Hi Statalist members,

I have a question about testing for measurement invariance in a two latent variable CFA with multiple groups using -sem- in stata 14.2. I found two methods to check for measurement invariance. The first method fixes loadings of a latent variable for item1 at 1 and intercept of item1 at 0 across all groups (https://stats.idre.ucla.edu/stata/fa...mand-stata-12/).

Code:
*Method 1
*Configural
sem (L1-> v1 v2 v3 v4) (L2 -> v5 v6 v7 v8)       ///
            (v1 <- L1 _cons@0)                               ///
            (v5  <- L2 _cons@0),                             ///
            group(grp1)  mean(L1 L2)                     ///
            ginvariant(none)                      
 
*Metric
sem (L1-> v1 v2 v3 v4) (L2 -> v5 v6 v7 v8)       ///
           (v1 <- L1 _cons@0)                                ///
           (v5   <- L2 _cons@0),                             ///
            group(grp1)  mean(L1 L2)                     ///
            ginvariant(mcoef)
The second method sets the mean of the latent variable to 0 and the variances to 1 in all groups (see https://blog.stata.com/2016/08/23/gr...nt-invariance/).

Code:
*Method 2
*Configural
sem (L1-> v1 v2 v3 v4) (L2 -> v5 v6 v7 v8),       ///
           group(grp1)  variance(L1@1 L2@1)      ///
           mean(L1@0 L2@0)                                ///
           ginvariant(none)
 
*Metric
sem (L1-> v1 v2 v3 v4) (L2 -> v5 v6 v7 v8),       ///
          group(grp1)  variance(L1@1 L2@1)       ///
          mean(L1@0 L2@0)                                ///
          ginvariant(mcoef)
I tried both methods. For the configural model both methods produced the same results for model fit. However, for the metric model there is a difference in model fit. Method 2 produces higher chi-square and has more degrees of freedom (a difference of 2 df when comparing two groups) as such resulting in somewhat different conclusions about metric invariance. I was wondering how to explain this difference and also what method is preferred if this difference in results is not related to my syntax.

I hope you can help me.
Thanks a lot!
Renske