I hope this is not off topic. I recently read "Item Response Modeling in Mplus: A Multi-Dimensional, Multi-Level, and Multi-Timepoint Example Bengt Muth´en & Tihomir Asparouhov" and did a similiar calculation. There the same phenomenon occured as in the cited paper: negative loadings. I´m not sure whether I got your point in the paper right: How do you interpret this? And maybe even more off topic: How do you calculate omega hierachical or any other formula that is based on loadings and not variances e.g. (Zinbarg RE, Revelle W, Yovel I, Li W. Cronbach's α, Revelle's β, and McDonald's ωh: Their relations with each other and two alternative conceptualizations of reliability. Psychometrika. 2005;70:123–133.)
I would be very glad if you could clarify this for me. Any help would be very appreciated.
The negative loadings I got in Table 2 were probably due to model misspecification because when I took the two-level structure into account, Table 3 did not have that problem. Neither did the Table 4 CFA.
If set the metric by fixing the factor variances at one instead of loadings, the formula with only loadings is fine.
thank you very much for your quick reply. Maybe I have another version of your paper, but in mine Table 3 (Table 3: Two-level analysis using bi-factor EFA and the WLSMV estimator. Student-level results.) are negative loadings. In Table 4 (Table 4: Two-level analysis using bi-factor CFA and the Bayes estimator.) there are none. Therefore I thought it could be a problem with the estimator (WLSMV vs. Bayes).
The question regarding omega was inexplicit. What I meant was wether to take absolute values to calculate the sum of the loadings or to take the real loadings (negative and positive) what would lead to a minor sum.
Once again I would be very thankful if you could settle this matter for me.
Yes, negative loadings are still there in Table 3 but it is less of an issue since only 1 is significant. Note that having negative loadings is not an error - it just may make the interpretation harder. Or, reflect that the model can still be improved.
I don't use omega so I am not an expert on that, but it looks like it refers to the general factor loadings (which are positive in my application). It would be strange if a general factor had negative loadings - if that is significant it seems that the item should be reversed.
thank you once again very much for your quick reply. Now I can follow your argumentation with the Table 3!
Regarding the omega problem - it´s is not only the general (there all my loadings are positive) but also the group factors and there negative loadings are a bit of a problem as they diminish the sum of the group factor loadings. But as you said you´re not an expert at that - so I´ll try to figure this out by myself. Anyway thank you a lot.