Sam Craft posted on Thursday, March 14, 2019 - 4:11 am
I'm testing for DIF between two groups using multi group CFA with binary outcomes.
Before testing for in-variance in factor loading and thresholds first i am testing for in-variance in variances and factor means but i'm experiencing two issues.
1. For variances, when comparing the nested model (variances constrained across the two groups) to the less restrictive model, the chi square value is negative.
2. For factor means, when when comparing the nested model (means constrained across the two groups) to the less restrictive model the degrees of freedom are the same for both models, so i can't compare the chi-square difference between the models.
You should not test for invariance of factor means and variances until you have imposed measurement invariance. I can't see how it would make sense to compare parameters for factors that don't mean the same thing.
Sam Craft posted on Tuesday, March 19, 2019 - 5:05 am
Okay thank you for your reply, that makes sense.
So i re-did this using the mplus default for variances and means. However when i allow thresholds and factor loadings for all items to be free across the two groups i get the message:
ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT DISTRIBUTION OF THE CATEGORICAL VARIABLES IN THE MODEL. THE FOLLOWING PARAMETERS WERE FIXED: Parameter 22, %CASE#1%: [ DSM7$1 ]
Why does this happen?
Sam Craft posted on Tuesday, March 19, 2019 - 7:46 am
Also, when comparing nested and comparison models for factor loading iteratively for individual items, some items produce a negative chi square value.
(if not related the above post) Does this indicate a problem with the data?
From the error message it sounds like your specification results in a non-identified model. To be able to diagnose why we need to see the full output - send to Support along with your license number.
Sam Craft posted on Thursday, March 28, 2019 - 3:46 am
I managed to resolve the above issues, but i have one final question.
When freeing both factor loadings and thresholds for each item (with variances @1 and means @0) the factor loadings for the first group are all negative. When thresholds are constrained to be equal in both groups the factor loadings are all positive and are more what i would expect.
When i hold the mean @1, the factor loadings are also positive, but the thresholds change slightly. I'm concerned that by doing this i may be misrepresenting the data. Can you offer any advice on this.
Getting all negative loadings for a factor simply reflects a harmless indeterminacy of factor analysis - you can change the sign of all of them and get exactly the same fit. So just report them as positive (with more than one factor, also change the signs of the correlations with those other factors).