Yves Rosseel]

> Could someone clarify:
>
> 1. Do cfi.robust and rmsea.robust implement Savalei’s cML(D),s
> corrections?

Yes. If they are available (i.e., not NA), these are the ones you should
report.

> 2. Is tli.robust based on the same correction?

Yes.

> 3. For binary WLSMV models, should the .robust values be reported in

> preference to the .scaled values?

Yes. The .scaled values are only printed for two reasons: 1) often, when
the correlation matrix of poly/tetra-choric correlations is not positive
definite, we cannot compute the .robust versions, and the .scaled
versions are the fallback; 2) reproducibility: many older studies only
report the .scaled versions (because the .robust ones did not exist yet)

> 4. What do the unqualified values represent in this setting?

Not sure what you mean by this?

Yves.

--
Yves Rosseel
Department of Data Analysis, Ghent University