Measurement invariance (chi-square)

[Sara]

Hello everyone,

I am testing measurement invariance across six groups with ordinal (Likert-type) items using lavaan. I have only one  factor. I estimated:

1. Configural invariance

2. Threshold invariance

3. Threshold + loadings  invariance

What I observed is the following:

• The threshold invariance model fits worse than the configural model, as expected.

• However, the threshold + loadings invariance model fits better than the threshold-only model, even though it is more constrained. I know that this can happen. 

• However, the χ² value for the scalar model is lower with more df compared to the threshold-only model. The chi-square difference test (lavTestLRT) is significant,  but it can be influenced by the large sample size. The difference in RMSEA is Δ = −0.015. The difference in CFI is Δ = −0.008. 

My questions are:

• Is this behavior expected with ordinal data and WLSMV? Or does it indicate a potential identification or estimation problem in my model? Should I rely only on the corrected chi-square difference test? 

Any clarification would be very helpful.

Thank you!