Hi
I ran a CFA, ESEM, bifactor CFA and bifactor ESEM with two instruments that I hypothesize as seriously overlapping (The CFA shows very high covariance of the two latent factors).
My question is
1)how to interpret the negative loadings that suddenly appear in the bifactor models.
PC->pc4 0.824(CFA), -0.139(B-CFA), -0.363(ESEM)
2)how to interpret the loading over 1 (AE->ae5) in the ESEM model
3)what is happening with PC->ae2 in the B-ESEM (PC->ae2 0.05(ESEM) -0.04(B-ESEM)
all the models are ran with Mplus.
Emiko Hirosawa Such "anomalous" results are rather typical in symmetrical bifactor models. The negative (-.139) loading of pc4 on the specific factor in your bifactor model is odd. This loading is also quite small (close to zero and perhaps not even statistically significant (?). At the same time, the same variable has a very high loading on the general factor (.922). This may indicate that your general factor is primarily defined by this variable (pc4) and not really a general factor. (The variable does not have a meaningful specific factor loading.) Again, this is a very common issue when applying symmetrical bifactor models that can be explained from a measurement theoretical perspective.
Check out the following papers in which potential explanations and solutions for this issue are discussed in detail:
Eid, M., Geiser, C., Koch, T., & Heene, M. (2017). Anomalous results in G-factor models: Explanations and alternatives. Psychological Methods, 22(3), 541–562. https://doi.org/10.1037/met0000083
Article Application of the Bifactor S - 1 Model to Multisource Ratin...
Article On the Meaning of the “ P Factor” in Symmetrical Bifactor Mo...
Article Giving G a Meaning: An Application of the Bifactor-(S-1) App...
Thank you Prof. Geiser
The articles you showed me look really interesting!
As you say, the negative (-.139) loading of pc4 is nonsignificant.
Actually, all the loadings of S-factor PC in the B-ESEM model are nonsignificant.
How to interpret this may be in the articles you pointed to but does this indicate that the S-factor does not hold?
Emiko Hirosawa Again, this is a very typical / often observed finding with symmetrical bifactor models: One of the specific factors often drops out or "collapses", as indicated in your example by the complete set of non-significant loadings. This means that the PC specific factor is not substantial and not needed in the model. It also means that the general factor is not really a general factor but instead a factor that is defined by the indicators pertaining to the PC facet. The papers that I listed in my initial response provide explanations and solutions for this issue.
Prof. Geiser I read the articles you recommended and need to really thank you for referring to them. I am not very well versed in mathematics and I have some questions corresponding to the details of the articles.
So, in my case,
a)the Bi-SYM model had one anomalous loading (reversed sign) but the loadings were significant (except AE4, PC4)
b)in the Bi-ESEM model, the PC factor completely collapsed. (no significant S-loadings for PC)
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My question is,
1)What explanation could be made for PC to completely collapse in the Bi-ESEM when it (at least partially) holds in the Bi-SYM? Or is the model considered corrupt even with one indicator showing anomaly?
2)The articles recommended that in my case a S-1 analysis will be more appropriate. Theoretically, PC is a more general concept so (and it is the one that fell apart) it makes sense that it will be modeled as the PC-Gen (in the attached picture[S-1]).
If the loadings on S-factor AE holds as significant (with no anomalies)
Will the interpretation be that AE holds over and above the effects of PC-Gen?
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I will be very grateful for any advice.
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