Confusing modification indices suggesting a change that is already specified in the model

[Shaun Fisher]

So I have a model which is:

MHShierarch.remodel2<- 'ENGAGED =~ MHS1 + MHS3 + MHS4 + MHS7 + MHS13
AWARENESS =~  MHS5 + MHS6 + MHS8 + MHS10 + MHS12
FUSION =~ MHS2 + MHS9 + MHS11
PSYFLEX =~ ENGAGED + AWARENESS + FUSION
MHS1 ~~ MHS4
MHS1 ~~ MHS7
MHS4 ~~ MHS13
MHS5 ~~ MHS10
MHS6 ~~ MHS10
MHS3 ~~ MHS4
MHS1 ~~ MHS3
MHS5 ~~ MHS12
MHS9 ~~ MHS11
MHS6 ~~ MHS12'

fit.remodel2 <- cfa(MHShierarch.remodel2, data = MHS_CFA_excell, meanstructure = TRUE, estimator = "MLM")

However, when I request modifcation indices this is what is coming out:

> modindices(fit.remodel2, alpha = 0.05, sort. = TRUE, minimum.value = 3.84)                        
      lhs op  rhs     mi    epc sepc.lv sepc.all sepc.nox                       
11     FUSION =~ MHS2 15.204  1.050   0.422    0.340    0.340                       
138     MHS13 ~~ MHS6  6.345  0.182   0.182    0.203    0.203                       
6   AWARENESS =~ MHS5  4.913 58.312  19.684   17.464   17.464                       
116      MHS3 ~~ MHS2  4.523  0.188   0.188    0.166    0.166                       
120      MHS4 ~~ MHS5  4.476  0.124   0.124    0.155    0.155                       

My confusion is why would the modification indices be producing "FUSION =~ MHS2" when this is already specified in the model?

Would really appreciate any guidance on this.

[Jeremy Miles]

Because it's the first item in the latent variable, it's constrained to 1, for identification.

I think that if you free it, the model won't be identified. You chould change the order, for example try:

FUSION =~ MHS9 + MHS2 + MHS11

To see what happens.

J

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