Clarification on Δχ² interpretation for metric invariance with WLSMV and Svetina et al. (2019)

[Sara]

Hi all,

I'm performing measurement invariance testing across six groups using lavaan with categorical data (4-point Likert), the WLSMV estimator, and the delta parameterization with Wu & Estabrook (2016) identification, following the procedure outlined in Svetina et al. (2019).

I am testing:

• Configural invariance

• Thresholds invariance

• Thresholds + loadings invariance

I use measEq.syntax() from the semTools package and compare models using both fitmeasures() (for ΔCFI and ΔRMSEA) and lavTestLRT() (for Δχ², Satorra-Bentler scaled).

In Svetina et al. (2019), I found this statement:

“Metric invariance is supported when ΔRMSEA ≤ 0.01 in conjuction with sig chi-square difference test and  ΔCFI ≥ –.004 for metric". 

 

In other words, this means that even if the chi-square difference test is significant (p < 0.05), but ΔCFI and ΔRMSEA stay within acceptable thresholds , metric invariance can be considered supported?

[Terrence Jorgensen]

FYI, this was answered on CrossValidated:

https://stats.stackexchange.com/questions/669027/clarification-on-%ce%94%cf%87%c2%b2-interpretation-for-metric-invariance-with-wlsmv-and-svetina