Dear Statalist members,

I have a question about measurement invariance testing for multigroup confirmatory factor analysis. I have worked on this for some time and would be happy for input.

I am fitting a CFA model using -sem- (in Stata 16) with two latent factors (“SMW”, “IWB”) from seven observed variables across three groups. The group variable is “timepoint” (2003, 2013 and 2017) while the seven observed variables are policies ("pol1"-"pol7") measured at these three time points for 33 countries in 2017 and 2013, and 26 countries in 2003. The total numbers of observations in the model are 92.

My question concerns the method used for checking measurement invariance. I am wondering which of the two following approach are most appropriate for estimating the “configural model”:
Code:
*Approach 1:
* Configural model
 
sem (SMW -> pol1 pol2 pol3 pol4) ///
            (IWB -> pol5 pol6 pol7) ///
            (pol1 <- SMW _cons@0) (pol5 <- IWB _cons@0 ), ///
            group(timepoint) ginvariant(none) mean(SMW IWB) ///
            vce(sbentler) cov( SMW*IWB e.pol2*e.pol1)
 
*Approach 2:
* Configural model
 
sem (SMW -> pol1 pol2 pol3 pol4) ///
            (IWB -> pol5 pol6 pol7), ///
            group(timepoint) ginvariant(none) means(SMW@0 IWB@0) ///
            vce(sbentler) cov( SMW*IWB e.pol2*e.pol1)
Approach 1 is from a previous Statalist post and Stata UCLA. Approach 2 is from Acock, A (2013) Discovering structural equation modelling using Stata. College Station: Stata Press.

The two approaches give different results. In approach 1, the estimation fails as it won’t converge. In approach 2, the model is estimated. Hence, I wonder which approach correct as it tell me whether I can proceed with the measurement invariance testing.
Additionally, it would be interesting with input on potential causes of the model convergence issue in approach 1.

All best,
Siri