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I want to examine measurement invariance across two nationalities for a construct measured with 3 items. First one is supposed to examine the configural fit before examining more restrictive models. However, when I have a three items model, the configural model has 0 df and the statistics are:

Chi2(df) = 0.00 (df= 0)

change in Chi 2(df) = NA

P = NA

CFI = 1

RMSEA = 0.000

Can I say something about the fit from these results? How should I interpret these results and write about this in a report?

I have used lavaan and semTools (packages in R), using the following code:

Code for a CFA model with 3 items and measurement invariance

model_3_items <-'
factor =~  item1 + item2 + item3
'
fit <- cfa(model_3_items, data=data, estimator="MLM")
summary(fit, fit.measures = T, standardized=T,  modindices=TRUE)

measurementInvariance(model = model_3_items, data = data, group = "Gender", estimator="MLM" , strict=TRUE)```


Thanks, 
Gorp  



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I found help fort his question in the very helpful lavaan google group, so I post the answer here:

"Can I say something about the fit from these results? How should I interpret these results and write about this in a report?"

"No, the model is just-identified. You have no extra information (df) with which to assess the fit of the configural model, but you can still test more constrained models in which parameters are equated."

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