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Dear Bengt and Linda: I have been running metric invariance models (with continuous indicators and latent variables) in Mplus for years, but I'm having trouble with scalar (intercept) invariance. From what I understand, in a multiplegroup model, factor loadings are constrained like this: f BY y1 y2 y3; y1 (1); y2 (2); y3 (3); And shouldn't intercepts be constrained like this: [y1] (4); [y2] (5); [y3] (6); However, that doesn't work. I get the SAME EXACT fit indices with intercept constraints imposed as I do without these constraints. And if I try it this way, I get an unidentifed model: MODEL WHITE: [y1]; [y2]; [y3]; MODEL BLACK: [y1]; [y2]; [y3]; What am I doing wrong? Thanks very much. Seth 


Please see the inputs under multiple group analysis in the Topic 1 course handout. The default in Mplus is to constrain the intercepts and factor loadings across groups. 


Hello, I learned that when testing for scalar invariance, on top of constraining the intercept to be equal across groups, one should also set the means of errors to be zero in all groups. Is this true, or is this your practice, Dr. Muthen? Aren't means of errors ALWAYS zero? Is this just some programming convention that SEM people do to make sure that the general rule that "means of errors are zero" does indeed hold in estimation? Have you ever heard of this programming technique? Thank you, Lisa 


As a followup question, Dr. Muthen: Is it even possible to set means of errors for measured variables to zero in Mplus? Would this be some sort of unusual modeling? 


Means of residuals are not parameters in the model. They cannot be fixed at zero. They are zero. 


Thank you! I agree. 


Hello, I try to show scalar invariance across times (Pre/Posttest) in one group. I have two factors and 4 itemparcels per factor. The configural and metric models are ok. Unfortunately there is a problem with the scalar invariance. The model fit seems ok, but the intercepts look really strange. I fixed the first factor loading to one (the others are free). I fixed also the first intercepts of the fixed loading items to zero. The problem is that the intercepts in the scalar invariance output are really different to the intercepts in the metric invariance output. For example: Y2 intercept (metric) – unstand./stand.: 55.043**/ 4.040** Y2 intercept (scalar) – unstand./stand.: 52.910 (nonsign.)/ 4.032 (nonsign.) Is that normal? Thank you very much. 


The standardized intercept is the unstandardized intercept divided by the standard deviation of the variable. Check the size of the standard deviation of the variable to see if this makes sense. 


Thank you very much. 


Hi, Dr. Muthen! When assessing indices during scalar invariance testing (for which intercepts are constrained), is it useful to attend to indices related to latent means? I guess the same question goes for other invariance tests  should one only attend to indices for imposed constraints, or is there reason that some constraints might affect other estimates? 


When intercepts are free, factor means must be fixed to zero. 

Jone Aliri posted on Tuesday, July 17, 2018  10:07 am



Hello, I have an ESEM with target rotation (categorical items) and I want to test sex invariance. If I use the "configural metric scalar" syntax I have an error because it cannot calculate the metric model, but if I put only "configural scalar" I can calculate the fit of the configural and the scalar models and calculate the diftest. Is it ok to do that? Thank you very much. 


I think that is sufficient. 


I am working with a group assessing measurement invariance of a singlefactor 13item scale with items measured on 5points. We are treating these items as ordinal and using the WLSMV estimator. Thanks to Mplus's invariance assessment features, the team can readily obtain chisquare statistics comparing configural to metric, configural to scalar, and metric to scalar models. The configuralmetric comparison is NS (chisquare=17.52, p=.49), yet the metricscalar comparison is significant at chisquare(38)=106.64, p<.0001. However, the various descriptive fit statistics are all highly similar across the three models, i.e., RMSEA=.06,.05.04; CFI=.993,.993,.991; SRMR=.024,.024,.026. I am trying to figure out how to advise the team in weighing the chisquare test evidence, which suggests metric invariance is upheld but not scalar invariance, versus the descriptive fit information, which seems to suggest the three models are approximately equivalent. We have found one article by Cheung & Rensvold, 2002, in the SEM Journal, which address goodness of fit indices for invariance comparisons, but your opinions + suggestions for any additional literature touching on this topic would be much appreciated. Ditto for any alternative approaches available in Mplus we could also consider (e.g., alignment to assess approximate invariance if appropriate for this context) would also be appreciated. Thank you, Tor Neilands 


With categorical outcomes, we recommend going straight from configural to scalar. Alignment is useful if you have several groups. See various alternatives on our web page: http://www.statmodel.com/MeasurementInvariance.shtml 

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