WLSMV vs. MLR for CFA/SEM with floor effects across Likert indicators — how to interpret CFI discrepancy?

[Antonia Zenker]

Hi all,

I'm still fairly new to lavaan and would appreciate some guidance. Thanks in advance!

I'm fitting a CFA/SEM in lavaan with an 8-factor measurement model, N > 800. All indicators are ordinal Likert-type items (5-point scale, 27 indicators in total). One factor is my main outcome for now, and the other seven are exogenous predictor constructs, which might become endogenous in later re-estimations.

The structural model regresses the outcome factor on the seven predictor factors plus a few manifest covariates (age, gender, usage frequency, and some single-item covariates).

When checking the item distributions, I noticed that for about one third of my 27 ordinal items, most responses fall at the scale minimum (floor effects).

I initially ran everything with estimator = "WLSMV" and ordered = <all 27 indicators>. After discussions with colleagues, I was advised to switch to estimator = "MLR" and treat the Likert items as numeric, on the grounds that (a) WLSMV is primarily intended for ordinal endogenous variables rather than ordinal exogenous predictors, and (b) the lavaan documentation notes that ordinal categorical variables are often treated as numeric in practice.

When comparing the same measurement model under both estimators, cfi.robust came out noticeably higher under WLSMV than under MLR. I wonder whether this gap is related to the floor effects since for several items effectively only about three of the five response categories are well occupied which might make the numeric treatment under MLR less appropriate. I'd appreciate your input on the following:

1. Should floor effects of this severity push us back toward WLSMV despite its practical downsides?
2. We also plan several bootstrapped mediation models later. Is this feasible with ML and a bootstrap approach given our data situation?
3. Is there a standard way to report fit indices and to explain why CFI comes out differently under MLR than under WLSMV?

I'm happy to share model syntax or distribution details if useful. Thank you very much in advance!

Best regards,
Antonia

[Jeremy Miles]

CFI is a function of two different values of chi-square: The null model, and the fitted model. If CFI changes it can be because one, or both, of those changed. 

If you could tell us the four values (WLSMV, MLR) x (fitted, null) it might give some clues as to what is happening. 

My *guess* is that the null chi-square is higher in the WLSMV model, because the WLMSV will give higher correlations with a floor effect. 

Jeremy

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