Measurement Invariance and Latent Mean Comparison with non-normal data: MLR or Bootstraped ML?

[Basil Maly]

Dear all,

I’m testing measurement invariance across three groups and subsequently want to compare latent means. However, the sample sizes are unequal and rather small in two groups ( n₁ = 168, n₂ = 484, n₃ = 197). The indicators are not normally distributed, and multivariate normality is not given. However, model estimation with both seems to be stable.

My questions:

1. Should I use MLR as the estimator, or ML with bootstrapped standard errors?
2. My model comparisons are based on the global fit indices CFI(robust) and RMSEA(robust). Would it be better to use permuteMeasEq in this case?

Thanks for all inputs!