Testing measurement invariance with constrained model parameters.

[Peter Kruyen]

Dear all,

I have the following multiple group SEM model, in which I constrained the factor loading of 'bal8.1' (to prevent the variance of this item to become negative; and several factor loadings larger than 1). I hope my syntax is correct here.

model <- 'INT =~ DN1 + DN2 + DN3 + DN4 + DN5 + DN6
 
            BAL   =~  bal2 + bal4 + bal5 + c(weight_bal8.1,weight_bal8.2)*bal8
            ANTOP =~ antop1 + antop7 + antop5 + antop8
            CORP  =~ corp3 + corp4 + corp5 + corp6
            OCC  =~ occ2 + occ3 + occ6 +  occ9 + occ12
            PFLEX =~ pflex1 + pflex3 + pflex4 + pflex6 + pflex7
 
            EMPL =~ BAL + ANTOP + OCC + CORP + PFLEX
 
            PERF =~ IP1 + IP2 + IP3 + IP4 + IP5 + IP6 + IP7 + IP8 +IP9
 
            weight_bal8.1 < 1
            weight_bal8.2 < 1'

Next, I run the SEM model (i.e., YoB contains two groups).

 fit <- cfa(model,
             ordered=c(intra,empl,perf),
             data=dataset_adj,
             missing="pairwise",
             group="YoB")

If I check for measurement invariance...

measurementInvarianceCat(model=fit,data=dataset_adj,group="YoB")

I get the error

Error in measurementInvarianceCat(model = fit, data = dataset_adj, group = "YoB") :
 Factor configuration is not the same across groups

What is wrong in my model specification? I'm very curious. Note that, the problem is not solved by changing c(weight_bal8.1,weight_bal8.2)*bal8 to weight_bal8*bal8. 

Thank you for your time and consideration!

Peter

[Edward Rigdon]

My first guess would be an interaction between "ordered" and "pairwise". If values are missing for one level of one variable in one group, then the "ordered" is going to produce different assortments of threshold parameters across groups, hence the models are not configurally the same. If you treat the variables as continuous, does the syntax work?

If this is the problem, then perhaps you might merge together some of the low-incidence categories of some variables.

--
You received this message because you are subscribed to the Google Groups "lavaan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+un...@googlegroups.com.
To post to this group, send email to lav...@googlegroups.com.
Visit this group at https://groups.google.com/group/lavaan.
For more options, visit https://groups.google.com/d/optout.

[Peter Kruyen]

Hi Edward,

That does make sense! And yes, you are correct without treating the variables as ordinal the syntax works (but the fit drops significantly too). Okay, I will go through the bivariate tables to check the low-incidence categories. 

Thank you!

Peter